TSTP Solution File: ITP226^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP226^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:22:03 EDT 2023
% Result : Timeout 300.12s 290.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.45/2.49 % Problem : ITP226^3 : TPTP v8.1.2. Released v8.1.0.
% 2.49/2.50 % Command : do_cvc5 %s %d
% 2.50/2.71 % Computer : n016.cluster.edu
% 2.50/2.71 % Model : x86_64 x86_64
% 2.50/2.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.50/2.71 % Memory : 8042.1875MB
% 2.50/2.71 % OS : Linux 3.10.0-693.el7.x86_64
% 2.50/2.71 % CPULimit : 300
% 2.50/2.71 % WCLimit : 300
% 2.50/2.71 % DateTime : Sun Aug 27 16:19:31 EDT 2023
% 2.50/2.71 % CPUTime :
% 5.07/5.26 %----Proving TH0
% 5.07/5.26 %------------------------------------------------------------------------------
% 5.07/5.26 % File : ITP226^3 : TPTP v8.1.2. Released v8.1.0.
% 5.07/5.26 % Domain : Interactive Theorem Proving
% 5.07/5.26 % Problem : Sledgehammer problem VEBT_Member 00468_022002
% 5.07/5.26 % Version : [Des22] axioms.
% 5.07/5.26 % English :
% 5.07/5.26
% 5.07/5.26 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.07/5.26 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.07/5.26 % Source : [Des22]
% 5.07/5.26 % Names : 0065_VEBT_Member_00468_022002 [Des22]
% 5.07/5.26
% 5.07/5.26 % Status : Theorem
% 5.07/5.26 % Rating : 0.77 v8.1.0
% 5.07/5.26 % Syntax : Number of formulae : 11247 (6243 unt;1053 typ; 0 def)
% 5.07/5.26 % Number of atoms : 26127 (11822 equ; 0 cnn)
% 5.07/5.26 % Maximal formula atoms : 71 ( 2 avg)
% 5.07/5.26 % Number of connectives : 100327 (2468 ~; 478 |;1489 &;87708 @)
% 5.07/5.26 % ( 0 <=>;8184 =>; 0 <=; 0 <~>)
% 5.07/5.26 % Maximal formula depth : 39 ( 5 avg)
% 5.07/5.26 % Number of types : 73 ( 72 usr)
% 5.07/5.26 % Number of type conns : 3714 (3714 >; 0 *; 0 +; 0 <<)
% 5.07/5.26 % Number of symbols : 984 ( 981 usr; 66 con; 0-8 aty)
% 5.07/5.26 % Number of variables : 22181 (1990 ^;19601 !; 590 ?;22181 :)
% 5.07/5.26 % SPC : TH0_THM_EQU_NAR
% 5.07/5.26
% 5.07/5.26 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.07/5.26 % from the van Emde Boas Trees session in the Archive of Formal
% 5.07/5.26 % proofs -
% 5.07/5.26 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.07/5.26 % 2022-02-17 19:06:37.269
% 5.07/5.26 %------------------------------------------------------------------------------
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% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.07/5.27 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.07/5.27 bNF_re6321650412969554871eger_o: ( int > code_integer > $o ) > ( ( int > $o ) > ( code_integer > $o ) > $o ) > ( int > int > $o ) > ( code_integer > code_integer > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.07/5.27 bNF_re398004352372739002nteger: ( int > code_integer > $o ) > ( ( int > int ) > ( code_integer > code_integer ) > $o ) > ( int > int > int ) > ( code_integer > code_integer > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 5.07/5.27 bNF_re6574881592172037608er_o_o: ( int > code_integer > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( code_integer > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.07/5.27 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 5.07/5.27 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.07/5.27 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.07/5.27 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 5.07/5.27 bNF_re1639080489988575423ural_o: ( nat > code_natural > $o ) > ( ( nat > $o ) > ( code_natural > $o ) > $o ) > ( nat > nat > $o ) > ( code_natural > code_natural > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 5.07/5.27 bNF_re88643428490162567atural: ( nat > code_natural > $o ) > ( ( nat > nat ) > ( code_natural > code_natural ) > $o ) > ( nat > nat > nat ) > ( code_natural > code_natural > code_natural ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_Eo_001_Eo,type,
% 5.07/5.27 bNF_re2785088596696291543al_o_o: ( nat > code_natural > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( code_natural > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 bNF_re5252274238750452962nteger: ( nat > code_natural > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( code_natural > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 bNF_re3704215830270325841atural: ( nat > code_natural > $o ) > ( nat > code_natural > $o ) > ( nat > nat ) > ( code_natural > code_natural ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.07/5.27 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 bNF_re4153400068438556298nteger: ( nat > nat > $o ) > ( int > code_integer > $o ) > ( nat > int ) > ( nat > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 5.07/5.27 bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.07/5.27 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 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 ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Oeucl__rel__int,type,
% 5.07/5.27 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 5.07/5.27 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 5.07/5.27 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 5.07/5.27 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 5.07/5.27 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.07/5.27 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.07/5.27 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Int__Oint,type,
% 5.07/5.27 euclid3395696857347342551nt_int: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Nat__Onat,type,
% 5.07/5.27 euclid3398187327856392827nt_nat: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Extended__Nat_OeSuc,type,
% 5.07/5.27 extended_eSuc: extended_enat > extended_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Extended__Nat_Oenat,type,
% 5.07/5.27 extended_enat2: nat > extended_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Extended__Nat_Oenat_Ocase__enat_001_Eo,type,
% 5.07/5.27 extended_case_enat_o: ( nat > $o ) > $o > extended_enat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Extended__Nat_Oenat_Ocase__enat_001t__Extended____Nat__Oenat,type,
% 5.07/5.27 extend3600170679010898289d_enat: ( nat > extended_enat ) > extended_enat > extended_enat > extended_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Extended__Nat_Oinfinity__class_Oinfinity_001t__Extended____Nat__Oenat,type,
% 5.07/5.27 extend5688581933313929465d_enat: extended_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 5.07/5.27 comm_s2602460028002588243omplex: complex > nat > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 5.07/5.27 comm_s4660882817536571857er_int: int > nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 5.07/5.27 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.07/5.27 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 5.07/5.27 comm_s7457072308508201937r_real: real > nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 semiri3624122377584611663nteger: nat > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 semiri2447717529341329178atural: nat > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.07/5.27 semiri5044797733671781792omplex: nat > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 5.07/5.27 semiri1406184849735516958ct_int: nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.07/5.27 semiri1408675320244567234ct_nat: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 5.07/5.27 semiri773545260158071498ct_rat: nat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.07/5.27 semiri2265585572941072030t_real: nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.07/5.27 invers8013647133539491842omplex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.07/5.27 inverse_inverse_rat: rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.07/5.27 inverse_inverse_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.07/5.27 at_bot_real: filter_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oat__top_001t__Int__Oint,type,
% 5.07/5.27 at_top_int: filter_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.07/5.27 at_top_nat: filter_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.07/5.27 at_top_real: filter_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.07/5.27 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.07/5.27 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Int__Oint,type,
% 5.07/5.27 filterlim_nat_int: ( nat > int ) > filter_int > filter_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.07/5.27 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.07/5.27 finite_card_complex: set_complex > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.07/5.27 finite_card_int: set_int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 finite_card_list_nat: set_list_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.07/5.27 finite_card_nat: set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.07/5.27 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 finite_card_set_nat: set_set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.07/5.27 finite3207457112153483333omplex: set_complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.07/5.27 finite_finite_int: set_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.07/5.27 finite_finite_nat: set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.07/5.27 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Int__Oint_001t__Nat__Onat,type,
% 5.07/5.27 bij_betw_int_nat: ( int > nat ) > set_int > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 bij_be8532844293280997160at_nat: ( list_nat > nat ) > set_list_nat > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.07/5.27 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Int__Oint,type,
% 5.07/5.27 bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 bij_be6293887246118711976st_nat: ( nat > list_nat ) > set_nat > set_list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 bij_be8693218025023041337at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Obij__betw_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 bij_be5333170631980326235at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.07/5.27 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.07/5.27 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 5.07/5.27 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.07/5.27 id_o: $o > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.07/5.27 id_nat: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Int__Oint_001t__Nat__Onat,type,
% 5.07/5.27 inj_on_int_nat: ( int > nat ) > set_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 inj_on_list_nat_nat: ( list_nat > nat ) > set_list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Int__Oint,type,
% 5.07/5.27 inj_on_nat_int: ( nat > int ) > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 inj_on_nat_list_nat: ( nat > list_nat ) > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 inj_on5538052773655684606at_nat: ( nat > product_prod_nat_nat ) > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.07/5.27 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 inj_on2178005380612969504at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.07/5.27 map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 5.07/5.27 map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 map_fu2787874002554666395nteger: ( code_natural > nat ) > ( int > code_integer ) > ( nat > int ) > code_natural > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.07/5.27 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.07/5.27 thf(sy_c_GCD_Obezw,type,
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% 5.07/5.27 thf(sy_c_GCD_Obezw__rel,type,
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% 5.07/5.27 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
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% 5.07/5.27 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Code____Numeral__Ointeger,type,
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% 5.07/5.27 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
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% 5.07/5.27 thf(sy_c_GCD_Ogcd__nat__rel,type,
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% 5.07/5.27 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
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% 5.07/5.27
% 5.07/5.27 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_If_001t__Rat__Orat,type,
% 5.07/5.27 if_rat: $o > rat > rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_If_001t__Real__Oreal,type,
% 5.07/5.27 if_real: $o > real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 5.07/5.27 if_set_int: $o > set_int > set_int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 5.07/5.27 infini8530281810654367211te_nat: set_nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_OAbs__Integ,type,
% 5.07/5.27 abs_Integ: product_prod_nat_nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_ONeg,type,
% 5.07/5.27 neg: num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_OPos,type,
% 5.07/5.27 pos: num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_ORep__Integ,type,
% 5.07/5.27 rep_Integ: int > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Ocr__int,type,
% 5.07/5.27 cr_int: product_prod_nat_nat > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Odup,type,
% 5.07/5.27 dup: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.07/5.27 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.07/5.27 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Ointrel,type,
% 5.07/5.27 intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Onat,type,
% 5.07/5.27 nat2: int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Opcr__int,type,
% 5.07/5.27 pcr_int: product_prod_nat_nat > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 5.07/5.27 power_int_real: real > int > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 ring_11222124179247155820nteger: set_Code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 5.07/5.27 ring_1_Ints_complex: set_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 5.07/5.27 ring_1_Ints_int: set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 5.07/5.27 ring_1_Ints_rat: set_rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.07/5.27 ring_1_Ints_real: set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 ring_18347121197199848620nteger: int > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.07/5.27 ring_17405671764205052669omplex: int > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.07/5.27 ring_1_of_int_int: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.07/5.27 ring_1_of_int_rat: int > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.07/5.27 ring_1_of_int_real: int > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Int_Osub,type,
% 5.07/5.27 sub: num > num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 5.07/5.27 inf_inf_int: int > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 5.07/5.27 inf_inf_nat: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Osemilattice__neutr_001t__Nat__Onat,type,
% 5.07/5.27 semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.07/5.27 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 5.07/5.27 sup_sup_int: int > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.07/5.27 sup_sup_nat: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 5.07/5.27 lattic8263393255366662781ax_int: set_int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.07/5.27 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
% 5.07/5.27 lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lifting_OQuotient_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.07/5.27 quotie3684837364556693515t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > ( ( nat > rat ) > real > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Lifting_OQuotient_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.07/5.27 quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.07/5.27 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.07/5.27 append_int: list_int > list_int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.07/5.27 append_nat: list_nat > list_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 fold_int_int: ( int > int > int ) > list_int > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 5.07/5.27 last_nat: list_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.07/5.27 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.07/5.27 cons_int: int > list_int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.07/5.27 cons_nat: nat > list_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.07/5.27 nil_int: list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.07/5.27 nil_nat: list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.07/5.27 hd_nat: list_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.07/5.27 set_o2: list_o > set_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.07/5.27 set_complex2: list_complex > set_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.07/5.27 set_int2: list_int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.07/5.27 set_nat2: list_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.07/5.27 set_real2: list_real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 set_set_nat2: list_set_nat > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.07/5.27 tl_nat: list_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001_Eo,type,
% 5.07/5.27 nth_o: list_o > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.07/5.27 nth_complex: list_complex > nat > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.07/5.27 nth_int: list_int > nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.07/5.27 nth_nat: list_nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.07/5.27 nth_num: list_num > nat > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.07/5.27 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.07/5.27 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.07/5.27 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.07/5.27 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.07/5.27 nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.07/5.27 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.07/5.27 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.07/5.27 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.07/5.27 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.07/5.27 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.07/5.27 nth_real: list_real > nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.07/5.27 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.07/5.27 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.07/5.27 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.07/5.27 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 5.07/5.27 product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.07/5.27 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.07/5.27 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.07/5.27 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.07/5.27 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.07/5.27 replicate_o: nat > $o > list_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.07/5.27 replicate_complex: nat > complex > list_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.07/5.27 replicate_int: nat > int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.07/5.27 replicate_nat: nat > nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.07/5.27 replicate_real: nat > real > list_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Orotate1_001_Eo,type,
% 5.07/5.27 rotate1_o: list_o > list_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 5.07/5.27 rotate1_int: list_int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 5.07/5.27 rotate1_nat: list_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.07/5.27 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.07/5.27 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oupt,type,
% 5.07/5.27 upt: nat > nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oupto,type,
% 5.07/5.27 upto: int > int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oupto__aux,type,
% 5.07/5.27 upto_aux: int > int > list_int > list_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_List_Oupto__rel,type,
% 5.07/5.27 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_OSuc,type,
% 5.07/5.27 suc: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.07/5.27 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.07/5.27 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.07/5.27 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Onat_Opred,type,
% 5.07/5.27 pred: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 5.07/5.27 semiring_1_Nats_int: set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 semiri4939895301339042750nteger: nat > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 semiri3763490453095760265atural: nat > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.07/5.27 semiri8010041392384452111omplex: nat > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.07/5.27 semiri1314217659103216013at_int: nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.07/5.27 semiri1316708129612266289at_nat: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.07/5.27 semiri681578069525770553at_rat: nat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.07/5.27 semiri5074537144036343181t_real: nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.07/5.27 size_size_list_o: list_o > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.07/5.27 size_s3451745648224563538omplex: list_complex > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.07/5.27 size_size_list_int: list_int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 size_size_list_nat: list_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.07/5.27 size_size_list_num: list_num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.07/5.27 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.07/5.27 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.07/5.27 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.07/5.27 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.07/5.27 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.07/5.27 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.07/5.27 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.07/5.27 size_size_list_real: list_real > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.07/5.27 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.07/5.27 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.07/5.27 size_size_num: num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.07/5.27 size_size_option_num: option_num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.07/5.27 size_size_char: char > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oint__decode,type,
% 5.07/5.27 nat_int_decode: nat > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oint__encode,type,
% 5.07/5.27 nat_int_encode: int > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 5.07/5.27 nat_list_decode: nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 5.07/5.27 nat_list_decode_rel: nat > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.07/5.27 nat_list_encode: list_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.07/5.27 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 5.07/5.27 nat_prod_decode: nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.07/5.27 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.07/5.27 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.07/5.27 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.07/5.27 nat_set_decode: nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.07/5.27 nat_set_encode: set_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.07/5.27 nat_triangle: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_NthRoot_Oroot,type,
% 5.07/5.27 root: nat > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_NthRoot_Osqrt,type,
% 5.07/5.27 sqrt: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_OBitM,type,
% 5.07/5.27 bitM: num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oinc,type,
% 5.07/5.27 inc: num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onat__of__num,type,
% 5.07/5.27 nat_of_num: num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.07/5.27 neg_nu7009210354673126013omplex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.07/5.27 neg_numeral_dbl_int: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.07/5.27 neg_numeral_dbl_rat: rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.07/5.27 neg_numeral_dbl_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.07/5.27 neg_nu6511756317524482435omplex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.07/5.27 neg_nu3811975205180677377ec_int: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.07/5.27 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.07/5.27 neg_nu6075765906172075777c_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.07/5.27 neg_nu8557863876264182079omplex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.07/5.27 neg_nu5851722552734809277nc_int: int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.07/5.27 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.07/5.27 neg_nu8295874005876285629c_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.07/5.27 neg_numeral_sub_int: num > num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum_OBit0,type,
% 5.07/5.27 bit0: num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum_OBit1,type,
% 5.07/5.27 bit1: num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum_OOne,type,
% 5.07/5.27 one: num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.07/5.27 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum_Osize__num,type,
% 5.07/5.27 size_num: num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onum__of__nat,type,
% 5.07/5.27 num_of_nat: nat > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 numera6620942414471956472nteger: num > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 numera5444537566228673987atural: num > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.07/5.27 numera6690914467698888265omplex: num > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.07/5.27 numera1916890842035813515d_enat: num > extended_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.07/5.27 numeral_numeral_int: num > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.07/5.27 numeral_numeral_nat: num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.07/5.27 numeral_numeral_rat: num > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.07/5.27 numeral_numeral_real: num > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Opow,type,
% 5.07/5.27 pow: num > num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Opred__numeral,type,
% 5.07/5.27 pred_numeral: num > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Num_Osqr,type,
% 5.07/5.27 sqr: num > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 5.07/5.27 none_num: option_num ).
% 5.07/5.27
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% 5.07/5.27 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Extended____Nat__Oenat,type,
% 5.07/5.27 produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.07/5.27 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.07/5.27 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.07/5.27 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.07/5.27 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.07/5.27 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.07/5.27 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.07/5.27 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.07/5.27 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.07/5.27 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.07/5.27 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.07/5.27 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.07/5.27 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 product_fst_int_int: product_prod_int_int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 product_snd_int_int: product_prod_int_int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 5.07/5.27 produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Quotient_OQuotient3_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.07/5.27 quotie8700032322157300518t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Quotient_OQuotient3_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.07/5.27 quotie6776551016481293500at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Oinc__shift,type,
% 5.07/5.27 inc_shift: code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Oiterate_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 5.07/5.27 iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Olog,type,
% 5.07/5.27 log: code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Olog__rel,type,
% 5.07/5.27 log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Ominus__shift,type,
% 5.07/5.27 minus_shift: code_natural > code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Onext,type,
% 5.07/5.27 next: produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Random_Orange,type,
% 5.07/5.27 range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_OAbs__Rat,type,
% 5.07/5.27 abs_Rat: product_prod_int_int > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_OFract,type,
% 5.07/5.27 fract: int > int > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_OFrct,type,
% 5.07/5.27 frct: product_prod_int_int > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_ORep__Rat,type,
% 5.07/5.27 rep_Rat: rat > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.07/5.27 field_5140801741446780682s_real: set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.07/5.27 field_7254667332652039916t_real: rat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Onormalize,type,
% 5.07/5.27 normalize: product_prod_int_int > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Oof__int,type,
% 5.07/5.27 of_int: int > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Opcr__rat,type,
% 5.07/5.27 pcr_rat: product_prod_int_int > rat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Opositive,type,
% 5.07/5.27 positive: rat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Oquotient__of,type,
% 5.07/5.27 quotient_of: rat > product_prod_int_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rat_Oratrel,type,
% 5.07/5.27 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_ORatreal,type,
% 5.07/5.27 ratreal: rat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_OReal,type,
% 5.07/5.27 real2: ( nat > rat ) > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Ocauchy,type,
% 5.07/5.27 cauchy: ( nat > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Ocr__real,type,
% 5.07/5.27 cr_real: ( nat > rat ) > real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Opcr__real,type,
% 5.07/5.27 pcr_real: ( nat > rat ) > real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Opositive,type,
% 5.07/5.27 positive2: real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Orealrel,type,
% 5.07/5.27 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Orep__real,type,
% 5.07/5.27 rep_real: real > nat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real_Ovanishes,type,
% 5.07/5.27 vanishes: ( nat > rat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.07/5.27 real_V2521375963428798218omplex: set_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.07/5.27 real_V3694042436643373181omplex: complex > complex > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.07/5.27 real_V975177566351809787t_real: real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.07/5.27 real_V1022390504157884413omplex: complex > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.07/5.27 real_V7735802525324610683m_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.07/5.27 real_V4546457046886955230omplex: real > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.07/5.27 real_V1803761363581548252l_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
% 5.07/5.27 field_nat: set_Pr1261947904930325089at_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Relation_OId_001t__Nat__Onat,type,
% 5.07/5.27 id_nat2: set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Relation_Otransp_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.07/5.27 transp_nat_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.07/5.27 algebr932160517623751201me_int: int > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.07/5.27 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 divide5121882707175180666atural: code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.07/5.27 divide1717551699836669952omplex: complex > complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.07/5.27 divide_divide_int: int > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.07/5.27 divide_divide_nat: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.07/5.27 divide_divide_rat: rat > rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.07/5.27 divide_divide_real: real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 dvd_dvd_Code_natural: code_natural > code_natural > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.07/5.27 dvd_dvd_complex: complex > complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.07/5.27 dvd_dvd_int: int > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.07/5.27 dvd_dvd_nat: nat > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.07/5.27 dvd_dvd_rat: rat > rat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.07/5.27 dvd_dvd_real: real > real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 modulo8411746178871703098atural: code_natural > code_natural > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.07/5.27 modulo_modulo_int: int > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.07/5.27 modulo_modulo_nat: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
% 5.07/5.27 unit_f2748546683901255202or_nat: nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 zero_n356916108424825756nteger: $o > code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Onatural,type,
% 5.07/5.27 zero_n8403883297036319079atural: $o > code_natural ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.07/5.27 zero_n1201886186963655149omplex: $o > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.07/5.27 zero_n2684676970156552555ol_int: $o > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.07/5.27 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.07/5.27 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.07/5.27 zero_n3304061248610475627l_real: $o > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.07/5.27 suminf_complex: ( nat > complex ) > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.07/5.27 suminf_int: ( nat > int ) > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.07/5.27 suminf_nat: ( nat > nat ) > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.07/5.27 suminf_real: ( nat > real ) > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.07/5.27 summable_complex: ( nat > complex ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.07/5.27 summable_int: ( nat > int ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.07/5.27 summable_nat: ( nat > nat ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.07/5.27 summable_real: ( nat > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.07/5.27 sums_complex: ( nat > complex ) > complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.07/5.27 sums_int: ( nat > int ) > int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.07/5.27 sums_nat: ( nat > nat ) > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.07/5.27 sums_real: ( nat > real ) > real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.07/5.27 collect_complex: ( complex > $o ) > set_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.07/5.27 collect_int: ( int > $o ) > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.07/5.27 collect_nat: ( nat > $o ) > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 5.07/5.27 collect_real: ( real > $o ) > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 5.07/5.27 pow_nat: set_nat > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 5.07/5.27 image_int_int: ( int > int ) > set_int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 5.07/5.27 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 5.07/5.27 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.07/5.27 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.07/5.27 image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 image_real_real: ( real > real ) > set_real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.07/5.27 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 5.07/5.27 insert_complex: complex > set_complex > set_complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.07/5.27 insert_int: int > set_int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.07/5.27 insert_nat: nat > set_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.07/5.27 insert_real: real > set_real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.07/5.27 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.07/5.27 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.07/5.27 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.07/5.27 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.07/5.27 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.07/5.27 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.07/5.27 set_or1266510415728281911st_int: int > int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.07/5.27 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.07/5.27 set_or7049704709247886629st_num: num > num > set_num ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.07/5.27 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.07/5.27 set_or1222579329274155063t_real: real > real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.07/5.27 set_or4662586982721622107an_int: int > int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.07/5.27 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.07/5.27 set_ord_atLeast_nat: nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.07/5.27 set_ord_atLeast_real: real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.07/5.27 set_ord_atMost_nat: nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.07/5.27 set_or6656581121297822940st_int: int > int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.07/5.27 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.07/5.27 set_or5832277885323065728an_int: int > int > set_int ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.07/5.27 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.07/5.27 set_or1633881224788618240n_real: real > real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.07/5.27 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.07/5.27 set_or5849166863359141190n_real: real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.07/5.27 set_ord_lessThan_nat: nat > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.07/5.27 set_or5984915006950818249n_real: real > set_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
% 5.07/5.27 abort_real: literal > ( product_unit > real ) > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_OLiteral,type,
% 5.07/5.27 literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_Ochar_OChar,type,
% 5.07/5.27 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_Ochar_Osize__char,type,
% 5.07/5.27 size_char: char > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.07/5.27 comm_s629917340098488124ar_nat: char > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.07/5.27 unique3096191561947761185of_nat: nat > char ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.07/5.27 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.07/5.27 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.07/5.27 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 5.07/5.27 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.07/5.27 topolo2815343760600316023s_real: real > filter_real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 5.07/5.27 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.07/5.27 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oarccos,type,
% 5.07/5.27 arccos: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.07/5.27 arcosh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oarcsin,type,
% 5.07/5.27 arcsin: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oarctan,type,
% 5.07/5.27 arctan: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.07/5.27 arsinh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.07/5.27 artanh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.07/5.27 cos_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.07/5.27 cos_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.07/5.27 cos_coeff: nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 5.07/5.27 cosh_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.07/5.27 cosh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 5.07/5.27 cot_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.07/5.27 cot_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.07/5.27 diffs_real: ( nat > real ) > nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.07/5.27 exp_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.07/5.27 exp_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.07/5.27 ln_ln_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Olog,type,
% 5.07/5.27 log2: real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Opi,type,
% 5.07/5.27 pi: real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.07/5.27 powr_real: real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Opowr__real,type,
% 5.07/5.27 powr_real2: real > real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.07/5.27 sin_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.07/5.27 sin_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.07/5.27 sin_coeff: nat > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 5.07/5.27 sinh_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.07/5.27 sinh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.07/5.27 tan_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.07/5.27 tan_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.07/5.27 tanh_complex: complex > complex ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.07/5.27 tanh_real: real > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.07/5.27 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.07/5.27 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.07/5.27 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.07/5.27 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.07/5.27 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 5.07/5.27 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 5.07/5.27 vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.07/5.27 vEBT_VEBT_high: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.07/5.27 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.07/5.27 vEBT_VEBT_low: nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.07/5.27 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.07/5.27 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.07/5.27 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.07/5.27 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.07/5.27 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.07/5.27 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.07/5.27 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.07/5.27 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.07/5.27 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.07/5.27 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.07/5.27 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.07/5.27 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.07/5.27 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.07/5.27 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.07/5.27 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.07/5.27 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.07/5.27 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 5.07/5.27 accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.07/5.27 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.07/5.27 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 5.07/5.27 accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.07/5.27 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Oless__than,type,
% 5.07/5.27 less_than: set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.07/5.27 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
% 5.07/5.27 wf_int: set_Pr958786334691620121nt_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.07/5.27 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.07/5.27 fChoice_real: ( real > $o ) > real ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001_Eo,type,
% 5.07/5.27 member_o: $o > set_o > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 5.07/5.27 member_Code_integer: code_integer > set_Code_integer > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.07/5.27 member_complex: complex > set_complex > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Int__Oint,type,
% 5.07/5.27 member_int: int > set_int > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.07/5.27 member_list_nat: list_nat > set_list_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Nat__Onat,type,
% 5.07/5.27 member_nat: nat > set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.07/5.27 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.07/5.27
% 5.07/5.27 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,
% 5.07/5.27 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Rat__Orat,type,
% 5.07/5.27 member_rat: rat > set_rat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Real__Oreal,type,
% 5.07/5.27 member_real: real > set_real > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.07/5.27 member_set_nat: set_nat > set_set_nat > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.07/5.27 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.07/5.27
% 5.07/5.27 thf(sy_v_n,type,
% 5.07/5.27 n: nat ).
% 5.07/5.27
% 5.07/5.27 thf(sy_v_t,type,
% 5.07/5.27 t: vEBT_VEBT ).
% 5.07/5.27
% 5.07/5.27 thf(sy_v_x,type,
% 5.07/5.27 x: nat ).
% 5.07/5.27
% 5.07/5.27 % Relevant facts (10154)
% 5.07/5.27 thf(fact_0_min__Null__member,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,X: nat] :
% 5.07/5.27 ( ( vEBT_VEBT_minNull @ T )
% 5.07/5.27 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.07/5.27
% 5.07/5.27 % min_Null_member
% 5.07/5.27 thf(fact_1_valid__eq,axiom,
% 5.07/5.27 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.07/5.27
% 5.07/5.27 % valid_eq
% 5.07/5.27 thf(fact_2_valid__eq1,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,D: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ T @ D )
% 5.07/5.27 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.07/5.27
% 5.07/5.27 % valid_eq1
% 5.07/5.27 thf(fact_3_valid__eq2,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,D: nat] :
% 5.07/5.27 ( ( vEBT_VEBT_valid @ T @ D )
% 5.07/5.27 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.07/5.27
% 5.07/5.27 % valid_eq2
% 5.07/5.27 thf(fact_4_both__member__options__equiv__member,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ T @ N )
% 5.07/5.27 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.07/5.27 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.07/5.27
% 5.07/5.27 % both_member_options_equiv_member
% 5.07/5.27 thf(fact_5_valid__member__both__member__options,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ T @ N )
% 5.07/5.27 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.07/5.27 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.07/5.27
% 5.07/5.27 % valid_member_both_member_options
% 5.07/5.27 thf(fact_6_valid__0__not,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT] :
% 5.07/5.27 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.07/5.27
% 5.07/5.27 % valid_0_not
% 5.07/5.27 thf(fact_7_valid__tree__deg__neq__0,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT] :
% 5.07/5.27 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.07/5.27
% 5.07/5.27 % valid_tree_deg_neq_0
% 5.07/5.27 thf(fact_8_deg__deg__n,axiom,
% 5.07/5.27 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.07/5.27 => ( Deg = N ) ) ).
% 5.07/5.27
% 5.07/5.27 % deg_deg_n
% 5.07/5.27 thf(fact_9_member__valid__both__member__options,axiom,
% 5.07/5.27 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.07/5.27 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.07/5.27 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.07/5.27 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.07/5.27
% 5.07/5.27 % member_valid_both_member_options
% 5.07/5.27 thf(fact_10_deg__not__0,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT,N: nat] :
% 5.07/5.27 ( ( vEBT_invar_vebt @ T @ N )
% 5.07/5.27 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.27
% 5.07/5.27 % deg_not_0
% 5.07/5.27 thf(fact_11_Leaf__0__not,axiom,
% 5.07/5.27 ! [A: $o,B: $o] :
% 5.07/5.27 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.07/5.27
% 5.07/5.27 % Leaf_0_not
% 5.07/5.27 thf(fact_12_not__min__Null__member,axiom,
% 5.07/5.27 ! [T: vEBT_VEBT] :
% 5.07/5.27 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.07/5.27 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.07/5.27
% 5.07/5.27 % not_min_Null_member
% 5.07/5.27 thf(fact_13_both__member__options__def,axiom,
% 5.07/5.27 ( vEBT_V8194947554948674370ptions
% 5.07/5.27 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.07/5.27 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.07/5.27 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.07/5.27
% 5.07/5.27 % both_member_options_def
% 5.07/5.27 thf(fact_14_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.07/5.28 ! [Uu: $o] :
% 5.07/5.28 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.minNull.simps(3)
% 5.07/5.28 thf(fact_15_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.07/5.28 ! [Uv: $o] :
% 5.07/5.28 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.minNull.simps(2)
% 5.07/5.28 thf(fact_16_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.07/5.28 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.minNull.simps(1)
% 5.07/5.28 thf(fact_17_buildup__gives__valid,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % buildup_gives_valid
% 5.07/5.28 thf(fact_18_bot__nat__0_Onot__eq__extremum,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( A != zero_zero_nat )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % bot_nat_0.not_eq_extremum
% 5.07/5.28 thf(fact_19_neq0__conv,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( N != zero_zero_nat )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % neq0_conv
% 5.07/5.28 thf(fact_20_less__nat__zero__code,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % less_nat_zero_code
% 5.07/5.28 thf(fact_21_not__gr__zero,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.07/5.28 = ( N = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % not_gr_zero
% 5.07/5.28 thf(fact_22_buildup__nothing__in__leaf,axiom,
% 5.07/5.28 ! [N: nat,X: nat] :
% 5.07/5.28 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.07/5.28
% 5.07/5.28 % buildup_nothing_in_leaf
% 5.07/5.28 thf(fact_23_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.07/5.28 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.07/5.28 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.naive_member.simps(2)
% 5.07/5.28 thf(fact_24_buildup__nothing__in__min__max,axiom,
% 5.07/5.28 ! [N: nat,X: nat] :
% 5.07/5.28 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.07/5.28
% 5.07/5.28 % buildup_nothing_in_min_max
% 5.07/5.28 thf(fact_25_VEBT_Oinject_I2_J,axiom,
% 5.07/5.28 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 5.07/5.28 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 5.07/5.28 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.07/5.28 = ( ( X21 = Y21 )
% 5.07/5.28 & ( X22 = Y22 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.inject(2)
% 5.07/5.28 thf(fact_26_VEBT_Oinject_I1_J,axiom,
% 5.07/5.28 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.07/5.28 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.07/5.28 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.07/5.28 = ( ( X11 = Y11 )
% 5.07/5.28 & ( X12 = Y12 )
% 5.07/5.28 & ( X13 = Y13 )
% 5.07/5.28 & ( X14 = Y14 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.inject(1)
% 5.07/5.28 thf(fact_27_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.07/5.28 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.07/5.28 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.membermima.simps(1)
% 5.07/5.28 thf(fact_28_vebt__buildup_Osimps_I1_J,axiom,
% 5.07/5.28 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.07/5.28 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.07/5.28
% 5.07/5.28 % vebt_buildup.simps(1)
% 5.07/5.28 thf(fact_29_zero__reorient,axiom,
% 5.07/5.28 ! [X: literal] :
% 5.07/5.28 ( ( zero_zero_literal = X )
% 5.07/5.28 = ( X = zero_zero_literal ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_reorient
% 5.07/5.28 thf(fact_30_zero__reorient,axiom,
% 5.07/5.28 ! [X: real] :
% 5.07/5.28 ( ( zero_zero_real = X )
% 5.07/5.28 = ( X = zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_reorient
% 5.07/5.28 thf(fact_31_zero__reorient,axiom,
% 5.07/5.28 ! [X: rat] :
% 5.07/5.28 ( ( zero_zero_rat = X )
% 5.07/5.28 = ( X = zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_reorient
% 5.07/5.28 thf(fact_32_zero__reorient,axiom,
% 5.07/5.28 ! [X: nat] :
% 5.07/5.28 ( ( zero_zero_nat = X )
% 5.07/5.28 = ( X = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_reorient
% 5.07/5.28 thf(fact_33_zero__reorient,axiom,
% 5.07/5.28 ! [X: int] :
% 5.07/5.28 ( ( zero_zero_int = X )
% 5.07/5.28 = ( X = zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_reorient
% 5.07/5.28 thf(fact_34_linorder__neqE__nat,axiom,
% 5.07/5.28 ! [X: nat,Y: nat] :
% 5.07/5.28 ( ( X != Y )
% 5.07/5.28 => ( ~ ( ord_less_nat @ X @ Y )
% 5.07/5.28 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % linorder_neqE_nat
% 5.07/5.28 thf(fact_35_infinite__descent,axiom,
% 5.07/5.28 ! [P: nat > $o,N: nat] :
% 5.07/5.28 ( ! [N2: nat] :
% 5.07/5.28 ( ~ ( P @ N2 )
% 5.07/5.28 => ? [M: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M @ N2 )
% 5.07/5.28 & ~ ( P @ M ) ) )
% 5.07/5.28 => ( P @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % infinite_descent
% 5.07/5.28 thf(fact_36_nat__less__induct,axiom,
% 5.07/5.28 ! [P: nat > $o,N: nat] :
% 5.07/5.28 ( ! [N2: nat] :
% 5.07/5.28 ( ! [M: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M @ N2 )
% 5.07/5.28 => ( P @ M ) )
% 5.07/5.28 => ( P @ N2 ) )
% 5.07/5.28 => ( P @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_less_induct
% 5.07/5.28 thf(fact_37_less__irrefl__nat,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ N ) ).
% 5.07/5.28
% 5.07/5.28 % less_irrefl_nat
% 5.07/5.28 thf(fact_38_less__not__refl3,axiom,
% 5.07/5.28 ! [S: nat,T: nat] :
% 5.07/5.28 ( ( ord_less_nat @ S @ T )
% 5.07/5.28 => ( S != T ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_not_refl3
% 5.07/5.28 thf(fact_39_less__not__refl2,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ N @ M2 )
% 5.07/5.28 => ( M2 != N ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_not_refl2
% 5.07/5.28 thf(fact_40_less__not__refl,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ N ) ).
% 5.07/5.28
% 5.07/5.28 % less_not_refl
% 5.07/5.28 thf(fact_41_nat__neq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( M2 != N )
% 5.07/5.28 = ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_neq_iff
% 5.07/5.28 thf(fact_42_zero__less__iff__neq__zero,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 = ( N != zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_less_iff_neq_zero
% 5.07/5.28 thf(fact_43_gr__implies__not__zero,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( N != zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr_implies_not_zero
% 5.07/5.28 thf(fact_44_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: complex,P: complex > $o] :
% 5.07/5.28 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_45_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: real,P: real > $o] :
% 5.07/5.28 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_46_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: list_nat,P: list_nat > $o] :
% 5.07/5.28 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_47_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: set_nat,P: set_nat > $o] :
% 5.07/5.28 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_48_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: nat,P: nat > $o] :
% 5.07/5.28 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_49_mem__Collect__eq,axiom,
% 5.07/5.28 ! [A: int,P: int > $o] :
% 5.07/5.28 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.07/5.28 = ( P @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % mem_Collect_eq
% 5.07/5.28 thf(fact_50_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_complex] :
% 5.07/5.28 ( ( collect_complex
% 5.07/5.28 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_51_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_real] :
% 5.07/5.28 ( ( collect_real
% 5.07/5.28 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_52_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_list_nat] :
% 5.07/5.28 ( ( collect_list_nat
% 5.07/5.28 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_53_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_set_nat] :
% 5.07/5.28 ( ( collect_set_nat
% 5.07/5.28 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_54_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_nat] :
% 5.07/5.28 ( ( collect_nat
% 5.07/5.28 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_55_Collect__mem__eq,axiom,
% 5.07/5.28 ! [A2: set_int] :
% 5.07/5.28 ( ( collect_int
% 5.07/5.28 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.07/5.28 = A2 ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_mem_eq
% 5.07/5.28 thf(fact_56_Collect__cong,axiom,
% 5.07/5.28 ! [P: real > $o,Q: real > $o] :
% 5.07/5.28 ( ! [X3: real] :
% 5.07/5.28 ( ( P @ X3 )
% 5.07/5.28 = ( Q @ X3 ) )
% 5.07/5.28 => ( ( collect_real @ P )
% 5.07/5.28 = ( collect_real @ Q ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_cong
% 5.07/5.28 thf(fact_57_Collect__cong,axiom,
% 5.07/5.28 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.07/5.28 ( ! [X3: list_nat] :
% 5.07/5.28 ( ( P @ X3 )
% 5.07/5.28 = ( Q @ X3 ) )
% 5.07/5.28 => ( ( collect_list_nat @ P )
% 5.07/5.28 = ( collect_list_nat @ Q ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_cong
% 5.07/5.28 thf(fact_58_Collect__cong,axiom,
% 5.07/5.28 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.07/5.28 ( ! [X3: set_nat] :
% 5.07/5.28 ( ( P @ X3 )
% 5.07/5.28 = ( Q @ X3 ) )
% 5.07/5.28 => ( ( collect_set_nat @ P )
% 5.07/5.28 = ( collect_set_nat @ Q ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_cong
% 5.07/5.28 thf(fact_59_Collect__cong,axiom,
% 5.07/5.28 ! [P: nat > $o,Q: nat > $o] :
% 5.07/5.28 ( ! [X3: nat] :
% 5.07/5.28 ( ( P @ X3 )
% 5.07/5.28 = ( Q @ X3 ) )
% 5.07/5.28 => ( ( collect_nat @ P )
% 5.07/5.28 = ( collect_nat @ Q ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_cong
% 5.07/5.28 thf(fact_60_Collect__cong,axiom,
% 5.07/5.28 ! [P: int > $o,Q: int > $o] :
% 5.07/5.28 ( ! [X3: int] :
% 5.07/5.28 ( ( P @ X3 )
% 5.07/5.28 = ( Q @ X3 ) )
% 5.07/5.28 => ( ( collect_int @ P )
% 5.07/5.28 = ( collect_int @ Q ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Collect_cong
% 5.07/5.28 thf(fact_61_not__less__zero,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % not_less_zero
% 5.07/5.28 thf(fact_62_gr__zeroI,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( N != zero_zero_nat )
% 5.07/5.28 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr_zeroI
% 5.07/5.28 thf(fact_63_infinite__descent0,axiom,
% 5.07/5.28 ! [P: nat > $o,N: nat] :
% 5.07/5.28 ( ( P @ zero_zero_nat )
% 5.07/5.28 => ( ! [N2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.07/5.28 => ( ~ ( P @ N2 )
% 5.07/5.28 => ? [M: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M @ N2 )
% 5.07/5.28 & ~ ( P @ M ) ) ) )
% 5.07/5.28 => ( P @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % infinite_descent0
% 5.07/5.28 thf(fact_64_gr__implies__not0,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( N != zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr_implies_not0
% 5.07/5.28 thf(fact_65_less__zeroE,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % less_zeroE
% 5.07/5.28 thf(fact_66_not__less0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % not_less0
% 5.07/5.28 thf(fact_67_not__gr0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.07/5.28 = ( N = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % not_gr0
% 5.07/5.28 thf(fact_68_gr0I,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( N != zero_zero_nat )
% 5.07/5.28 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr0I
% 5.07/5.28 thf(fact_69_bot__nat__0_Oextremum__strict,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % bot_nat_0.extremum_strict
% 5.07/5.28 thf(fact_70_VEBT_Oexhaust,axiom,
% 5.07/5.28 ! [Y: vEBT_VEBT] :
% 5.07/5.28 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.07/5.28 ( Y
% 5.07/5.28 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.07/5.28 => ~ ! [X212: $o,X222: $o] :
% 5.07/5.28 ( Y
% 5.07/5.28 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.exhaust
% 5.07/5.28 thf(fact_71_VEBT_Odistinct_I1_J,axiom,
% 5.07/5.28 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 5.07/5.28 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.07/5.28 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.distinct(1)
% 5.07/5.28 thf(fact_72_deg1Leaf,axiom,
% 5.07/5.28 ! [T: vEBT_VEBT] :
% 5.07/5.28 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.07/5.28 = ( ? [A3: $o,B2: $o] :
% 5.07/5.28 ( T
% 5.07/5.28 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % deg1Leaf
% 5.07/5.28 thf(fact_73_deg__1__Leaf,axiom,
% 5.07/5.28 ! [T: vEBT_VEBT] :
% 5.07/5.28 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.07/5.28 => ? [A4: $o,B3: $o] :
% 5.07/5.28 ( T
% 5.07/5.28 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % deg_1_Leaf
% 5.07/5.28 thf(fact_74_deg__1__Leafy,axiom,
% 5.07/5.28 ! [T: vEBT_VEBT,N: nat] :
% 5.07/5.28 ( ( vEBT_invar_vebt @ T @ N )
% 5.07/5.28 => ( ( N = one_one_nat )
% 5.07/5.28 => ? [A4: $o,B3: $o] :
% 5.07/5.28 ( T
% 5.07/5.28 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % deg_1_Leafy
% 5.07/5.28 thf(fact_75_field__lbound__gt__zero,axiom,
% 5.07/5.28 ! [D1: real,D2: real] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.07/5.28 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.07/5.28 => ? [E: real] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ E )
% 5.07/5.28 & ( ord_less_real @ E @ D1 )
% 5.07/5.28 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % field_lbound_gt_zero
% 5.07/5.28 thf(fact_76_field__lbound__gt__zero,axiom,
% 5.07/5.28 ! [D1: rat,D2: rat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.07/5.28 => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 5.07/5.28 => ? [E: rat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.07/5.28 & ( ord_less_rat @ E @ D1 )
% 5.07/5.28 & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % field_lbound_gt_zero
% 5.07/5.28 thf(fact_77_less__numeral__extra_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(3)
% 5.07/5.28 thf(fact_78_less__numeral__extra_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(3)
% 5.07/5.28 thf(fact_79_less__numeral__extra_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(3)
% 5.07/5.28 thf(fact_80_less__numeral__extra_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(3)
% 5.07/5.28 thf(fact_81_deg__SUcn__Node,axiom,
% 5.07/5.28 ! [Tree: vEBT_VEBT,N: nat] :
% 5.07/5.28 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.07/5.28 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.07/5.28 ( Tree
% 5.07/5.28 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % deg_SUcn_Node
% 5.07/5.28 thf(fact_82_VEBT_Osize__gen_I2_J,axiom,
% 5.07/5.28 ! [X21: $o,X22: $o] :
% 5.07/5.28 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.size_gen(2)
% 5.07/5.28 thf(fact_83_VEBT_Osize_I4_J,axiom,
% 5.07/5.28 ! [X21: $o,X22: $o] :
% 5.07/5.28 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT.size(4)
% 5.07/5.28 thf(fact_84_of__nat__0__less__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_less_iff
% 5.07/5.28 thf(fact_85_of__nat__0__less__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_less_iff
% 5.07/5.28 thf(fact_86_of__nat__0__less__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_less_iff
% 5.07/5.28 thf(fact_87_of__nat__0__less__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_less_iff
% 5.07/5.28 thf(fact_88_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.07/5.28 ! [A: $o,B: $o,X: nat] :
% 5.07/5.28 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.07/5.28 = ( ( ( X = zero_zero_nat )
% 5.07/5.28 => A )
% 5.07/5.28 & ( ( X != zero_zero_nat )
% 5.07/5.28 => ( ( ( X = one_one_nat )
% 5.07/5.28 => B )
% 5.07/5.28 & ( X = one_one_nat ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.naive_member.simps(1)
% 5.07/5.28 thf(fact_89_vebt__member_Osimps_I1_J,axiom,
% 5.07/5.28 ! [A: $o,B: $o,X: nat] :
% 5.07/5.28 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.07/5.28 = ( ( ( X = zero_zero_nat )
% 5.07/5.28 => A )
% 5.07/5.28 & ( ( X != zero_zero_nat )
% 5.07/5.28 => ( ( ( X = one_one_nat )
% 5.07/5.28 => B )
% 5.07/5.28 & ( X = one_one_nat ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % vebt_member.simps(1)
% 5.07/5.28 thf(fact_90_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.07/5.28 ! [X: vEBT_VEBT] :
% 5.07/5.28 ( ( vEBT_VEBT_minNull @ X )
% 5.07/5.28 => ( ( X
% 5.07/5.28 != ( vEBT_Leaf @ $false @ $false ) )
% 5.07/5.28 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.07/5.28 ( X
% 5.07/5.28 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.minNull.elims(2)
% 5.07/5.28 thf(fact_91_old_Onat_Oinject,axiom,
% 5.07/5.28 ! [Nat: nat,Nat2: nat] :
% 5.07/5.28 ( ( ( suc @ Nat )
% 5.07/5.28 = ( suc @ Nat2 ) )
% 5.07/5.28 = ( Nat = Nat2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % old.nat.inject
% 5.07/5.28 thf(fact_92_nat_Oinject,axiom,
% 5.07/5.28 ! [X23: nat,Y2: nat] :
% 5.07/5.28 ( ( ( suc @ X23 )
% 5.07/5.28 = ( suc @ Y2 ) )
% 5.07/5.28 = ( X23 = Y2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat.inject
% 5.07/5.28 thf(fact_93_of__nat__eq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri8010041392384452111omplex @ M2 )
% 5.07/5.28 = ( semiri8010041392384452111omplex @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_iff
% 5.07/5.28 thf(fact_94_of__nat__eq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri5074537144036343181t_real @ M2 )
% 5.07/5.28 = ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_iff
% 5.07/5.28 thf(fact_95_of__nat__eq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri681578069525770553at_rat @ M2 )
% 5.07/5.28 = ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_iff
% 5.07/5.28 thf(fact_96_of__nat__eq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 5.07/5.28 = ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_iff
% 5.07/5.28 thf(fact_97_of__nat__eq__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_iff
% 5.07/5.28 thf(fact_98_lessI,axiom,
% 5.07/5.28 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % lessI
% 5.07/5.28 thf(fact_99_Suc__mono,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_mono
% 5.07/5.28 thf(fact_100_Suc__less__eq,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_less_eq
% 5.07/5.28 thf(fact_101_of__nat__0,axiom,
% 5.07/5.28 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0
% 5.07/5.28 thf(fact_102_of__nat__0,axiom,
% 5.07/5.28 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0
% 5.07/5.28 thf(fact_103_of__nat__0,axiom,
% 5.07/5.28 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0
% 5.07/5.28 thf(fact_104_of__nat__0,axiom,
% 5.07/5.28 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0
% 5.07/5.28 thf(fact_105_of__nat__0,axiom,
% 5.07/5.28 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0
% 5.07/5.28 thf(fact_106_of__nat__0__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( zero_zero_complex
% 5.07/5.28 = ( semiri8010041392384452111omplex @ N ) )
% 5.07/5.28 = ( zero_zero_nat = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_eq_iff
% 5.07/5.28 thf(fact_107_of__nat__0__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( zero_zero_real
% 5.07/5.28 = ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 = ( zero_zero_nat = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_eq_iff
% 5.07/5.28 thf(fact_108_of__nat__0__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( zero_zero_rat
% 5.07/5.28 = ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 = ( zero_zero_nat = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_eq_iff
% 5.07/5.28 thf(fact_109_of__nat__0__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( zero_zero_nat
% 5.07/5.28 = ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 = ( zero_zero_nat = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_eq_iff
% 5.07/5.28 thf(fact_110_of__nat__0__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( zero_zero_int
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( zero_zero_nat = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_0_eq_iff
% 5.07/5.28 thf(fact_111_of__nat__eq__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( ( semiri8010041392384452111omplex @ M2 )
% 5.07/5.28 = zero_zero_complex )
% 5.07/5.28 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_0_iff
% 5.07/5.28 thf(fact_112_of__nat__eq__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( ( semiri5074537144036343181t_real @ M2 )
% 5.07/5.28 = zero_zero_real )
% 5.07/5.28 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_0_iff
% 5.07/5.28 thf(fact_113_of__nat__eq__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( ( semiri681578069525770553at_rat @ M2 )
% 5.07/5.28 = zero_zero_rat )
% 5.07/5.28 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_0_iff
% 5.07/5.28 thf(fact_114_of__nat__eq__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 5.07/5.28 = zero_zero_nat )
% 5.07/5.28 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_0_iff
% 5.07/5.28 thf(fact_115_of__nat__eq__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.07/5.28 = zero_zero_int )
% 5.07/5.28 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_0_iff
% 5.07/5.28 thf(fact_116_of__nat__less__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_iff
% 5.07/5.28 thf(fact_117_of__nat__less__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_iff
% 5.07/5.28 thf(fact_118_of__nat__less__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_iff
% 5.07/5.28 thf(fact_119_of__nat__less__iff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_iff
% 5.07/5.28 thf(fact_120_less__Suc0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.07/5.28 = ( N = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_Suc0
% 5.07/5.28 thf(fact_121_zero__less__Suc,axiom,
% 5.07/5.28 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_less_Suc
% 5.07/5.28 thf(fact_122_of__nat__eq__1__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ( semiri8010041392384452111omplex @ N )
% 5.07/5.28 = one_one_complex )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_1_iff
% 5.07/5.28 thf(fact_123_of__nat__eq__1__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ( semiri5074537144036343181t_real @ N )
% 5.07/5.28 = one_one_real )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_1_iff
% 5.07/5.28 thf(fact_124_of__nat__eq__1__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ( semiri681578069525770553at_rat @ N )
% 5.07/5.28 = one_one_rat )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_1_iff
% 5.07/5.28 thf(fact_125_of__nat__eq__1__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.07/5.28 = one_one_nat )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_1_iff
% 5.07/5.28 thf(fact_126_of__nat__eq__1__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ( semiri1314217659103216013at_int @ N )
% 5.07/5.28 = one_one_int )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_eq_1_iff
% 5.07/5.28 thf(fact_127_of__nat__1__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( one_one_complex
% 5.07/5.28 = ( semiri8010041392384452111omplex @ N ) )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1_eq_iff
% 5.07/5.28 thf(fact_128_of__nat__1__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( one_one_real
% 5.07/5.28 = ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1_eq_iff
% 5.07/5.28 thf(fact_129_of__nat__1__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( one_one_rat
% 5.07/5.28 = ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1_eq_iff
% 5.07/5.28 thf(fact_130_of__nat__1__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( one_one_nat
% 5.07/5.28 = ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1_eq_iff
% 5.07/5.28 thf(fact_131_of__nat__1__eq__iff,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( one_one_int
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( N = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1_eq_iff
% 5.07/5.28 thf(fact_132_of__nat__1,axiom,
% 5.07/5.28 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.07/5.28 = one_one_complex ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1
% 5.07/5.28 thf(fact_133_of__nat__1,axiom,
% 5.07/5.28 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.07/5.28 = one_one_real ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1
% 5.07/5.28 thf(fact_134_of__nat__1,axiom,
% 5.07/5.28 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.07/5.28 = one_one_rat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1
% 5.07/5.28 thf(fact_135_of__nat__1,axiom,
% 5.07/5.28 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.07/5.28 = one_one_nat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1
% 5.07/5.28 thf(fact_136_of__nat__1,axiom,
% 5.07/5.28 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.07/5.28 = one_one_int ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_1
% 5.07/5.28 thf(fact_137_less__one,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ N @ one_one_nat )
% 5.07/5.28 = ( N = zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_one
% 5.07/5.28 thf(fact_138_one__reorient,axiom,
% 5.07/5.28 ! [X: complex] :
% 5.07/5.28 ( ( one_one_complex = X )
% 5.07/5.28 = ( X = one_one_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_reorient
% 5.07/5.28 thf(fact_139_one__reorient,axiom,
% 5.07/5.28 ! [X: real] :
% 5.07/5.28 ( ( one_one_real = X )
% 5.07/5.28 = ( X = one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_reorient
% 5.07/5.28 thf(fact_140_one__reorient,axiom,
% 5.07/5.28 ! [X: rat] :
% 5.07/5.28 ( ( one_one_rat = X )
% 5.07/5.28 = ( X = one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_reorient
% 5.07/5.28 thf(fact_141_one__reorient,axiom,
% 5.07/5.28 ! [X: nat] :
% 5.07/5.28 ( ( one_one_nat = X )
% 5.07/5.28 = ( X = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_reorient
% 5.07/5.28 thf(fact_142_one__reorient,axiom,
% 5.07/5.28 ! [X: int] :
% 5.07/5.28 ( ( one_one_int = X )
% 5.07/5.28 = ( X = one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_reorient
% 5.07/5.28 thf(fact_143_n__not__Suc__n,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( N
% 5.07/5.28 != ( suc @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % n_not_Suc_n
% 5.07/5.28 thf(fact_144_Suc__inject,axiom,
% 5.07/5.28 ! [X: nat,Y: nat] :
% 5.07/5.28 ( ( ( suc @ X )
% 5.07/5.28 = ( suc @ Y ) )
% 5.07/5.28 => ( X = Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_inject
% 5.07/5.28 thf(fact_145_of__nat__neq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.07/5.28 != zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_neq_0
% 5.07/5.28 thf(fact_146_of__nat__neq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.07/5.28 != zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_neq_0
% 5.07/5.28 thf(fact_147_of__nat__neq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.07/5.28 != zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_neq_0
% 5.07/5.28 thf(fact_148_of__nat__neq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.07/5.28 != zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_neq_0
% 5.07/5.28 thf(fact_149_of__nat__neq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.07/5.28 != zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_neq_0
% 5.07/5.28 thf(fact_150_One__nat__def,axiom,
% 5.07/5.28 ( one_one_nat
% 5.07/5.28 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % One_nat_def
% 5.07/5.28 thf(fact_151_less__numeral__extra_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(4)
% 5.07/5.28 thf(fact_152_less__numeral__extra_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(4)
% 5.07/5.28 thf(fact_153_less__numeral__extra_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(4)
% 5.07/5.28 thf(fact_154_less__numeral__extra_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(4)
% 5.07/5.28 thf(fact_155_size__neq__size__imp__neq,axiom,
% 5.07/5.28 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.07/5.28 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.07/5.28 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.07/5.28 => ( X != Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % size_neq_size_imp_neq
% 5.07/5.28 thf(fact_156_size__neq__size__imp__neq,axiom,
% 5.07/5.28 ! [X: list_o,Y: list_o] :
% 5.07/5.28 ( ( ( size_size_list_o @ X )
% 5.07/5.28 != ( size_size_list_o @ Y ) )
% 5.07/5.28 => ( X != Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % size_neq_size_imp_neq
% 5.07/5.28 thf(fact_157_size__neq__size__imp__neq,axiom,
% 5.07/5.28 ! [X: list_nat,Y: list_nat] :
% 5.07/5.28 ( ( ( size_size_list_nat @ X )
% 5.07/5.28 != ( size_size_list_nat @ Y ) )
% 5.07/5.28 => ( X != Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % size_neq_size_imp_neq
% 5.07/5.28 thf(fact_158_size__neq__size__imp__neq,axiom,
% 5.07/5.28 ! [X: list_int,Y: list_int] :
% 5.07/5.28 ( ( ( size_size_list_int @ X )
% 5.07/5.28 != ( size_size_list_int @ Y ) )
% 5.07/5.28 => ( X != Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % size_neq_size_imp_neq
% 5.07/5.28 thf(fact_159_size__neq__size__imp__neq,axiom,
% 5.07/5.28 ! [X: num,Y: num] :
% 5.07/5.28 ( ( ( size_size_num @ X )
% 5.07/5.28 != ( size_size_num @ Y ) )
% 5.07/5.28 => ( X != Y ) ) ).
% 5.07/5.28
% 5.07/5.28 % size_neq_size_imp_neq
% 5.07/5.28 thf(fact_160_nat__induct__non__zero,axiom,
% 5.07/5.28 ! [N: nat,P: nat > $o] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ( P @ one_one_nat )
% 5.07/5.28 => ( ! [N2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.07/5.28 => ( ( P @ N2 )
% 5.07/5.28 => ( P @ ( suc @ N2 ) ) ) )
% 5.07/5.28 => ( P @ N ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_induct_non_zero
% 5.07/5.28 thf(fact_161_nat_Odistinct_I1_J,axiom,
% 5.07/5.28 ! [X23: nat] :
% 5.07/5.28 ( zero_zero_nat
% 5.07/5.28 != ( suc @ X23 ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat.distinct(1)
% 5.07/5.28 thf(fact_162_old_Onat_Odistinct_I2_J,axiom,
% 5.07/5.28 ! [Nat2: nat] :
% 5.07/5.28 ( ( suc @ Nat2 )
% 5.07/5.28 != zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % old.nat.distinct(2)
% 5.07/5.28 thf(fact_163_old_Onat_Odistinct_I1_J,axiom,
% 5.07/5.28 ! [Nat2: nat] :
% 5.07/5.28 ( zero_zero_nat
% 5.07/5.28 != ( suc @ Nat2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % old.nat.distinct(1)
% 5.07/5.28 thf(fact_164_nat_OdiscI,axiom,
% 5.07/5.28 ! [Nat: nat,X23: nat] :
% 5.07/5.28 ( ( Nat
% 5.07/5.28 = ( suc @ X23 ) )
% 5.07/5.28 => ( Nat != zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat.discI
% 5.07/5.28 thf(fact_165_old_Onat_Oexhaust,axiom,
% 5.07/5.28 ! [Y: nat] :
% 5.07/5.28 ( ( Y != zero_zero_nat )
% 5.07/5.28 => ~ ! [Nat3: nat] :
% 5.07/5.28 ( Y
% 5.07/5.28 != ( suc @ Nat3 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % old.nat.exhaust
% 5.07/5.28 thf(fact_166_vebt__buildup_Ocases,axiom,
% 5.07/5.28 ! [X: nat] :
% 5.07/5.28 ( ( X != zero_zero_nat )
% 5.07/5.28 => ( ( X
% 5.07/5.28 != ( suc @ zero_zero_nat ) )
% 5.07/5.28 => ~ ! [Va: nat] :
% 5.07/5.28 ( X
% 5.07/5.28 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % vebt_buildup.cases
% 5.07/5.28 thf(fact_167_nat__induct,axiom,
% 5.07/5.28 ! [P: nat > $o,N: nat] :
% 5.07/5.28 ( ( P @ zero_zero_nat )
% 5.07/5.28 => ( ! [N2: nat] :
% 5.07/5.28 ( ( P @ N2 )
% 5.07/5.28 => ( P @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( P @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_induct
% 5.07/5.28 thf(fact_168_diff__induct,axiom,
% 5.07/5.28 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 5.07/5.28 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.07/5.28 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.07/5.28 => ( ! [X3: nat,Y3: nat] :
% 5.07/5.28 ( ( P @ X3 @ Y3 )
% 5.07/5.28 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.07/5.28 => ( P @ M2 @ N ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_induct
% 5.07/5.28 thf(fact_169_zero__induct,axiom,
% 5.07/5.28 ! [P: nat > $o,K: nat] :
% 5.07/5.28 ( ( P @ K )
% 5.07/5.28 => ( ! [N2: nat] :
% 5.07/5.28 ( ( P @ ( suc @ N2 ) )
% 5.07/5.28 => ( P @ N2 ) )
% 5.07/5.28 => ( P @ zero_zero_nat ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_induct
% 5.07/5.28 thf(fact_170_Suc__neq__Zero,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( suc @ M2 )
% 5.07/5.28 != zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_neq_Zero
% 5.07/5.28 thf(fact_171_Zero__neq__Suc,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( zero_zero_nat
% 5.07/5.28 != ( suc @ M2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % Zero_neq_Suc
% 5.07/5.28 thf(fact_172_Zero__not__Suc,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( zero_zero_nat
% 5.07/5.28 != ( suc @ M2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % Zero_not_Suc
% 5.07/5.28 thf(fact_173_not0__implies__Suc,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( N != zero_zero_nat )
% 5.07/5.28 => ? [M3: nat] :
% 5.07/5.28 ( N
% 5.07/5.28 = ( suc @ M3 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % not0_implies_Suc
% 5.07/5.28 thf(fact_174_Nat_OlessE,axiom,
% 5.07/5.28 ! [I: nat,K: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I @ K )
% 5.07/5.28 => ( ( K
% 5.07/5.28 != ( suc @ I ) )
% 5.07/5.28 => ~ ! [J: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I @ J )
% 5.07/5.28 => ( K
% 5.07/5.28 != ( suc @ J ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Nat.lessE
% 5.07/5.28 thf(fact_175_Suc__lessD,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_lessD
% 5.07/5.28 thf(fact_176_Suc__lessE,axiom,
% 5.07/5.28 ! [I: nat,K: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.07/5.28 => ~ ! [J: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I @ J )
% 5.07/5.28 => ( K
% 5.07/5.28 != ( suc @ J ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_lessE
% 5.07/5.28 thf(fact_177_Suc__lessI,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ( ( suc @ M2 )
% 5.07/5.28 != N )
% 5.07/5.28 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_lessI
% 5.07/5.28 thf(fact_178_less__SucE,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.07/5.28 => ( ~ ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( M2 = N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_SucE
% 5.07/5.28 thf(fact_179_less__SucI,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_SucI
% 5.07/5.28 thf(fact_180_Ex__less__Suc,axiom,
% 5.07/5.28 ! [N: nat,P: nat > $o] :
% 5.07/5.28 ( ( ? [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.07/5.28 & ( P @ I2 ) ) )
% 5.07/5.28 = ( ( P @ N )
% 5.07/5.28 | ? [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ N )
% 5.07/5.28 & ( P @ I2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Ex_less_Suc
% 5.07/5.28 thf(fact_181_less__Suc__eq,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.07/5.28 = ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 | ( M2 = N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_Suc_eq
% 5.07/5.28 thf(fact_182_not__less__eq,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 5.07/5.28 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % not_less_eq
% 5.07/5.28 thf(fact_183_All__less__Suc,axiom,
% 5.07/5.28 ! [N: nat,P: nat > $o] :
% 5.07/5.28 ( ( ! [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.07/5.28 => ( P @ I2 ) ) )
% 5.07/5.28 = ( ( P @ N )
% 5.07/5.28 & ! [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ N )
% 5.07/5.28 => ( P @ I2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % All_less_Suc
% 5.07/5.28 thf(fact_184_Suc__less__eq2,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.07/5.28 = ( ? [M4: nat] :
% 5.07/5.28 ( ( M2
% 5.07/5.28 = ( suc @ M4 ) )
% 5.07/5.28 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_less_eq2
% 5.07/5.28 thf(fact_185_less__antisym,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ~ ( ord_less_nat @ N @ M2 )
% 5.07/5.28 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.07/5.28 => ( M2 = N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_antisym
% 5.07/5.28 thf(fact_186_Suc__less__SucD,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_less_SucD
% 5.07/5.28 thf(fact_187_less__trans__Suc,axiom,
% 5.07/5.28 ! [I: nat,J2: nat,K: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I @ J2 )
% 5.07/5.28 => ( ( ord_less_nat @ J2 @ K )
% 5.07/5.28 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_trans_Suc
% 5.07/5.28 thf(fact_188_less__Suc__induct,axiom,
% 5.07/5.28 ! [I: nat,J2: nat,P: nat > nat > $o] :
% 5.07/5.28 ( ( ord_less_nat @ I @ J2 )
% 5.07/5.28 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.07/5.28 => ( ! [I3: nat,J: nat,K2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I3 @ J )
% 5.07/5.28 => ( ( ord_less_nat @ J @ K2 )
% 5.07/5.28 => ( ( P @ I3 @ J )
% 5.07/5.28 => ( ( P @ J @ K2 )
% 5.07/5.28 => ( P @ I3 @ K2 ) ) ) ) )
% 5.07/5.28 => ( P @ I @ J2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_Suc_induct
% 5.07/5.28 thf(fact_189_strict__inc__induct,axiom,
% 5.07/5.28 ! [I: nat,J2: nat,P: nat > $o] :
% 5.07/5.28 ( ( ord_less_nat @ I @ J2 )
% 5.07/5.28 => ( ! [I3: nat] :
% 5.07/5.28 ( ( J2
% 5.07/5.28 = ( suc @ I3 ) )
% 5.07/5.28 => ( P @ I3 ) )
% 5.07/5.28 => ( ! [I3: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I3 @ J2 )
% 5.07/5.28 => ( ( P @ ( suc @ I3 ) )
% 5.07/5.28 => ( P @ I3 ) ) )
% 5.07/5.28 => ( P @ I ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % strict_inc_induct
% 5.07/5.28 thf(fact_190_not__less__less__Suc__eq,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ~ ( ord_less_nat @ N @ M2 )
% 5.07/5.28 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.07/5.28 = ( N = M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % not_less_less_Suc_eq
% 5.07/5.28 thf(fact_191_less__numeral__extra_I1_J,axiom,
% 5.07/5.28 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(1)
% 5.07/5.28 thf(fact_192_less__numeral__extra_I1_J,axiom,
% 5.07/5.28 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(1)
% 5.07/5.28 thf(fact_193_less__numeral__extra_I1_J,axiom,
% 5.07/5.28 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(1)
% 5.07/5.28 thf(fact_194_less__numeral__extra_I1_J,axiom,
% 5.07/5.28 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.07/5.28
% 5.07/5.28 % less_numeral_extra(1)
% 5.07/5.28 thf(fact_195_of__nat__less__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_0_iff
% 5.07/5.28 thf(fact_196_of__nat__less__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_0_iff
% 5.07/5.28 thf(fact_197_of__nat__less__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_0_iff
% 5.07/5.28 thf(fact_198_of__nat__less__0__iff,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_0_iff
% 5.07/5.28 thf(fact_199_less__imp__of__nat__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_imp_of_nat_less
% 5.07/5.28 thf(fact_200_less__imp__of__nat__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_imp_of_nat_less
% 5.07/5.28 thf(fact_201_less__imp__of__nat__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_imp_of_nat_less
% 5.07/5.28 thf(fact_202_less__imp__of__nat__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_imp_of_nat_less
% 5.07/5.28 thf(fact_203_of__nat__less__imp__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_imp_less
% 5.07/5.28 thf(fact_204_of__nat__less__imp__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_imp_less
% 5.07/5.28 thf(fact_205_of__nat__less__imp__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_imp_less
% 5.07/5.28 thf(fact_206_of__nat__less__imp__less,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % of_nat_less_imp_less
% 5.07/5.28 thf(fact_207_lift__Suc__mono__less,axiom,
% 5.07/5.28 ! [F: nat > real,N: nat,N3: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ N @ N3 )
% 5.07/5.28 => ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less
% 5.07/5.28 thf(fact_208_lift__Suc__mono__less,axiom,
% 5.07/5.28 ! [F: nat > rat,N: nat,N3: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ N @ N3 )
% 5.07/5.28 => ( ord_less_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less
% 5.07/5.28 thf(fact_209_lift__Suc__mono__less,axiom,
% 5.07/5.28 ! [F: nat > num,N: nat,N3: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ N @ N3 )
% 5.07/5.28 => ( ord_less_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less
% 5.07/5.28 thf(fact_210_lift__Suc__mono__less,axiom,
% 5.07/5.28 ! [F: nat > nat,N: nat,N3: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ N @ N3 )
% 5.07/5.28 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less
% 5.07/5.28 thf(fact_211_lift__Suc__mono__less,axiom,
% 5.07/5.28 ! [F: nat > int,N: nat,N3: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ N @ N3 )
% 5.07/5.28 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less
% 5.07/5.28 thf(fact_212_lift__Suc__mono__less__iff,axiom,
% 5.07/5.28 ! [F: nat > real,N: nat,M2: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less_iff
% 5.07/5.28 thf(fact_213_lift__Suc__mono__less__iff,axiom,
% 5.07/5.28 ! [F: nat > rat,N: nat,M2: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less_iff
% 5.07/5.28 thf(fact_214_lift__Suc__mono__less__iff,axiom,
% 5.07/5.28 ! [F: nat > num,N: nat,M2: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less_iff
% 5.07/5.28 thf(fact_215_lift__Suc__mono__less__iff,axiom,
% 5.07/5.28 ! [F: nat > nat,N: nat,M2: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less_iff
% 5.07/5.28 thf(fact_216_lift__Suc__mono__less__iff,axiom,
% 5.07/5.28 ! [F: nat > int,N: nat,M2: nat] :
% 5.07/5.28 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.28 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % lift_Suc_mono_less_iff
% 5.07/5.28 thf(fact_217_Ex__less__Suc2,axiom,
% 5.07/5.28 ! [N: nat,P: nat > $o] :
% 5.07/5.28 ( ( ? [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.07/5.28 & ( P @ I2 ) ) )
% 5.07/5.28 = ( ( P @ zero_zero_nat )
% 5.07/5.28 | ? [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ N )
% 5.07/5.28 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Ex_less_Suc2
% 5.07/5.28 thf(fact_218_gr0__conv__Suc,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 = ( ? [M5: nat] :
% 5.07/5.28 ( N
% 5.07/5.28 = ( suc @ M5 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr0_conv_Suc
% 5.07/5.28 thf(fact_219_All__less__Suc2,axiom,
% 5.07/5.28 ! [N: nat,P: nat > $o] :
% 5.07/5.28 ( ( ! [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.07/5.28 => ( P @ I2 ) ) )
% 5.07/5.28 = ( ( P @ zero_zero_nat )
% 5.07/5.28 & ! [I2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ I2 @ N )
% 5.07/5.28 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % All_less_Suc2
% 5.07/5.28 thf(fact_220_gr0__implies__Suc,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ? [M3: nat] :
% 5.07/5.28 ( N
% 5.07/5.28 = ( suc @ M3 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % gr0_implies_Suc
% 5.07/5.28 thf(fact_221_less__Suc__eq__0__disj,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.07/5.28 = ( ( M2 = zero_zero_nat )
% 5.07/5.28 | ? [J3: nat] :
% 5.07/5.28 ( ( M2
% 5.07/5.28 = ( suc @ J3 ) )
% 5.07/5.28 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_Suc_eq_0_disj
% 5.07/5.28 thf(fact_222_vebt__member_Osimps_I2_J,axiom,
% 5.07/5.28 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.07/5.28 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.07/5.28
% 5.07/5.28 % vebt_member.simps(2)
% 5.07/5.28 thf(fact_223_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.07/5.28 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.minNull.simps(4)
% 5.07/5.28 thf(fact_224_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.07/5.28 ! [Uu: $o,Uv: $o,D: nat] :
% 5.07/5.28 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.07/5.28 = ( D = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.valid'.simps(1)
% 5.07/5.28 thf(fact_225_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.07/5.28 ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 5.07/5.28 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Uz ) ).
% 5.07/5.28
% 5.07/5.28 % VEBT_internal.membermima.simps(2)
% 5.07/5.28 thf(fact_226_invar__vebt_Ointros_I1_J,axiom,
% 5.07/5.28 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % invar_vebt.intros(1)
% 5.07/5.28 thf(fact_227_vebt__buildup_Osimps_I2_J,axiom,
% 5.07/5.28 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.07/5.28 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.07/5.28
% 5.07/5.28 % vebt_buildup.simps(2)
% 5.07/5.28 thf(fact_228_zero__less__one,axiom,
% 5.07/5.28 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.07/5.28
% 5.07/5.28 % zero_less_one
% 5.07/5.28 thf(fact_229_zero__less__one,axiom,
% 5.07/5.28 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.07/5.28
% 5.07/5.28 % zero_less_one
% 5.07/5.28 thf(fact_230_zero__less__one,axiom,
% 5.07/5.28 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.07/5.28
% 5.07/5.28 % zero_less_one
% 5.07/5.28 thf(fact_231_zero__less__one,axiom,
% 5.07/5.28 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.07/5.28
% 5.07/5.28 % zero_less_one
% 5.07/5.28 thf(fact_232_not__one__less__zero,axiom,
% 5.07/5.28 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % not_one_less_zero
% 5.07/5.28 thf(fact_233_not__one__less__zero,axiom,
% 5.07/5.28 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % not_one_less_zero
% 5.07/5.28 thf(fact_234_not__one__less__zero,axiom,
% 5.07/5.28 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % not_one_less_zero
% 5.07/5.28 thf(fact_235_not__one__less__zero,axiom,
% 5.07/5.28 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % not_one_less_zero
% 5.07/5.28 thf(fact_236_pos__int__cases,axiom,
% 5.07/5.28 ! [K: int] :
% 5.07/5.28 ( ( ord_less_int @ zero_zero_int @ K )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( ( K
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.28 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % pos_int_cases
% 5.07/5.28 thf(fact_237_zero__less__imp__eq__int,axiom,
% 5.07/5.28 ! [K: int] :
% 5.07/5.28 ( ( ord_less_int @ zero_zero_int @ K )
% 5.07/5.28 => ? [N2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.07/5.28 & ( K
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_less_imp_eq_int
% 5.07/5.28 thf(fact_238_list__decode_Ocases,axiom,
% 5.07/5.28 ! [X: nat] :
% 5.07/5.28 ( ( X != zero_zero_nat )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( X
% 5.07/5.28 != ( suc @ N2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % list_decode.cases
% 5.07/5.28 thf(fact_239_exists__least__lemma,axiom,
% 5.07/5.28 ! [P: nat > $o] :
% 5.07/5.28 ( ~ ( P @ zero_zero_nat )
% 5.07/5.28 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.07/5.28 => ? [N2: nat] :
% 5.07/5.28 ( ~ ( P @ N2 )
% 5.07/5.28 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % exists_least_lemma
% 5.07/5.28 thf(fact_240_reals__Archimedean2,axiom,
% 5.07/5.28 ! [X: real] :
% 5.07/5.28 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % reals_Archimedean2
% 5.07/5.28 thf(fact_241_reals__Archimedean2,axiom,
% 5.07/5.28 ! [X: rat] :
% 5.07/5.28 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % reals_Archimedean2
% 5.07/5.28 thf(fact_242_zero__neq__one,axiom,
% 5.07/5.28 zero_zero_complex != one_one_complex ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_one
% 5.07/5.28 thf(fact_243_zero__neq__one,axiom,
% 5.07/5.28 zero_zero_real != one_one_real ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_one
% 5.07/5.28 thf(fact_244_zero__neq__one,axiom,
% 5.07/5.28 zero_zero_rat != one_one_rat ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_one
% 5.07/5.28 thf(fact_245_zero__neq__one,axiom,
% 5.07/5.28 zero_zero_nat != one_one_nat ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_one
% 5.07/5.28 thf(fact_246_zero__neq__one,axiom,
% 5.07/5.28 zero_zero_int != one_one_int ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_one
% 5.07/5.28 thf(fact_247_dbl__inc__simps_I2_J,axiom,
% 5.07/5.28 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.07/5.28 = one_one_complex ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(2)
% 5.07/5.28 thf(fact_248_dbl__inc__simps_I2_J,axiom,
% 5.07/5.28 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.07/5.28 = one_one_real ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(2)
% 5.07/5.28 thf(fact_249_dbl__inc__simps_I2_J,axiom,
% 5.07/5.28 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.07/5.28 = one_one_rat ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(2)
% 5.07/5.28 thf(fact_250_dbl__inc__simps_I2_J,axiom,
% 5.07/5.28 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.07/5.28 = one_one_int ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(2)
% 5.07/5.28 thf(fact_251_Suc__diff__1,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.07/5.28 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_diff_1
% 5.07/5.28 thf(fact_252_arcosh__1,axiom,
% 5.07/5.28 ( ( arcosh_real @ one_one_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % arcosh_1
% 5.07/5.28 thf(fact_253_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( minus_minus_real @ A @ A )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % cancel_comm_monoid_add_class.diff_cancel
% 5.07/5.28 thf(fact_254_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ A @ A )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % cancel_comm_monoid_add_class.diff_cancel
% 5.07/5.28 thf(fact_255_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ A @ A )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % cancel_comm_monoid_add_class.diff_cancel
% 5.07/5.28 thf(fact_256_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( minus_minus_int @ A @ A )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % cancel_comm_monoid_add_class.diff_cancel
% 5.07/5.28 thf(fact_257_diff__zero,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_zero
% 5.07/5.28 thf(fact_258_diff__zero,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_zero
% 5.07/5.28 thf(fact_259_diff__zero,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_zero
% 5.07/5.28 thf(fact_260_diff__zero,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_zero
% 5.07/5.28 thf(fact_261_zero__diff,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % zero_diff
% 5.07/5.28 thf(fact_262_diff__0__right,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0_right
% 5.07/5.28 thf(fact_263_diff__0__right,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0_right
% 5.07/5.28 thf(fact_264_diff__0__right,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0_right
% 5.07/5.28 thf(fact_265_diff__self,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( minus_minus_real @ A @ A )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % diff_self
% 5.07/5.28 thf(fact_266_diff__self,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ A @ A )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % diff_self
% 5.07/5.28 thf(fact_267_diff__self,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( minus_minus_int @ A @ A )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % diff_self
% 5.07/5.28 thf(fact_268_diff__Suc__Suc,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.07/5.28 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_Suc_Suc
% 5.07/5.28 thf(fact_269_Suc__diff__diff,axiom,
% 5.07/5.28 ! [M2: nat,N: nat,K: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K ) )
% 5.07/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_diff_diff
% 5.07/5.28 thf(fact_270_diff__self__eq__0,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ M2 @ M2 )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % diff_self_eq_0
% 5.07/5.28 thf(fact_271_diff__0__eq__0,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0_eq_0
% 5.07/5.28 thf(fact_272_diff__gt__0__iff__gt,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.07/5.28 = ( ord_less_real @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_gt_0_iff_gt
% 5.07/5.28 thf(fact_273_diff__gt__0__iff__gt,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.07/5.28 = ( ord_less_rat @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_gt_0_iff_gt
% 5.07/5.28 thf(fact_274_diff__gt__0__iff__gt,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.07/5.28 = ( ord_less_int @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_gt_0_iff_gt
% 5.07/5.28 thf(fact_275_diff__numeral__special_I9_J,axiom,
% 5.07/5.28 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(9)
% 5.07/5.28 thf(fact_276_diff__numeral__special_I9_J,axiom,
% 5.07/5.28 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(9)
% 5.07/5.28 thf(fact_277_diff__numeral__special_I9_J,axiom,
% 5.07/5.28 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(9)
% 5.07/5.28 thf(fact_278_diff__numeral__special_I9_J,axiom,
% 5.07/5.28 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(9)
% 5.07/5.28 thf(fact_279_zero__less__diff,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 5.07/5.28 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_less_diff
% 5.07/5.28 thf(fact_280_diff__Suc__1,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.07/5.28 = N ) ).
% 5.07/5.28
% 5.07/5.28 % diff_Suc_1
% 5.07/5.28 thf(fact_281_Suc__pred,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.07/5.28 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_pred
% 5.07/5.28 thf(fact_282_int__int__eq,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.07/5.28 = ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( M2 = N ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_int_eq
% 5.07/5.28 thf(fact_283_diff__eq__diff__eq,axiom,
% 5.07/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.07/5.28 ( ( ( minus_minus_rat @ A @ B )
% 5.07/5.28 = ( minus_minus_rat @ C @ D ) )
% 5.07/5.28 => ( ( A = B )
% 5.07/5.28 = ( C = D ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_eq_diff_eq
% 5.07/5.28 thf(fact_284_diff__eq__diff__eq,axiom,
% 5.07/5.28 ! [A: int,B: int,C: int,D: int] :
% 5.07/5.28 ( ( ( minus_minus_int @ A @ B )
% 5.07/5.28 = ( minus_minus_int @ C @ D ) )
% 5.07/5.28 => ( ( A = B )
% 5.07/5.28 = ( C = D ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_eq_diff_eq
% 5.07/5.28 thf(fact_285_diff__right__commute,axiom,
% 5.07/5.28 ! [A: rat,C: rat,B: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.07/5.28 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_right_commute
% 5.07/5.28 thf(fact_286_diff__right__commute,axiom,
% 5.07/5.28 ! [A: nat,C: nat,B: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.07/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_right_commute
% 5.07/5.28 thf(fact_287_diff__right__commute,axiom,
% 5.07/5.28 ! [A: int,C: int,B: int] :
% 5.07/5.28 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.07/5.28 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_right_commute
% 5.07/5.28 thf(fact_288_diff__commute,axiom,
% 5.07/5.28 ! [I: nat,J2: nat,K: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J2 ) @ K )
% 5.07/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_commute
% 5.07/5.28 thf(fact_289_less__int__code_I1_J,axiom,
% 5.07/5.28 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % less_int_code(1)
% 5.07/5.28 thf(fact_290_eq__iff__diff__eq__0,axiom,
% 5.07/5.28 ( ( ^ [Y4: real,Z: real] : ( Y4 = Z ) )
% 5.07/5.28 = ( ^ [A3: real,B2: real] :
% 5.07/5.28 ( ( minus_minus_real @ A3 @ B2 )
% 5.07/5.28 = zero_zero_real ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % eq_iff_diff_eq_0
% 5.07/5.28 thf(fact_291_eq__iff__diff__eq__0,axiom,
% 5.07/5.28 ( ( ^ [Y4: rat,Z: rat] : ( Y4 = Z ) )
% 5.07/5.28 = ( ^ [A3: rat,B2: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ A3 @ B2 )
% 5.07/5.28 = zero_zero_rat ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % eq_iff_diff_eq_0
% 5.07/5.28 thf(fact_292_eq__iff__diff__eq__0,axiom,
% 5.07/5.28 ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 5.07/5.28 = ( ^ [A3: int,B2: int] :
% 5.07/5.28 ( ( minus_minus_int @ A3 @ B2 )
% 5.07/5.28 = zero_zero_int ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % eq_iff_diff_eq_0
% 5.07/5.28 thf(fact_293_diff__strict__right__mono,axiom,
% 5.07/5.28 ! [A: real,B: real,C: real] :
% 5.07/5.28 ( ( ord_less_real @ A @ B )
% 5.07/5.28 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_right_mono
% 5.07/5.28 thf(fact_294_diff__strict__right__mono,axiom,
% 5.07/5.28 ! [A: rat,B: rat,C: rat] :
% 5.07/5.28 ( ( ord_less_rat @ A @ B )
% 5.07/5.28 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_right_mono
% 5.07/5.28 thf(fact_295_diff__strict__right__mono,axiom,
% 5.07/5.28 ! [A: int,B: int,C: int] :
% 5.07/5.28 ( ( ord_less_int @ A @ B )
% 5.07/5.28 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_right_mono
% 5.07/5.28 thf(fact_296_diff__strict__left__mono,axiom,
% 5.07/5.28 ! [B: real,A: real,C: real] :
% 5.07/5.28 ( ( ord_less_real @ B @ A )
% 5.07/5.28 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_left_mono
% 5.07/5.28 thf(fact_297_diff__strict__left__mono,axiom,
% 5.07/5.28 ! [B: rat,A: rat,C: rat] :
% 5.07/5.28 ( ( ord_less_rat @ B @ A )
% 5.07/5.28 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_left_mono
% 5.07/5.28 thf(fact_298_diff__strict__left__mono,axiom,
% 5.07/5.28 ! [B: int,A: int,C: int] :
% 5.07/5.28 ( ( ord_less_int @ B @ A )
% 5.07/5.28 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_left_mono
% 5.07/5.28 thf(fact_299_diff__eq__diff__less,axiom,
% 5.07/5.28 ! [A: real,B: real,C: real,D: real] :
% 5.07/5.28 ( ( ( minus_minus_real @ A @ B )
% 5.07/5.28 = ( minus_minus_real @ C @ D ) )
% 5.07/5.28 => ( ( ord_less_real @ A @ B )
% 5.07/5.28 = ( ord_less_real @ C @ D ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_eq_diff_less
% 5.07/5.28 thf(fact_300_diff__eq__diff__less,axiom,
% 5.07/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.07/5.28 ( ( ( minus_minus_rat @ A @ B )
% 5.07/5.28 = ( minus_minus_rat @ C @ D ) )
% 5.07/5.28 => ( ( ord_less_rat @ A @ B )
% 5.07/5.28 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_eq_diff_less
% 5.07/5.28 thf(fact_301_diff__eq__diff__less,axiom,
% 5.07/5.28 ! [A: int,B: int,C: int,D: int] :
% 5.07/5.28 ( ( ( minus_minus_int @ A @ B )
% 5.07/5.28 = ( minus_minus_int @ C @ D ) )
% 5.07/5.28 => ( ( ord_less_int @ A @ B )
% 5.07/5.28 = ( ord_less_int @ C @ D ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_eq_diff_less
% 5.07/5.28 thf(fact_302_diff__strict__mono,axiom,
% 5.07/5.28 ! [A: real,B: real,D: real,C: real] :
% 5.07/5.28 ( ( ord_less_real @ A @ B )
% 5.07/5.28 => ( ( ord_less_real @ D @ C )
% 5.07/5.28 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_mono
% 5.07/5.28 thf(fact_303_diff__strict__mono,axiom,
% 5.07/5.28 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.07/5.28 ( ( ord_less_rat @ A @ B )
% 5.07/5.28 => ( ( ord_less_rat @ D @ C )
% 5.07/5.28 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_mono
% 5.07/5.28 thf(fact_304_diff__strict__mono,axiom,
% 5.07/5.28 ! [A: int,B: int,D: int,C: int] :
% 5.07/5.28 ( ( ord_less_int @ A @ B )
% 5.07/5.28 => ( ( ord_less_int @ D @ C )
% 5.07/5.28 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_strict_mono
% 5.07/5.28 thf(fact_305_zero__induct__lemma,axiom,
% 5.07/5.28 ! [P: nat > $o,K: nat,I: nat] :
% 5.07/5.28 ( ( P @ K )
% 5.07/5.28 => ( ! [N2: nat] :
% 5.07/5.28 ( ( P @ ( suc @ N2 ) )
% 5.07/5.28 => ( P @ N2 ) )
% 5.07/5.28 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_induct_lemma
% 5.07/5.28 thf(fact_306_diffs0__imp__equal,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( ( minus_minus_nat @ M2 @ N )
% 5.07/5.28 = zero_zero_nat )
% 5.07/5.28 => ( ( ( minus_minus_nat @ N @ M2 )
% 5.07/5.28 = zero_zero_nat )
% 5.07/5.28 => ( M2 = N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diffs0_imp_equal
% 5.07/5.28 thf(fact_307_minus__nat_Odiff__0,axiom,
% 5.07/5.28 ! [M2: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 5.07/5.28 = M2 ) ).
% 5.07/5.28
% 5.07/5.28 % minus_nat.diff_0
% 5.07/5.28 thf(fact_308_less__imp__diff__less,axiom,
% 5.07/5.28 ! [J2: nat,K: nat,N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ J2 @ K )
% 5.07/5.28 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_imp_diff_less
% 5.07/5.28 thf(fact_309_diff__less__mono2,axiom,
% 5.07/5.28 ! [M2: nat,N: nat,L: nat] :
% 5.07/5.28 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.28 => ( ( ord_less_nat @ M2 @ L )
% 5.07/5.28 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_less_mono2
% 5.07/5.28 thf(fact_310_less__iff__diff__less__0,axiom,
% 5.07/5.28 ( ord_less_real
% 5.07/5.28 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_iff_diff_less_0
% 5.07/5.28 thf(fact_311_less__iff__diff__less__0,axiom,
% 5.07/5.28 ( ord_less_rat
% 5.07/5.28 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_iff_diff_less_0
% 5.07/5.28 thf(fact_312_less__iff__diff__less__0,axiom,
% 5.07/5.28 ( ord_less_int
% 5.07/5.28 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_iff_diff_less_0
% 5.07/5.28 thf(fact_313_Suc__diff__Suc,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ N @ M2 )
% 5.07/5.28 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 5.07/5.28 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_diff_Suc
% 5.07/5.28 thf(fact_314_diff__less__Suc,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_less_Suc
% 5.07/5.28 thf(fact_315_diff__less,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.07/5.28 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_less
% 5.07/5.28 thf(fact_316_diff__Suc__eq__diff__pred,axiom,
% 5.07/5.28 ! [M2: nat,N: nat] :
% 5.07/5.28 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 5.07/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_Suc_eq_diff_pred
% 5.07/5.28 thf(fact_317_diff__Suc__less,axiom,
% 5.07/5.28 ! [N: nat,I: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_Suc_less
% 5.07/5.28 thf(fact_318_linorder__neqE__linordered__idom,axiom,
% 5.07/5.28 ! [X: real,Y: real] :
% 5.07/5.28 ( ( X != Y )
% 5.07/5.28 => ( ~ ( ord_less_real @ X @ Y )
% 5.07/5.28 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % linorder_neqE_linordered_idom
% 5.07/5.28 thf(fact_319_linorder__neqE__linordered__idom,axiom,
% 5.07/5.28 ! [X: rat,Y: rat] :
% 5.07/5.28 ( ( X != Y )
% 5.07/5.28 => ( ~ ( ord_less_rat @ X @ Y )
% 5.07/5.28 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % linorder_neqE_linordered_idom
% 5.07/5.28 thf(fact_320_linorder__neqE__linordered__idom,axiom,
% 5.07/5.28 ! [X: int,Y: int] :
% 5.07/5.28 ( ( X != Y )
% 5.07/5.28 => ( ~ ( ord_less_int @ X @ Y )
% 5.07/5.28 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % linorder_neqE_linordered_idom
% 5.07/5.28 thf(fact_321_Suc__diff__eq__diff__pred,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 5.07/5.28 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_diff_eq_diff_pred
% 5.07/5.28 thf(fact_322_Suc__pred_H,axiom,
% 5.07/5.28 ! [N: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.28 => ( N
% 5.07/5.28 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % Suc_pred'
% 5.07/5.28 thf(fact_323_artanh__0,axiom,
% 5.07/5.28 ( ( artanh_real @ zero_zero_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % artanh_0
% 5.07/5.28 thf(fact_324_arsinh__0,axiom,
% 5.07/5.28 ( ( arsinh_real @ zero_zero_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % arsinh_0
% 5.07/5.28 thf(fact_325_nat__int__comparison_I2_J,axiom,
% 5.07/5.28 ( ord_less_nat
% 5.07/5.28 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_int_comparison(2)
% 5.07/5.28 thf(fact_326_int__ops_I1_J,axiom,
% 5.07/5.28 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % int_ops(1)
% 5.07/5.28 thf(fact_327_option_Osize_I3_J,axiom,
% 5.07/5.28 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.07/5.28 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % option.size(3)
% 5.07/5.28 thf(fact_328_option_Osize_I3_J,axiom,
% 5.07/5.28 ( ( size_size_option_num @ none_num )
% 5.07/5.28 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % option.size(3)
% 5.07/5.28 thf(fact_329_ln__one,axiom,
% 5.07/5.28 ( ( ln_ln_real @ one_one_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % ln_one
% 5.07/5.28 thf(fact_330_int__ops_I2_J,axiom,
% 5.07/5.28 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.07/5.28 = one_one_int ) ).
% 5.07/5.28
% 5.07/5.28 % int_ops(2)
% 5.07/5.28 thf(fact_331_neg__int__cases,axiom,
% 5.07/5.28 ! [K: int] :
% 5.07/5.28 ( ( ord_less_int @ K @ zero_zero_int )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( ( K
% 5.07/5.28 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.07/5.28 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_int_cases
% 5.07/5.28 thf(fact_332_nat__approx__posE,axiom,
% 5.07/5.28 ! [E2: real] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_approx_posE
% 5.07/5.28 thf(fact_333_nat__approx__posE,axiom,
% 5.07/5.28 ! [E2: rat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % nat_approx_posE
% 5.07/5.28 thf(fact_334_neg__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ( uminus_uminus_int @ A )
% 5.07/5.28 = ( uminus_uminus_int @ B ) )
% 5.07/5.28 = ( A = B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_iff_equal
% 5.07/5.28 thf(fact_335_neg__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ( uminus_uminus_real @ A )
% 5.07/5.28 = ( uminus_uminus_real @ B ) )
% 5.07/5.28 = ( A = B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_iff_equal
% 5.07/5.28 thf(fact_336_neg__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: complex,B: complex] :
% 5.07/5.28 ( ( ( uminus1482373934393186551omplex @ A )
% 5.07/5.28 = ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.28 = ( A = B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_iff_equal
% 5.07/5.28 thf(fact_337_neg__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( ( uminus1351360451143612070nteger @ A )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.28 = ( A = B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_iff_equal
% 5.07/5.28 thf(fact_338_neg__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ( uminus_uminus_rat @ A )
% 5.07/5.28 = ( uminus_uminus_rat @ B ) )
% 5.07/5.28 = ( A = B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_iff_equal
% 5.07/5.28 thf(fact_339_add_Oinverse__inverse,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_inverse
% 5.07/5.28 thf(fact_340_add_Oinverse__inverse,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_inverse
% 5.07/5.28 thf(fact_341_add_Oinverse__inverse,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_inverse
% 5.07/5.28 thf(fact_342_add_Oinverse__inverse,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_inverse
% 5.07/5.28 thf(fact_343_add_Oinverse__inverse,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_inverse
% 5.07/5.28 thf(fact_344_verit__minus__simplify_I4_J,axiom,
% 5.07/5.28 ! [B: int] :
% 5.07/5.28 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 5.07/5.28 = B ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(4)
% 5.07/5.28 thf(fact_345_verit__minus__simplify_I4_J,axiom,
% 5.07/5.28 ! [B: real] :
% 5.07/5.28 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 5.07/5.28 = B ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(4)
% 5.07/5.28 thf(fact_346_verit__minus__simplify_I4_J,axiom,
% 5.07/5.28 ! [B: complex] :
% 5.07/5.28 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.28 = B ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(4)
% 5.07/5.28 thf(fact_347_verit__minus__simplify_I4_J,axiom,
% 5.07/5.28 ! [B: code_integer] :
% 5.07/5.28 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.28 = B ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(4)
% 5.07/5.28 thf(fact_348_verit__minus__simplify_I4_J,axiom,
% 5.07/5.28 ! [B: rat] :
% 5.07/5.28 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 5.07/5.28 = B ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(4)
% 5.07/5.28 thf(fact_349_div__0,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % div_0
% 5.07/5.28 thf(fact_350_div__0,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % div_0
% 5.07/5.28 thf(fact_351_div__0,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % div_0
% 5.07/5.28 thf(fact_352_div__0,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % div_0
% 5.07/5.28 thf(fact_353_div__0,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % div_0
% 5.07/5.28 thf(fact_354_div__by__0,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_0
% 5.07/5.28 thf(fact_355_div__by__0,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_0
% 5.07/5.28 thf(fact_356_div__by__0,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_0
% 5.07/5.28 thf(fact_357_div__by__0,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.07/5.28 = zero_zero_nat ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_0
% 5.07/5.28 thf(fact_358_div__by__0,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_0
% 5.07/5.28 thf(fact_359_add_Oinverse__neutral,axiom,
% 5.07/5.28 ( ( uminus_uminus_int @ zero_zero_int )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_neutral
% 5.07/5.28 thf(fact_360_add_Oinverse__neutral,axiom,
% 5.07/5.28 ( ( uminus_uminus_real @ zero_zero_real )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_neutral
% 5.07/5.28 thf(fact_361_add_Oinverse__neutral,axiom,
% 5.07/5.28 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_neutral
% 5.07/5.28 thf(fact_362_add_Oinverse__neutral,axiom,
% 5.07/5.28 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.07/5.28 = zero_z3403309356797280102nteger ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_neutral
% 5.07/5.28 thf(fact_363_add_Oinverse__neutral,axiom,
% 5.07/5.28 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % add.inverse_neutral
% 5.07/5.28 thf(fact_364_neg__0__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( zero_zero_int
% 5.07/5.28 = ( uminus_uminus_int @ A ) )
% 5.07/5.28 = ( zero_zero_int = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_equal_iff_equal
% 5.07/5.28 thf(fact_365_neg__0__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( zero_zero_real
% 5.07/5.28 = ( uminus_uminus_real @ A ) )
% 5.07/5.28 = ( zero_zero_real = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_equal_iff_equal
% 5.07/5.28 thf(fact_366_neg__0__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( zero_zero_complex
% 5.07/5.28 = ( uminus1482373934393186551omplex @ A ) )
% 5.07/5.28 = ( zero_zero_complex = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_equal_iff_equal
% 5.07/5.28 thf(fact_367_neg__0__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( zero_z3403309356797280102nteger
% 5.07/5.28 = ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_equal_iff_equal
% 5.07/5.28 thf(fact_368_neg__0__equal__iff__equal,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( zero_zero_rat
% 5.07/5.28 = ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = ( zero_zero_rat = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_equal_iff_equal
% 5.07/5.28 thf(fact_369_neg__equal__0__iff__equal,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ( uminus_uminus_int @ A )
% 5.07/5.28 = zero_zero_int )
% 5.07/5.28 = ( A = zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_0_iff_equal
% 5.07/5.28 thf(fact_370_neg__equal__0__iff__equal,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ( uminus_uminus_real @ A )
% 5.07/5.28 = zero_zero_real )
% 5.07/5.28 = ( A = zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_0_iff_equal
% 5.07/5.28 thf(fact_371_neg__equal__0__iff__equal,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( ( uminus1482373934393186551omplex @ A )
% 5.07/5.28 = zero_zero_complex )
% 5.07/5.28 = ( A = zero_zero_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_0_iff_equal
% 5.07/5.28 thf(fact_372_neg__equal__0__iff__equal,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ( uminus1351360451143612070nteger @ A )
% 5.07/5.28 = zero_z3403309356797280102nteger )
% 5.07/5.28 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_0_iff_equal
% 5.07/5.28 thf(fact_373_neg__equal__0__iff__equal,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ( uminus_uminus_rat @ A )
% 5.07/5.28 = zero_zero_rat )
% 5.07/5.28 = ( A = zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_0_iff_equal
% 5.07/5.28 thf(fact_374_equal__neg__zero,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_int @ A ) )
% 5.07/5.28 = ( A = zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % equal_neg_zero
% 5.07/5.28 thf(fact_375_equal__neg__zero,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_real @ A ) )
% 5.07/5.28 = ( A = zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % equal_neg_zero
% 5.07/5.28 thf(fact_376_equal__neg__zero,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.07/5.28
% 5.07/5.28 % equal_neg_zero
% 5.07/5.28 thf(fact_377_equal__neg__zero,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = ( A = zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % equal_neg_zero
% 5.07/5.28 thf(fact_378_neg__equal__zero,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ( uminus_uminus_int @ A )
% 5.07/5.28 = A )
% 5.07/5.28 = ( A = zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_zero
% 5.07/5.28 thf(fact_379_neg__equal__zero,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ( uminus_uminus_real @ A )
% 5.07/5.28 = A )
% 5.07/5.28 = ( A = zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_zero
% 5.07/5.28 thf(fact_380_neg__equal__zero,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ( uminus1351360451143612070nteger @ A )
% 5.07/5.28 = A )
% 5.07/5.28 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_zero
% 5.07/5.28 thf(fact_381_neg__equal__zero,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ( uminus_uminus_rat @ A )
% 5.07/5.28 = A )
% 5.07/5.28 = ( A = zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_equal_zero
% 5.07/5.28 thf(fact_382_neg__less__iff__less,axiom,
% 5.07/5.28 ! [B: int,A: int] :
% 5.07/5.28 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.07/5.28 = ( ord_less_int @ A @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_iff_less
% 5.07/5.28 thf(fact_383_neg__less__iff__less,axiom,
% 5.07/5.28 ! [B: real,A: real] :
% 5.07/5.28 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.07/5.28 = ( ord_less_real @ A @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_iff_less
% 5.07/5.28 thf(fact_384_neg__less__iff__less,axiom,
% 5.07/5.28 ! [B: code_integer,A: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_iff_less
% 5.07/5.28 thf(fact_385_neg__less__iff__less,axiom,
% 5.07/5.28 ! [B: rat,A: rat] :
% 5.07/5.28 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = ( ord_less_rat @ A @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_iff_less
% 5.07/5.28 thf(fact_386_div__by__1,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_1
% 5.07/5.28 thf(fact_387_div__by__1,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( divide_divide_real @ A @ one_one_real )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_1
% 5.07/5.28 thf(fact_388_div__by__1,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_1
% 5.07/5.28 thf(fact_389_div__by__1,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_1
% 5.07/5.28 thf(fact_390_div__by__1,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( divide_divide_int @ A @ one_one_int )
% 5.07/5.28 = A ) ).
% 5.07/5.28
% 5.07/5.28 % div_by_1
% 5.07/5.28 thf(fact_391_minus__diff__eq,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.07/5.28 = ( minus_minus_int @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_eq
% 5.07/5.28 thf(fact_392_minus__diff__eq,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.07/5.28 = ( minus_minus_real @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_eq
% 5.07/5.28 thf(fact_393_minus__diff__eq,axiom,
% 5.07/5.28 ! [A: complex,B: complex] :
% 5.07/5.28 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.07/5.28 = ( minus_minus_complex @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_eq
% 5.07/5.28 thf(fact_394_minus__diff__eq,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.07/5.28 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_eq
% 5.07/5.28 thf(fact_395_minus__diff__eq,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.07/5.28 = ( minus_minus_rat @ B @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_eq
% 5.07/5.28 thf(fact_396_less__neg__neg,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.07/5.28 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_neg_neg
% 5.07/5.28 thf(fact_397_less__neg__neg,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.07/5.28 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_neg_neg
% 5.07/5.28 thf(fact_398_less__neg__neg,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_neg_neg
% 5.07/5.28 thf(fact_399_less__neg__neg,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_neg_neg
% 5.07/5.28 thf(fact_400_neg__less__pos,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.07/5.28 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_pos
% 5.07/5.28 thf(fact_401_neg__less__pos,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.07/5.28 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_pos
% 5.07/5.28 thf(fact_402_neg__less__pos,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_pos
% 5.07/5.28 thf(fact_403_neg__less__pos,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.07/5.28 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_pos
% 5.07/5.28 thf(fact_404_neg__0__less__iff__less,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.07/5.28 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_less_iff_less
% 5.07/5.28 thf(fact_405_neg__0__less__iff__less,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.07/5.28 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_less_iff_less
% 5.07/5.28 thf(fact_406_neg__0__less__iff__less,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_less_iff_less
% 5.07/5.28 thf(fact_407_neg__0__less__iff__less,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.07/5.28 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_0_less_iff_less
% 5.07/5.28 thf(fact_408_neg__less__0__iff__less,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.07/5.28 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_0_iff_less
% 5.07/5.28 thf(fact_409_neg__less__0__iff__less,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.07/5.28 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_0_iff_less
% 5.07/5.28 thf(fact_410_neg__less__0__iff__less,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_0_iff_less
% 5.07/5.28 thf(fact_411_neg__less__0__iff__less,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.07/5.28 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % neg_less_0_iff_less
% 5.07/5.28 thf(fact_412_div__self,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( A != zero_zero_complex )
% 5.07/5.28 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.07/5.28 = one_one_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % div_self
% 5.07/5.28 thf(fact_413_div__self,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( A != zero_zero_real )
% 5.07/5.28 => ( ( divide_divide_real @ A @ A )
% 5.07/5.28 = one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % div_self
% 5.07/5.28 thf(fact_414_div__self,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( A != zero_zero_rat )
% 5.07/5.28 => ( ( divide_divide_rat @ A @ A )
% 5.07/5.28 = one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % div_self
% 5.07/5.28 thf(fact_415_div__self,axiom,
% 5.07/5.28 ! [A: nat] :
% 5.07/5.28 ( ( A != zero_zero_nat )
% 5.07/5.28 => ( ( divide_divide_nat @ A @ A )
% 5.07/5.28 = one_one_nat ) ) ).
% 5.07/5.28
% 5.07/5.28 % div_self
% 5.07/5.28 thf(fact_416_div__self,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( A != zero_zero_int )
% 5.07/5.28 => ( ( divide_divide_int @ A @ A )
% 5.07/5.28 = one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % div_self
% 5.07/5.28 thf(fact_417_verit__minus__simplify_I3_J,axiom,
% 5.07/5.28 ! [B: int] :
% 5.07/5.28 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.07/5.28 = ( uminus_uminus_int @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(3)
% 5.07/5.28 thf(fact_418_verit__minus__simplify_I3_J,axiom,
% 5.07/5.28 ! [B: real] :
% 5.07/5.28 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.07/5.28 = ( uminus_uminus_real @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(3)
% 5.07/5.28 thf(fact_419_verit__minus__simplify_I3_J,axiom,
% 5.07/5.28 ! [B: complex] :
% 5.07/5.28 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.07/5.28 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(3)
% 5.07/5.28 thf(fact_420_verit__minus__simplify_I3_J,axiom,
% 5.07/5.28 ! [B: code_integer] :
% 5.07/5.28 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(3)
% 5.07/5.28 thf(fact_421_verit__minus__simplify_I3_J,axiom,
% 5.07/5.28 ! [B: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.07/5.28 = ( uminus_uminus_rat @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_minus_simplify(3)
% 5.07/5.28 thf(fact_422_diff__0,axiom,
% 5.07/5.28 ! [A: int] :
% 5.07/5.28 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.07/5.28 = ( uminus_uminus_int @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0
% 5.07/5.28 thf(fact_423_diff__0,axiom,
% 5.07/5.28 ! [A: real] :
% 5.07/5.28 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.07/5.28 = ( uminus_uminus_real @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0
% 5.07/5.28 thf(fact_424_diff__0,axiom,
% 5.07/5.28 ! [A: complex] :
% 5.07/5.28 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.07/5.28 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0
% 5.07/5.28 thf(fact_425_diff__0,axiom,
% 5.07/5.28 ! [A: code_integer] :
% 5.07/5.28 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0
% 5.07/5.28 thf(fact_426_diff__0,axiom,
% 5.07/5.28 ! [A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.07/5.28 = ( uminus_uminus_rat @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % diff_0
% 5.07/5.28 thf(fact_427_negative__eq__positive,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.28 = ( semiri1314217659103216013at_int @ M2 ) )
% 5.07/5.28 = ( ( N = zero_zero_nat )
% 5.07/5.28 & ( M2 = zero_zero_nat ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % negative_eq_positive
% 5.07/5.28 thf(fact_428_dbl__inc__simps_I4_J,axiom,
% 5.07/5.28 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.07/5.28 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(4)
% 5.07/5.28 thf(fact_429_dbl__inc__simps_I4_J,axiom,
% 5.07/5.28 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.07/5.28 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(4)
% 5.07/5.28 thf(fact_430_dbl__inc__simps_I4_J,axiom,
% 5.07/5.28 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.07/5.28 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(4)
% 5.07/5.28 thf(fact_431_dbl__inc__simps_I4_J,axiom,
% 5.07/5.28 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(4)
% 5.07/5.28 thf(fact_432_dbl__inc__simps_I4_J,axiom,
% 5.07/5.28 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.07/5.28 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % dbl_inc_simps(4)
% 5.07/5.28 thf(fact_433_diff__numeral__special_I12_J,axiom,
% 5.07/5.28 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(12)
% 5.07/5.28 thf(fact_434_diff__numeral__special_I12_J,axiom,
% 5.07/5.28 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.07/5.28 = zero_zero_real ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(12)
% 5.07/5.28 thf(fact_435_diff__numeral__special_I12_J,axiom,
% 5.07/5.28 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.07/5.28 = zero_zero_complex ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(12)
% 5.07/5.28 thf(fact_436_diff__numeral__special_I12_J,axiom,
% 5.07/5.28 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.07/5.28 = zero_z3403309356797280102nteger ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(12)
% 5.07/5.28 thf(fact_437_diff__numeral__special_I12_J,axiom,
% 5.07/5.28 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.07/5.28 = zero_zero_rat ) ).
% 5.07/5.28
% 5.07/5.28 % diff_numeral_special(12)
% 5.07/5.28 thf(fact_438_negative__zless,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 5.07/5.28
% 5.07/5.28 % negative_zless
% 5.07/5.28 thf(fact_439_minus__equation__iff,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ( uminus_uminus_int @ A )
% 5.07/5.28 = B )
% 5.07/5.28 = ( ( uminus_uminus_int @ B )
% 5.07/5.28 = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_equation_iff
% 5.07/5.28 thf(fact_440_minus__equation__iff,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ( uminus_uminus_real @ A )
% 5.07/5.28 = B )
% 5.07/5.28 = ( ( uminus_uminus_real @ B )
% 5.07/5.28 = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_equation_iff
% 5.07/5.28 thf(fact_441_minus__equation__iff,axiom,
% 5.07/5.28 ! [A: complex,B: complex] :
% 5.07/5.28 ( ( ( uminus1482373934393186551omplex @ A )
% 5.07/5.28 = B )
% 5.07/5.28 = ( ( uminus1482373934393186551omplex @ B )
% 5.07/5.28 = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_equation_iff
% 5.07/5.28 thf(fact_442_minus__equation__iff,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( ( uminus1351360451143612070nteger @ A )
% 5.07/5.28 = B )
% 5.07/5.28 = ( ( uminus1351360451143612070nteger @ B )
% 5.07/5.28 = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_equation_iff
% 5.07/5.28 thf(fact_443_minus__equation__iff,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ( uminus_uminus_rat @ A )
% 5.07/5.28 = B )
% 5.07/5.28 = ( ( uminus_uminus_rat @ B )
% 5.07/5.28 = A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_equation_iff
% 5.07/5.28 thf(fact_444_equation__minus__iff,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_int @ B ) )
% 5.07/5.28 = ( B
% 5.07/5.28 = ( uminus_uminus_int @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % equation_minus_iff
% 5.07/5.28 thf(fact_445_equation__minus__iff,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_real @ B ) )
% 5.07/5.28 = ( B
% 5.07/5.28 = ( uminus_uminus_real @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % equation_minus_iff
% 5.07/5.28 thf(fact_446_equation__minus__iff,axiom,
% 5.07/5.28 ! [A: complex,B: complex] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.28 = ( B
% 5.07/5.28 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % equation_minus_iff
% 5.07/5.28 thf(fact_447_equation__minus__iff,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.28 = ( B
% 5.07/5.28 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % equation_minus_iff
% 5.07/5.28 thf(fact_448_equation__minus__iff,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( A
% 5.07/5.28 = ( uminus_uminus_rat @ B ) )
% 5.07/5.28 = ( B
% 5.07/5.28 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % equation_minus_iff
% 5.07/5.28 thf(fact_449_verit__negate__coefficient_I3_J,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( A = B )
% 5.07/5.28 => ( ( uminus_uminus_int @ A )
% 5.07/5.28 = ( uminus_uminus_int @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(3)
% 5.07/5.28 thf(fact_450_verit__negate__coefficient_I3_J,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( A = B )
% 5.07/5.28 => ( ( uminus_uminus_real @ A )
% 5.07/5.28 = ( uminus_uminus_real @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(3)
% 5.07/5.28 thf(fact_451_verit__negate__coefficient_I3_J,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( A = B )
% 5.07/5.28 => ( ( uminus1351360451143612070nteger @ A )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(3)
% 5.07/5.28 thf(fact_452_verit__negate__coefficient_I3_J,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( A = B )
% 5.07/5.28 => ( ( uminus_uminus_rat @ A )
% 5.07/5.28 = ( uminus_uminus_rat @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(3)
% 5.07/5.28 thf(fact_453_minus__int__code_I2_J,axiom,
% 5.07/5.28 ! [L: int] :
% 5.07/5.28 ( ( minus_minus_int @ zero_zero_int @ L )
% 5.07/5.28 = ( uminus_uminus_int @ L ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_int_code(2)
% 5.07/5.28 thf(fact_454_verit__negate__coefficient_I2_J,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ord_less_int @ A @ B )
% 5.07/5.28 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(2)
% 5.07/5.28 thf(fact_455_verit__negate__coefficient_I2_J,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ord_less_real @ A @ B )
% 5.07/5.28 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(2)
% 5.07/5.28 thf(fact_456_verit__negate__coefficient_I2_J,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.07/5.28 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(2)
% 5.07/5.28 thf(fact_457_verit__negate__coefficient_I2_J,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ord_less_rat @ A @ B )
% 5.07/5.28 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % verit_negate_coefficient(2)
% 5.07/5.28 thf(fact_458_less__minus__iff,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.28 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_iff
% 5.07/5.28 thf(fact_459_less__minus__iff,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.07/5.28 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_iff
% 5.07/5.28 thf(fact_460_less__minus__iff,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_iff
% 5.07/5.28 thf(fact_461_less__minus__iff,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.07/5.28 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_iff
% 5.07/5.28 thf(fact_462_minus__less__iff,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.07/5.28 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_less_iff
% 5.07/5.28 thf(fact_463_minus__less__iff,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.07/5.28 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_less_iff
% 5.07/5.28 thf(fact_464_minus__less__iff,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.07/5.28 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_less_iff
% 5.07/5.28 thf(fact_465_minus__less__iff,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.07/5.28 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_less_iff
% 5.07/5.28 thf(fact_466_one__neq__neg__one,axiom,
% 5.07/5.28 ( one_one_int
% 5.07/5.28 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_neq_neg_one
% 5.07/5.28 thf(fact_467_one__neq__neg__one,axiom,
% 5.07/5.28 ( one_one_real
% 5.07/5.28 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_neq_neg_one
% 5.07/5.28 thf(fact_468_one__neq__neg__one,axiom,
% 5.07/5.28 ( one_one_complex
% 5.07/5.28 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_neq_neg_one
% 5.07/5.28 thf(fact_469_one__neq__neg__one,axiom,
% 5.07/5.28 ( one_one_Code_integer
% 5.07/5.28 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_neq_neg_one
% 5.07/5.28 thf(fact_470_one__neq__neg__one,axiom,
% 5.07/5.28 ( one_one_rat
% 5.07/5.28 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % one_neq_neg_one
% 5.07/5.28 thf(fact_471_minus__diff__commute,axiom,
% 5.07/5.28 ! [B: int,A: int] :
% 5.07/5.28 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.07/5.28 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_commute
% 5.07/5.28 thf(fact_472_minus__diff__commute,axiom,
% 5.07/5.28 ! [B: real,A: real] :
% 5.07/5.28 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.07/5.28 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_commute
% 5.07/5.28 thf(fact_473_minus__diff__commute,axiom,
% 5.07/5.28 ! [B: complex,A: complex] :
% 5.07/5.28 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.07/5.28 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_commute
% 5.07/5.28 thf(fact_474_minus__diff__commute,axiom,
% 5.07/5.28 ! [B: code_integer,A: code_integer] :
% 5.07/5.28 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.07/5.28 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_commute
% 5.07/5.28 thf(fact_475_minus__diff__commute,axiom,
% 5.07/5.28 ! [B: rat,A: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.07/5.28 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_commute
% 5.07/5.28 thf(fact_476_minus__diff__minus,axiom,
% 5.07/5.28 ! [A: int,B: int] :
% 5.07/5.28 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.07/5.28 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_minus
% 5.07/5.28 thf(fact_477_minus__diff__minus,axiom,
% 5.07/5.28 ! [A: real,B: real] :
% 5.07/5.28 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.07/5.28 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_minus
% 5.07/5.28 thf(fact_478_minus__diff__minus,axiom,
% 5.07/5.28 ! [A: complex,B: complex] :
% 5.07/5.28 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.28 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_minus
% 5.07/5.28 thf(fact_479_minus__diff__minus,axiom,
% 5.07/5.28 ! [A: code_integer,B: code_integer] :
% 5.07/5.28 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.28 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_minus
% 5.07/5.28 thf(fact_480_minus__diff__minus,axiom,
% 5.07/5.28 ! [A: rat,B: rat] :
% 5.07/5.28 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.07/5.28 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % minus_diff_minus
% 5.07/5.28 thf(fact_481_minus__int__code_I1_J,axiom,
% 5.07/5.28 ! [K: int] :
% 5.07/5.28 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.07/5.28 = K ) ).
% 5.07/5.28
% 5.07/5.28 % minus_int_code(1)
% 5.07/5.28 thf(fact_482_uminus__int__code_I1_J,axiom,
% 5.07/5.28 ( ( uminus_uminus_int @ zero_zero_int )
% 5.07/5.28 = zero_zero_int ) ).
% 5.07/5.28
% 5.07/5.28 % uminus_int_code(1)
% 5.07/5.28 thf(fact_483_int__less__induct,axiom,
% 5.07/5.28 ! [I: int,K: int,P: int > $o] :
% 5.07/5.28 ( ( ord_less_int @ I @ K )
% 5.07/5.28 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.07/5.28 => ( ! [I3: int] :
% 5.07/5.28 ( ( ord_less_int @ I3 @ K )
% 5.07/5.28 => ( ( P @ I3 )
% 5.07/5.28 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.07/5.28 => ( P @ I ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_less_induct
% 5.07/5.28 thf(fact_484_int__diff__cases,axiom,
% 5.07/5.28 ! [Z2: int] :
% 5.07/5.28 ~ ! [M3: nat,N2: nat] :
% 5.07/5.28 ( Z2
% 5.07/5.28 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_diff_cases
% 5.07/5.28 thf(fact_485_int__cases2,axiom,
% 5.07/5.28 ! [Z2: int] :
% 5.07/5.28 ( ! [N2: nat] :
% 5.07/5.28 ( Z2
% 5.07/5.28 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( Z2
% 5.07/5.28 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_cases2
% 5.07/5.28 thf(fact_486_zero__neq__neg__one,axiom,
% 5.07/5.28 ( zero_zero_int
% 5.07/5.28 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_neg_one
% 5.07/5.28 thf(fact_487_zero__neq__neg__one,axiom,
% 5.07/5.28 ( zero_zero_real
% 5.07/5.28 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_neg_one
% 5.07/5.28 thf(fact_488_zero__neq__neg__one,axiom,
% 5.07/5.28 ( zero_zero_complex
% 5.07/5.28 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_neg_one
% 5.07/5.28 thf(fact_489_zero__neq__neg__one,axiom,
% 5.07/5.28 ( zero_z3403309356797280102nteger
% 5.07/5.28 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_neg_one
% 5.07/5.28 thf(fact_490_zero__neq__neg__one,axiom,
% 5.07/5.28 ( zero_zero_rat
% 5.07/5.28 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % zero_neq_neg_one
% 5.07/5.28 thf(fact_491_less__minus__one__simps_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(4)
% 5.07/5.28 thf(fact_492_less__minus__one__simps_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(4)
% 5.07/5.28 thf(fact_493_less__minus__one__simps_I4_J,axiom,
% 5.07/5.28 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(4)
% 5.07/5.28 thf(fact_494_less__minus__one__simps_I4_J,axiom,
% 5.07/5.28 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(4)
% 5.07/5.28 thf(fact_495_less__minus__one__simps_I2_J,axiom,
% 5.07/5.28 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(2)
% 5.07/5.28 thf(fact_496_less__minus__one__simps_I2_J,axiom,
% 5.07/5.28 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(2)
% 5.07/5.28 thf(fact_497_less__minus__one__simps_I2_J,axiom,
% 5.07/5.28 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(2)
% 5.07/5.28 thf(fact_498_less__minus__one__simps_I2_J,axiom,
% 5.07/5.28 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(2)
% 5.07/5.28 thf(fact_499_int__cases,axiom,
% 5.07/5.28 ! [Z2: int] :
% 5.07/5.28 ( ! [N2: nat] :
% 5.07/5.28 ( Z2
% 5.07/5.28 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( Z2
% 5.07/5.28 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_cases
% 5.07/5.28 thf(fact_500_int__of__nat__induct,axiom,
% 5.07/5.28 ! [P: int > $o,Z2: int] :
% 5.07/5.28 ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.28 => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 5.07/5.28 => ( P @ Z2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_of_nat_induct
% 5.07/5.28 thf(fact_501_not__int__zless__negative,axiom,
% 5.07/5.28 ! [N: nat,M2: nat] :
% 5.07/5.28 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % not_int_zless_negative
% 5.07/5.28 thf(fact_502_int__ops_I6_J,axiom,
% 5.07/5.28 ! [A: nat,B: nat] :
% 5.07/5.28 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.07/5.28 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.07/5.28 = zero_zero_int ) )
% 5.07/5.28 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.07/5.28 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.07/5.28 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.07/5.28
% 5.07/5.28 % int_ops(6)
% 5.07/5.28 thf(fact_503_less__minus__one__simps_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(3)
% 5.07/5.28 thf(fact_504_less__minus__one__simps_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(3)
% 5.07/5.28 thf(fact_505_less__minus__one__simps_I3_J,axiom,
% 5.07/5.28 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(3)
% 5.07/5.28 thf(fact_506_less__minus__one__simps_I3_J,axiom,
% 5.07/5.28 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(3)
% 5.07/5.28 thf(fact_507_less__minus__one__simps_I1_J,axiom,
% 5.07/5.28 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(1)
% 5.07/5.28 thf(fact_508_less__minus__one__simps_I1_J,axiom,
% 5.07/5.28 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(1)
% 5.07/5.28 thf(fact_509_less__minus__one__simps_I1_J,axiom,
% 5.07/5.28 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(1)
% 5.07/5.28 thf(fact_510_less__minus__one__simps_I1_J,axiom,
% 5.07/5.28 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.07/5.28
% 5.07/5.28 % less_minus_one_simps(1)
% 5.07/5.28 thf(fact_511_int__cases4,axiom,
% 5.07/5.28 ! [M2: int] :
% 5.07/5.28 ( ! [N2: nat] :
% 5.07/5.28 ( M2
% 5.07/5.28 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.28 => ~ ! [N2: nat] :
% 5.07/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.07/5.28 => ( M2
% 5.07/5.29 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_cases4
% 5.07/5.29 thf(fact_512_verit__comp__simplify1_I1_J,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ~ ( ord_less_real @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(1)
% 5.07/5.29 thf(fact_513_verit__comp__simplify1_I1_J,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ~ ( ord_less_rat @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(1)
% 5.07/5.29 thf(fact_514_verit__comp__simplify1_I1_J,axiom,
% 5.07/5.29 ! [A: num] :
% 5.07/5.29 ~ ( ord_less_num @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(1)
% 5.07/5.29 thf(fact_515_verit__comp__simplify1_I1_J,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ~ ( ord_less_nat @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(1)
% 5.07/5.29 thf(fact_516_verit__comp__simplify1_I1_J,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ~ ( ord_less_int @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(1)
% 5.07/5.29 thf(fact_517_int__if,axiom,
% 5.07/5.29 ! [P: $o,A: nat,B: nat] :
% 5.07/5.29 ( ( P
% 5.07/5.29 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.07/5.29 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.07/5.29 & ( ~ P
% 5.07/5.29 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.07/5.29 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_if
% 5.07/5.29 thf(fact_518_nat__int__comparison_I1_J,axiom,
% 5.07/5.29 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 5.07/5.29 = ( ^ [A3: nat,B2: nat] :
% 5.07/5.29 ( ( semiri1314217659103216013at_int @ A3 )
% 5.07/5.29 = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_int_comparison(1)
% 5.07/5.29 thf(fact_519_int__cases3,axiom,
% 5.07/5.29 ! [K: int] :
% 5.07/5.29 ( ( K != zero_zero_int )
% 5.07/5.29 => ( ! [N2: nat] :
% 5.07/5.29 ( ( K
% 5.07/5.29 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.07/5.29 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.07/5.29 => ~ ! [N2: nat] :
% 5.07/5.29 ( ( K
% 5.07/5.29 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.07/5.29 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_cases3
% 5.07/5.29 thf(fact_520_negD,axiom,
% 5.07/5.29 ! [X: int] :
% 5.07/5.29 ( ( ord_less_int @ X @ zero_zero_int )
% 5.07/5.29 => ? [N2: nat] :
% 5.07/5.29 ( X
% 5.07/5.29 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % negD
% 5.07/5.29 thf(fact_521_negative__zless__0,axiom,
% 5.07/5.29 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % negative_zless_0
% 5.07/5.29 thf(fact_522_divide__less__0__1__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.07/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_0_1_iff
% 5.07/5.29 thf(fact_523_divide__less__0__1__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.07/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_0_1_iff
% 5.07/5.29 thf(fact_524_divide__less__eq__1__neg,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.07/5.29 = ( ord_less_real @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1_neg
% 5.07/5.29 thf(fact_525_divide__less__eq__1__neg,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.07/5.29 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1_neg
% 5.07/5.29 thf(fact_526_divide__less__eq__1__pos,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.07/5.29 = ( ord_less_real @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1_pos
% 5.07/5.29 thf(fact_527_divide__less__eq__1__pos,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.07/5.29 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1_pos
% 5.07/5.29 thf(fact_528_less__divide__eq__1__neg,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ord_less_real @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1_neg
% 5.07/5.29 thf(fact_529_less__divide__eq__1__neg,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1_neg
% 5.07/5.29 thf(fact_530_less__divide__eq__1__pos,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ord_less_real @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1_pos
% 5.07/5.29 thf(fact_531_less__divide__eq__1__pos,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1_pos
% 5.07/5.29 thf(fact_532_zero__less__divide__1__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.07/5.29 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_less_divide_1_iff
% 5.07/5.29 thf(fact_533_zero__less__divide__1__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.07/5.29 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_less_divide_1_iff
% 5.07/5.29 thf(fact_534_divide__minus1,axiom,
% 5.07/5.29 ! [X: real] :
% 5.07/5.29 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.07/5.29 = ( uminus_uminus_real @ X ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_minus1
% 5.07/5.29 thf(fact_535_divide__minus1,axiom,
% 5.07/5.29 ! [X: complex] :
% 5.07/5.29 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.07/5.29 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_minus1
% 5.07/5.29 thf(fact_536_divide__minus1,axiom,
% 5.07/5.29 ! [X: rat] :
% 5.07/5.29 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.07/5.29 = ( uminus_uminus_rat @ X ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_minus1
% 5.07/5.29 thf(fact_537_div__minus1__right,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.07/5.29 = ( uminus_uminus_int @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus1_right
% 5.07/5.29 thf(fact_538_div__minus1__right,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.07/5.29 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus1_right
% 5.07/5.29 thf(fact_539_divide__eq__1__iff,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.07/5.29 = one_one_complex )
% 5.07/5.29 = ( ( B != zero_zero_complex )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_1_iff
% 5.07/5.29 thf(fact_540_divide__eq__1__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ A @ B )
% 5.07/5.29 = one_one_real )
% 5.07/5.29 = ( ( B != zero_zero_real )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_1_iff
% 5.07/5.29 thf(fact_541_divide__eq__1__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ A @ B )
% 5.07/5.29 = one_one_rat )
% 5.07/5.29 = ( ( B != zero_zero_rat )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_1_iff
% 5.07/5.29 thf(fact_542_one__eq__divide__iff,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( one_one_complex
% 5.07/5.29 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.07/5.29 = ( ( B != zero_zero_complex )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_eq_divide_iff
% 5.07/5.29 thf(fact_543_one__eq__divide__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( one_one_real
% 5.07/5.29 = ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( ( B != zero_zero_real )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_eq_divide_iff
% 5.07/5.29 thf(fact_544_one__eq__divide__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( one_one_rat
% 5.07/5.29 = ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( ( B != zero_zero_rat )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_eq_divide_iff
% 5.07/5.29 thf(fact_545_divide__self,axiom,
% 5.07/5.29 ! [A: complex] :
% 5.07/5.29 ( ( A != zero_zero_complex )
% 5.07/5.29 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.07/5.29 = one_one_complex ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self
% 5.07/5.29 thf(fact_546_divide__self,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( A != zero_zero_real )
% 5.07/5.29 => ( ( divide_divide_real @ A @ A )
% 5.07/5.29 = one_one_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self
% 5.07/5.29 thf(fact_547_divide__self,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( A != zero_zero_rat )
% 5.07/5.29 => ( ( divide_divide_rat @ A @ A )
% 5.07/5.29 = one_one_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self
% 5.07/5.29 thf(fact_548_division__ring__divide__zero,axiom,
% 5.07/5.29 ! [A: complex] :
% 5.07/5.29 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.07/5.29 = zero_zero_complex ) ).
% 5.07/5.29
% 5.07/5.29 % division_ring_divide_zero
% 5.07/5.29 thf(fact_549_division__ring__divide__zero,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.07/5.29 = zero_zero_real ) ).
% 5.07/5.29
% 5.07/5.29 % division_ring_divide_zero
% 5.07/5.29 thf(fact_550_division__ring__divide__zero,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.07/5.29 = zero_zero_rat ) ).
% 5.07/5.29
% 5.07/5.29 % division_ring_divide_zero
% 5.07/5.29 thf(fact_551_divide__cancel__right,axiom,
% 5.07/5.29 ! [A: complex,C: complex,B: complex] :
% 5.07/5.29 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.07/5.29 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.07/5.29 = ( ( C = zero_zero_complex )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_right
% 5.07/5.29 thf(fact_552_divide__cancel__right,axiom,
% 5.07/5.29 ! [A: real,C: real,B: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ A @ C )
% 5.07/5.29 = ( divide_divide_real @ B @ C ) )
% 5.07/5.29 = ( ( C = zero_zero_real )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_right
% 5.07/5.29 thf(fact_553_divide__cancel__right,axiom,
% 5.07/5.29 ! [A: rat,C: rat,B: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ A @ C )
% 5.07/5.29 = ( divide_divide_rat @ B @ C ) )
% 5.07/5.29 = ( ( C = zero_zero_rat )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_right
% 5.07/5.29 thf(fact_554_divide__cancel__left,axiom,
% 5.07/5.29 ! [C: complex,A: complex,B: complex] :
% 5.07/5.29 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.07/5.29 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.07/5.29 = ( ( C = zero_zero_complex )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_left
% 5.07/5.29 thf(fact_555_divide__cancel__left,axiom,
% 5.07/5.29 ! [C: real,A: real,B: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ C @ A )
% 5.07/5.29 = ( divide_divide_real @ C @ B ) )
% 5.07/5.29 = ( ( C = zero_zero_real )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_left
% 5.07/5.29 thf(fact_556_divide__cancel__left,axiom,
% 5.07/5.29 ! [C: rat,A: rat,B: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ C @ A )
% 5.07/5.29 = ( divide_divide_rat @ C @ B ) )
% 5.07/5.29 = ( ( C = zero_zero_rat )
% 5.07/5.29 | ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_cancel_left
% 5.07/5.29 thf(fact_557_divide__eq__0__iff,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.07/5.29 = zero_zero_complex )
% 5.07/5.29 = ( ( A = zero_zero_complex )
% 5.07/5.29 | ( B = zero_zero_complex ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_0_iff
% 5.07/5.29 thf(fact_558_divide__eq__0__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ A @ B )
% 5.07/5.29 = zero_zero_real )
% 5.07/5.29 = ( ( A = zero_zero_real )
% 5.07/5.29 | ( B = zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_0_iff
% 5.07/5.29 thf(fact_559_divide__eq__0__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ A @ B )
% 5.07/5.29 = zero_zero_rat )
% 5.07/5.29 = ( ( A = zero_zero_rat )
% 5.07/5.29 | ( B = zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_0_iff
% 5.07/5.29 thf(fact_560_div__minus__minus,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( divide_divide_int @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus_minus
% 5.07/5.29 thf(fact_561_div__minus__minus,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.29 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus_minus
% 5.07/5.29 thf(fact_562_div__by__Suc__0,axiom,
% 5.07/5.29 ! [M2: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.07/5.29 = M2 ) ).
% 5.07/5.29
% 5.07/5.29 % div_by_Suc_0
% 5.07/5.29 thf(fact_563_div__less,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.29 => ( ( divide_divide_nat @ M2 @ N )
% 5.07/5.29 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_less
% 5.07/5.29 thf(fact_564_zero__eq__1__divide__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( zero_zero_real
% 5.07/5.29 = ( divide_divide_real @ one_one_real @ A ) )
% 5.07/5.29 = ( A = zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_eq_1_divide_iff
% 5.07/5.29 thf(fact_565_zero__eq__1__divide__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( zero_zero_rat
% 5.07/5.29 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.07/5.29 = ( A = zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_eq_1_divide_iff
% 5.07/5.29 thf(fact_566_one__divide__eq__0__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.07/5.29 = zero_zero_real )
% 5.07/5.29 = ( A = zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_divide_eq_0_iff
% 5.07/5.29 thf(fact_567_one__divide__eq__0__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.07/5.29 = zero_zero_rat )
% 5.07/5.29 = ( A = zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_divide_eq_0_iff
% 5.07/5.29 thf(fact_568_eq__divide__eq__1,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( one_one_real
% 5.07/5.29 = ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ( A != zero_zero_real )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % eq_divide_eq_1
% 5.07/5.29 thf(fact_569_eq__divide__eq__1,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( one_one_rat
% 5.07/5.29 = ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ( A != zero_zero_rat )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % eq_divide_eq_1
% 5.07/5.29 thf(fact_570_divide__eq__eq__1,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ B @ A )
% 5.07/5.29 = one_one_real )
% 5.07/5.29 = ( ( A != zero_zero_real )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_eq_1
% 5.07/5.29 thf(fact_571_divide__eq__eq__1,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ B @ A )
% 5.07/5.29 = one_one_rat )
% 5.07/5.29 = ( ( A != zero_zero_rat )
% 5.07/5.29 & ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_eq_1
% 5.07/5.29 thf(fact_572_divide__self__if,axiom,
% 5.07/5.29 ! [A: complex] :
% 5.07/5.29 ( ( ( A = zero_zero_complex )
% 5.07/5.29 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.07/5.29 = zero_zero_complex ) )
% 5.07/5.29 & ( ( A != zero_zero_complex )
% 5.07/5.29 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.07/5.29 = one_one_complex ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self_if
% 5.07/5.29 thf(fact_573_divide__self__if,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ( A = zero_zero_real )
% 5.07/5.29 => ( ( divide_divide_real @ A @ A )
% 5.07/5.29 = zero_zero_real ) )
% 5.07/5.29 & ( ( A != zero_zero_real )
% 5.07/5.29 => ( ( divide_divide_real @ A @ A )
% 5.07/5.29 = one_one_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self_if
% 5.07/5.29 thf(fact_574_divide__self__if,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ( A = zero_zero_rat )
% 5.07/5.29 => ( ( divide_divide_rat @ A @ A )
% 5.07/5.29 = zero_zero_rat ) )
% 5.07/5.29 & ( ( A != zero_zero_rat )
% 5.07/5.29 => ( ( divide_divide_rat @ A @ A )
% 5.07/5.29 = one_one_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_self_if
% 5.07/5.29 thf(fact_575_linordered__field__no__ub,axiom,
% 5.07/5.29 ! [X4: real] :
% 5.07/5.29 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 5.07/5.29
% 5.07/5.29 % linordered_field_no_ub
% 5.07/5.29 thf(fact_576_linordered__field__no__ub,axiom,
% 5.07/5.29 ! [X4: rat] :
% 5.07/5.29 ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 5.07/5.29
% 5.07/5.29 % linordered_field_no_ub
% 5.07/5.29 thf(fact_577_linordered__field__no__lb,axiom,
% 5.07/5.29 ! [X4: real] :
% 5.07/5.29 ? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) ).
% 5.07/5.29
% 5.07/5.29 % linordered_field_no_lb
% 5.07/5.29 thf(fact_578_linordered__field__no__lb,axiom,
% 5.07/5.29 ! [X4: rat] :
% 5.07/5.29 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X4 ) ).
% 5.07/5.29
% 5.07/5.29 % linordered_field_no_lb
% 5.07/5.29 thf(fact_579_diff__divide__distrib,axiom,
% 5.07/5.29 ! [A: complex,B: complex,C: complex] :
% 5.07/5.29 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.07/5.29 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_divide_distrib
% 5.07/5.29 thf(fact_580_diff__divide__distrib,axiom,
% 5.07/5.29 ! [A: real,B: real,C: real] :
% 5.07/5.29 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.07/5.29 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_divide_distrib
% 5.07/5.29 thf(fact_581_diff__divide__distrib,axiom,
% 5.07/5.29 ! [A: rat,B: rat,C: rat] :
% 5.07/5.29 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.07/5.29 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_divide_distrib
% 5.07/5.29 thf(fact_582_div__minus__right,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus_right
% 5.07/5.29 thf(fact_583_div__minus__right,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.29 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_minus_right
% 5.07/5.29 thf(fact_584_minus__divide__left,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_left
% 5.07/5.29 thf(fact_585_minus__divide__left,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.07/5.29 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_left
% 5.07/5.29 thf(fact_586_minus__divide__left,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_left
% 5.07/5.29 thf(fact_587_minus__divide__divide,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.07/5.29 = ( divide_divide_real @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_divide
% 5.07/5.29 thf(fact_588_minus__divide__divide,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.29 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_divide
% 5.07/5.29 thf(fact_589_minus__divide__divide,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.07/5.29 = ( divide_divide_rat @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_divide
% 5.07/5.29 thf(fact_590_minus__divide__right,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_right
% 5.07/5.29 thf(fact_591_minus__divide__right,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.07/5.29 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_right
% 5.07/5.29 thf(fact_592_minus__divide__right,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_divide_right
% 5.07/5.29 thf(fact_593_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M2 @ N ) )
% 5.07/5.29 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.07/5.29 thf(fact_594_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) )
% 5.07/5.29 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.07/5.29 thf(fact_595_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ( divide_divide_nat @ M2 @ N )
% 5.07/5.29 = zero_zero_nat )
% 5.07/5.29 = ( ( ord_less_nat @ M2 @ N )
% 5.07/5.29 | ( N = zero_zero_nat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Euclidean_Division.div_eq_0_iff
% 5.07/5.29 thf(fact_596_divide__strict__right__mono__neg,axiom,
% 5.07/5.29 ! [B: real,A: real,C: real] :
% 5.07/5.29 ( ( ord_less_real @ B @ A )
% 5.07/5.29 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.07/5.29 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_strict_right_mono_neg
% 5.07/5.29 thf(fact_597_divide__strict__right__mono__neg,axiom,
% 5.07/5.29 ! [B: rat,A: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_rat @ B @ A )
% 5.07/5.29 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.07/5.29 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_strict_right_mono_neg
% 5.07/5.29 thf(fact_598_divide__strict__right__mono,axiom,
% 5.07/5.29 ! [A: real,B: real,C: real] :
% 5.07/5.29 ( ( ord_less_real @ A @ B )
% 5.07/5.29 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.07/5.29 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_strict_right_mono
% 5.07/5.29 thf(fact_599_divide__strict__right__mono,axiom,
% 5.07/5.29 ! [A: rat,B: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_rat @ A @ B )
% 5.07/5.29 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.07/5.29 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_strict_right_mono
% 5.07/5.29 thf(fact_600_zero__less__divide__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.07/5.29 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_less_divide_iff
% 5.07/5.29 thf(fact_601_zero__less__divide__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.07/5.29 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_less_divide_iff
% 5.07/5.29 thf(fact_602_divide__less__cancel,axiom,
% 5.07/5.29 ! [A: real,C: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.07/5.29 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.07/5.29 => ( ord_less_real @ A @ B ) )
% 5.07/5.29 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.07/5.29 => ( ord_less_real @ B @ A ) )
% 5.07/5.29 & ( C != zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_cancel
% 5.07/5.29 thf(fact_603_divide__less__cancel,axiom,
% 5.07/5.29 ! [A: rat,C: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.07/5.29 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.07/5.29 => ( ord_less_rat @ A @ B ) )
% 5.07/5.29 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.07/5.29 => ( ord_less_rat @ B @ A ) )
% 5.07/5.29 & ( C != zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_cancel
% 5.07/5.29 thf(fact_604_divide__less__0__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.07/5.29 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.07/5.29 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_0_iff
% 5.07/5.29 thf(fact_605_divide__less__0__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.07/5.29 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.07/5.29 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_0_iff
% 5.07/5.29 thf(fact_606_divide__pos__pos,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ X )
% 5.07/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.07/5.29 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_pos_pos
% 5.07/5.29 thf(fact_607_divide__pos__pos,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.07/5.29 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.07/5.29 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_pos_pos
% 5.07/5.29 thf(fact_608_divide__pos__neg,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ X )
% 5.07/5.29 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.07/5.29 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_pos_neg
% 5.07/5.29 thf(fact_609_divide__pos__neg,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.07/5.29 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.07/5.29 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_pos_neg
% 5.07/5.29 thf(fact_610_divide__neg__pos,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_real @ X @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.07/5.29 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_neg_pos
% 5.07/5.29 thf(fact_611_divide__neg__pos,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.07/5.29 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_neg_pos
% 5.07/5.29 thf(fact_612_divide__neg__neg,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_real @ X @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.07/5.29 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_neg_neg
% 5.07/5.29 thf(fact_613_divide__neg__neg,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.07/5.29 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_neg_neg
% 5.07/5.29 thf(fact_614_right__inverse__eq,axiom,
% 5.07/5.29 ! [B: complex,A: complex] :
% 5.07/5.29 ( ( B != zero_zero_complex )
% 5.07/5.29 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.07/5.29 = one_one_complex )
% 5.07/5.29 = ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % right_inverse_eq
% 5.07/5.29 thf(fact_615_right__inverse__eq,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( B != zero_zero_real )
% 5.07/5.29 => ( ( ( divide_divide_real @ A @ B )
% 5.07/5.29 = one_one_real )
% 5.07/5.29 = ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % right_inverse_eq
% 5.07/5.29 thf(fact_616_right__inverse__eq,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( B != zero_zero_rat )
% 5.07/5.29 => ( ( ( divide_divide_rat @ A @ B )
% 5.07/5.29 = one_one_rat )
% 5.07/5.29 = ( A = B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % right_inverse_eq
% 5.07/5.29 thf(fact_617_nonzero__minus__divide__right,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( B != zero_zero_real )
% 5.07/5.29 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_right
% 5.07/5.29 thf(fact_618_nonzero__minus__divide__right,axiom,
% 5.07/5.29 ! [B: complex,A: complex] :
% 5.07/5.29 ( ( B != zero_zero_complex )
% 5.07/5.29 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.07/5.29 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_right
% 5.07/5.29 thf(fact_619_nonzero__minus__divide__right,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( B != zero_zero_rat )
% 5.07/5.29 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_right
% 5.07/5.29 thf(fact_620_nonzero__minus__divide__divide,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( B != zero_zero_real )
% 5.07/5.29 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.07/5.29 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_divide
% 5.07/5.29 thf(fact_621_nonzero__minus__divide__divide,axiom,
% 5.07/5.29 ! [B: complex,A: complex] :
% 5.07/5.29 ( ( B != zero_zero_complex )
% 5.07/5.29 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.07/5.29 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_divide
% 5.07/5.29 thf(fact_622_nonzero__minus__divide__divide,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( B != zero_zero_rat )
% 5.07/5.29 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.07/5.29 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nonzero_minus_divide_divide
% 5.07/5.29 thf(fact_623_div__eq__dividend__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.07/5.29 => ( ( ( divide_divide_nat @ M2 @ N )
% 5.07/5.29 = M2 )
% 5.07/5.29 = ( N = one_one_nat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_eq_dividend_iff
% 5.07/5.29 thf(fact_624_div__less__dividend,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_nat @ one_one_nat @ N )
% 5.07/5.29 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.07/5.29 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_less_dividend
% 5.07/5.29 thf(fact_625_less__divide__eq__1,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_real @ A @ B ) )
% 5.07/5.29 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1
% 5.07/5.29 thf(fact_626_less__divide__eq__1,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_rat @ A @ B ) )
% 5.07/5.29 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_divide_eq_1
% 5.07/5.29 thf(fact_627_divide__less__eq__1,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.07/5.29 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_real @ B @ A ) )
% 5.07/5.29 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_real @ A @ B ) )
% 5.07/5.29 | ( A = zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1
% 5.07/5.29 thf(fact_628_divide__less__eq__1,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.07/5.29 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_rat @ B @ A ) )
% 5.07/5.29 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_rat @ A @ B ) )
% 5.07/5.29 | ( A = zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_less_eq_1
% 5.07/5.29 thf(fact_629_divide__eq__minus__1__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ( divide_divide_real @ A @ B )
% 5.07/5.29 = ( uminus_uminus_real @ one_one_real ) )
% 5.07/5.29 = ( ( B != zero_zero_real )
% 5.07/5.29 & ( A
% 5.07/5.29 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_minus_1_iff
% 5.07/5.29 thf(fact_630_divide__eq__minus__1__iff,axiom,
% 5.07/5.29 ! [A: complex,B: complex] :
% 5.07/5.29 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.07/5.29 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.07/5.29 = ( ( B != zero_zero_complex )
% 5.07/5.29 & ( A
% 5.07/5.29 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_minus_1_iff
% 5.07/5.29 thf(fact_631_divide__eq__minus__1__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ( divide_divide_rat @ A @ B )
% 5.07/5.29 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.07/5.29 = ( ( B != zero_zero_rat )
% 5.07/5.29 & ( A
% 5.07/5.29 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_eq_minus_1_iff
% 5.07/5.29 thf(fact_632_div__if,axiom,
% 5.07/5.29 ( divide_divide_nat
% 5.07/5.29 = ( ^ [M5: nat,N4: nat] :
% 5.07/5.29 ( if_nat
% 5.07/5.29 @ ( ( ord_less_nat @ M5 @ N4 )
% 5.07/5.29 | ( N4 = zero_zero_nat ) )
% 5.07/5.29 @ zero_zero_nat
% 5.07/5.29 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_if
% 5.07/5.29 thf(fact_633_bits__div__by__1,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_by_1
% 5.07/5.29 thf(fact_634_bits__div__by__1,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( divide_divide_int @ A @ one_one_int )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_by_1
% 5.07/5.29 thf(fact_635_bits__div__by__0,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_by_0
% 5.07/5.29 thf(fact_636_bits__div__by__0,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_by_0
% 5.07/5.29 thf(fact_637_bits__div__0,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_0
% 5.07/5.29 thf(fact_638_bits__div__0,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % bits_div_0
% 5.07/5.29 thf(fact_639_div__eq__minus1,axiom,
% 5.07/5.29 ! [B: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.07/5.29 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_eq_minus1
% 5.07/5.29 thf(fact_640_div__geq,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.29 => ( ~ ( ord_less_nat @ M2 @ N )
% 5.07/5.29 => ( ( divide_divide_nat @ M2 @ N )
% 5.07/5.29 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_geq
% 5.07/5.29 thf(fact_641_int__div__less__self,axiom,
% 5.07/5.29 ! [X: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ X )
% 5.07/5.29 => ( ( ord_less_int @ one_one_int @ K )
% 5.07/5.29 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_div_less_self
% 5.07/5.29 thf(fact_642_dbl__dec__simps_I2_J,axiom,
% 5.07/5.29 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.07/5.29 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(2)
% 5.07/5.29 thf(fact_643_dbl__dec__simps_I2_J,axiom,
% 5.07/5.29 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.07/5.29 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(2)
% 5.07/5.29 thf(fact_644_dbl__dec__simps_I2_J,axiom,
% 5.07/5.29 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.07/5.29 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(2)
% 5.07/5.29 thf(fact_645_dbl__dec__simps_I2_J,axiom,
% 5.07/5.29 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.07/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(2)
% 5.07/5.29 thf(fact_646_dbl__dec__simps_I2_J,axiom,
% 5.07/5.29 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.07/5.29 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(2)
% 5.07/5.29 thf(fact_647_dbl__dec__simps_I3_J,axiom,
% 5.07/5.29 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.07/5.29 = one_one_complex ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(3)
% 5.07/5.29 thf(fact_648_dbl__dec__simps_I3_J,axiom,
% 5.07/5.29 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.07/5.29 = one_one_real ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(3)
% 5.07/5.29 thf(fact_649_dbl__dec__simps_I3_J,axiom,
% 5.07/5.29 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.07/5.29 = one_one_rat ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(3)
% 5.07/5.29 thf(fact_650_dbl__dec__simps_I3_J,axiom,
% 5.07/5.29 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.07/5.29 = one_one_int ) ).
% 5.07/5.29
% 5.07/5.29 % dbl_dec_simps(3)
% 5.07/5.29 thf(fact_651_zdiv__int,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.07/5.29 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zdiv_int
% 5.07/5.29 thf(fact_652_div__neg__pos__less0,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_int @ A @ zero_zero_int )
% 5.07/5.29 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_neg_pos_less0
% 5.07/5.29 thf(fact_653_neg__imp__zdiv__neg__iff,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ B @ zero_zero_int )
% 5.07/5.29 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.07/5.29 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_imp_zdiv_neg_iff
% 5.07/5.29 thf(fact_654_pos__imp__zdiv__neg__iff,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.07/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % pos_imp_zdiv_neg_iff
% 5.07/5.29 thf(fact_655_option_Osize__gen_I1_J,axiom,
% 5.07/5.29 ! [X: product_prod_nat_nat > nat] :
% 5.07/5.29 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.07/5.29 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % option.size_gen(1)
% 5.07/5.29 thf(fact_656_option_Osize__gen_I1_J,axiom,
% 5.07/5.29 ! [X: num > nat] :
% 5.07/5.29 ( ( size_option_num @ X @ none_num )
% 5.07/5.29 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % option.size_gen(1)
% 5.07/5.29 thf(fact_657_int__power__div__base,axiom,
% 5.07/5.29 ! [M2: nat,K: int] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.07/5.29 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.07/5.29 => ( ( divide_divide_int @ ( power_power_int @ K @ M2 ) @ K )
% 5.07/5.29 = ( power_power_int @ K @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_power_div_base
% 5.07/5.29 thf(fact_658_one__less__nat__eq,axiom,
% 5.07/5.29 ! [Z2: int] :
% 5.07/5.29 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 5.07/5.29 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % one_less_nat_eq
% 5.07/5.29 thf(fact_659_Divides_Oadjust__mod__def,axiom,
% 5.07/5.29 ( adjust_mod
% 5.07/5.29 = ( ^ [L2: int,R: int] : ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Divides.adjust_mod_def
% 5.07/5.29 thf(fact_660_le__div__geq,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( divide_divide_nat @ M2 @ N )
% 5.07/5.29 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_div_geq
% 5.07/5.29 thf(fact_661_zdiv__zminus1__eq__if,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( B != zero_zero_int )
% 5.07/5.29 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 = zero_zero_int )
% 5.07/5.29 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.07/5.29 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.07/5.29 & ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 != zero_zero_int )
% 5.07/5.29 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.07/5.29 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zdiv_zminus1_eq_if
% 5.07/5.29 thf(fact_662_zdiv__zminus2__eq__if,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( B != zero_zero_int )
% 5.07/5.29 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 = zero_zero_int )
% 5.07/5.29 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.07/5.29 & ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 != zero_zero_int )
% 5.07/5.29 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zdiv_zminus2_eq_if
% 5.07/5.29 thf(fact_663_zmod__minus1,axiom,
% 5.07/5.29 ! [B: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.07/5.29 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zmod_minus1
% 5.07/5.29 thf(fact_664_Nitpick_Ocase__nat__unfold,axiom,
% 5.07/5.29 ( case_nat_o
% 5.07/5.29 = ( ^ [X2: $o,F2: nat > $o,N4: nat] :
% 5.07/5.29 ( ( ( N4 = zero_zero_nat )
% 5.07/5.29 => X2 )
% 5.07/5.29 & ( ( N4 != zero_zero_nat )
% 5.07/5.29 => ( F2 @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Nitpick.case_nat_unfold
% 5.07/5.29 thf(fact_665_Nitpick_Ocase__nat__unfold,axiom,
% 5.07/5.29 ( case_nat_nat
% 5.07/5.29 = ( ^ [X2: nat,F2: nat > nat,N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ X2 @ ( F2 @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Nitpick.case_nat_unfold
% 5.07/5.29 thf(fact_666_Nitpick_Ocase__nat__unfold,axiom,
% 5.07/5.29 ( case_nat_option_num
% 5.07/5.29 = ( ^ [X2: option_num,F2: nat > option_num,N4: nat] : ( if_option_num @ ( N4 = zero_zero_nat ) @ X2 @ ( F2 @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Nitpick.case_nat_unfold
% 5.07/5.29 thf(fact_667_divide__le__eq__1__neg,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.07/5.29 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_eq_1_neg
% 5.07/5.29 thf(fact_668_divide__le__eq__1__neg,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_eq_1_neg
% 5.07/5.29 thf(fact_669_divide__le__eq__1__pos,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.07/5.29 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_eq_1_pos
% 5.07/5.29 thf(fact_670_divide__le__eq__1__pos,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.07/5.29 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_eq_1_pos
% 5.07/5.29 thf(fact_671_le__zero__eq,axiom,
% 5.07/5.29 ! [N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.07/5.29 = ( N = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_zero_eq
% 5.07/5.29 thf(fact_672_neg__le__iff__le,axiom,
% 5.07/5.29 ! [B: real,A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_iff_le
% 5.07/5.29 thf(fact_673_neg__le__iff__le,axiom,
% 5.07/5.29 ! [B: code_integer,A: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_iff_le
% 5.07/5.29 thf(fact_674_neg__le__iff__le,axiom,
% 5.07/5.29 ! [B: rat,A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_iff_le
% 5.07/5.29 thf(fact_675_neg__le__iff__le,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.07/5.29 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_iff_le
% 5.07/5.29 thf(fact_676_compl__le__compl__iff,axiom,
% 5.07/5.29 ! [X: set_nat,Y: set_nat] :
% 5.07/5.29 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 5.07/5.29 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 5.07/5.29
% 5.07/5.29 % compl_le_compl_iff
% 5.07/5.29 thf(fact_677_mod__self,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ A )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % mod_self
% 5.07/5.29 thf(fact_678_mod__self,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ A @ A )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % mod_self
% 5.07/5.29 thf(fact_679_mod__self,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ A )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % mod_self
% 5.07/5.29 thf(fact_680_mod__self,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ A @ A )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % mod_self
% 5.07/5.29 thf(fact_681_mod__by__0,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_0
% 5.07/5.29 thf(fact_682_mod__by__0,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_0
% 5.07/5.29 thf(fact_683_mod__by__0,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_0
% 5.07/5.29 thf(fact_684_mod__by__0,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 5.07/5.29 = A ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_0
% 5.07/5.29 thf(fact_685_mod__0,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % mod_0
% 5.07/5.29 thf(fact_686_mod__0,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % mod_0
% 5.07/5.29 thf(fact_687_mod__0,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % mod_0
% 5.07/5.29 thf(fact_688_mod__0,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % mod_0
% 5.07/5.29 thf(fact_689_bits__mod__0,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_0
% 5.07/5.29 thf(fact_690_bits__mod__0,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_0
% 5.07/5.29 thf(fact_691_bits__mod__0,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_0
% 5.07/5.29 thf(fact_692_bits__mod__0,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_0
% 5.07/5.29 thf(fact_693_Suc__le__mono,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 5.07/5.29 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % Suc_le_mono
% 5.07/5.29 thf(fact_694_le0,axiom,
% 5.07/5.29 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.07/5.29
% 5.07/5.29 % le0
% 5.07/5.29 thf(fact_695_bot__nat__0_Oextremum,axiom,
% 5.07/5.29 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.07/5.29
% 5.07/5.29 % bot_nat_0.extremum
% 5.07/5.29 thf(fact_696_minus__mod__self2,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.07/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_mod_self2
% 5.07/5.29 thf(fact_697_minus__mod__self2,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.07/5.29 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_mod_self2
% 5.07/5.29 thf(fact_698_mod__minus__minus,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_minus
% 5.07/5.29 thf(fact_699_mod__minus__minus,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.29 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_minus
% 5.07/5.29 thf(fact_700_diff__diff__cancel,axiom,
% 5.07/5.29 ! [I: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ N )
% 5.07/5.29 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.07/5.29 = I ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_diff_cancel
% 5.07/5.29 thf(fact_701_negative__zle,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % negative_zle
% 5.07/5.29 thf(fact_702_nat__int,axiom,
% 5.07/5.29 ! [N: nat] :
% 5.07/5.29 ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.29 = N ) ).
% 5.07/5.29
% 5.07/5.29 % nat_int
% 5.07/5.29 thf(fact_703_diff__ge__0__iff__ge,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.07/5.29 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_ge_0_iff_ge
% 5.07/5.29 thf(fact_704_diff__ge__0__iff__ge,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.07/5.29 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_ge_0_iff_ge
% 5.07/5.29 thf(fact_705_diff__ge__0__iff__ge,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.07/5.29 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_ge_0_iff_ge
% 5.07/5.29 thf(fact_706_neg__0__le__iff__le,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_0_le_iff_le
% 5.07/5.29 thf(fact_707_neg__0__le__iff__le,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_0_le_iff_le
% 5.07/5.29 thf(fact_708_neg__0__le__iff__le,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_0_le_iff_le
% 5.07/5.29 thf(fact_709_neg__0__le__iff__le,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.07/5.29 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_0_le_iff_le
% 5.07/5.29 thf(fact_710_neg__le__0__iff__le,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.07/5.29 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_0_iff_le
% 5.07/5.29 thf(fact_711_neg__le__0__iff__le,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_0_iff_le
% 5.07/5.29 thf(fact_712_neg__le__0__iff__le,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.07/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_0_iff_le
% 5.07/5.29 thf(fact_713_neg__le__0__iff__le,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.07/5.29 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_le_0_iff_le
% 5.07/5.29 thf(fact_714_less__eq__neg__nonpos,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_eq_neg_nonpos
% 5.07/5.29 thf(fact_715_less__eq__neg__nonpos,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_eq_neg_nonpos
% 5.07/5.29 thf(fact_716_less__eq__neg__nonpos,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_eq_neg_nonpos
% 5.07/5.29 thf(fact_717_less__eq__neg__nonpos,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.07/5.29 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_eq_neg_nonpos
% 5.07/5.29 thf(fact_718_neg__less__eq__nonneg,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.07/5.29 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_less_eq_nonneg
% 5.07/5.29 thf(fact_719_neg__less__eq__nonneg,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_less_eq_nonneg
% 5.07/5.29 thf(fact_720_neg__less__eq__nonneg,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.07/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_less_eq_nonneg
% 5.07/5.29 thf(fact_721_neg__less__eq__nonneg,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.07/5.29 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_less_eq_nonneg
% 5.07/5.29 thf(fact_722_mod__by__1,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_1
% 5.07/5.29 thf(fact_723_mod__by__1,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_1
% 5.07/5.29 thf(fact_724_mod__by__1,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_1
% 5.07/5.29 thf(fact_725_mod__by__1,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % mod_by_1
% 5.07/5.29 thf(fact_726_bits__mod__by__1,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_by_1
% 5.07/5.29 thf(fact_727_bits__mod__by__1,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_by_1
% 5.07/5.29 thf(fact_728_bits__mod__by__1,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_by_1
% 5.07/5.29 thf(fact_729_bits__mod__by__1,axiom,
% 5.07/5.29 ! [A: code_natural] :
% 5.07/5.29 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_by_1
% 5.07/5.29 thf(fact_730_mod__div__trivial,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % mod_div_trivial
% 5.07/5.29 thf(fact_731_mod__div__trivial,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % mod_div_trivial
% 5.07/5.29 thf(fact_732_mod__div__trivial,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % mod_div_trivial
% 5.07/5.29 thf(fact_733_mod__div__trivial,axiom,
% 5.07/5.29 ! [A: code_natural,B: code_natural] :
% 5.07/5.29 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % mod_div_trivial
% 5.07/5.29 thf(fact_734_bits__mod__div__trivial,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_div_trivial
% 5.07/5.29 thf(fact_735_bits__mod__div__trivial,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_div_trivial
% 5.07/5.29 thf(fact_736_bits__mod__div__trivial,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_div_trivial
% 5.07/5.29 thf(fact_737_bits__mod__div__trivial,axiom,
% 5.07/5.29 ! [A: code_natural,B: code_natural] :
% 5.07/5.29 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 5.07/5.29 = zero_z2226904508553997617atural ) ).
% 5.07/5.29
% 5.07/5.29 % bits_mod_div_trivial
% 5.07/5.29 thf(fact_738_of__nat__le__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_iff
% 5.07/5.29 thf(fact_739_of__nat__le__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_iff
% 5.07/5.29 thf(fact_740_of__nat__le__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_iff
% 5.07/5.29 thf(fact_741_of__nat__le__iff,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_iff
% 5.07/5.29 thf(fact_742_minus__mod__self1,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.07/5.29 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_mod_self1
% 5.07/5.29 thf(fact_743_minus__mod__self1,axiom,
% 5.07/5.29 ! [B: code_integer,A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_mod_self1
% 5.07/5.29 thf(fact_744_diff__is__0__eq,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ( minus_minus_nat @ M2 @ N )
% 5.07/5.29 = zero_zero_nat )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_is_0_eq
% 5.07/5.29 thf(fact_745_diff__is__0__eq_H,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ( minus_minus_nat @ M2 @ N )
% 5.07/5.29 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_is_0_eq'
% 5.07/5.29 thf(fact_746_nat__0__iff,axiom,
% 5.07/5.29 ! [I: int] :
% 5.07/5.29 ( ( ( nat2 @ I )
% 5.07/5.29 = zero_zero_nat )
% 5.07/5.29 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_0_iff
% 5.07/5.29 thf(fact_747_nat__le__0,axiom,
% 5.07/5.29 ! [Z2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 5.07/5.29 => ( ( nat2 @ Z2 )
% 5.07/5.29 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_le_0
% 5.07/5.29 thf(fact_748_int__nat__eq,axiom,
% 5.07/5.29 ! [Z2: int] :
% 5.07/5.29 ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.07/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 5.07/5.29 = Z2 ) )
% 5.07/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.07/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 5.07/5.29 = zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_nat_eq
% 5.07/5.29 thf(fact_749_div__pos__pos__trivial,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.07/5.29 => ( ( ord_less_int @ K @ L )
% 5.07/5.29 => ( ( divide_divide_int @ K @ L )
% 5.07/5.29 = zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_pos_pos_trivial
% 5.07/5.29 thf(fact_750_div__neg__neg__trivial,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.07/5.29 => ( ( ord_less_int @ L @ K )
% 5.07/5.29 => ( ( divide_divide_int @ K @ L )
% 5.07/5.29 = zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_neg_neg_trivial
% 5.07/5.29 thf(fact_751_zle__diff1__eq,axiom,
% 5.07/5.29 ! [W: int,Z2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z2 @ one_one_int ) )
% 5.07/5.29 = ( ord_less_int @ W @ Z2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % zle_diff1_eq
% 5.07/5.29 thf(fact_752_mod__pos__pos__trivial,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.07/5.29 => ( ( ord_less_int @ K @ L )
% 5.07/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.07/5.29 = K ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_pos_pos_trivial
% 5.07/5.29 thf(fact_753_mod__neg__neg__trivial,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.07/5.29 => ( ( ord_less_int @ L @ K )
% 5.07/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.07/5.29 = K ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_neg_neg_trivial
% 5.07/5.29 thf(fact_754_zero__le__divide__1__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_le_divide_1_iff
% 5.07/5.29 thf(fact_755_zero__le__divide__1__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_le_divide_1_iff
% 5.07/5.29 thf(fact_756_divide__le__0__1__iff,axiom,
% 5.07/5.29 ! [A: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.07/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_0_1_iff
% 5.07/5.29 thf(fact_757_divide__le__0__1__iff,axiom,
% 5.07/5.29 ! [A: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_0_1_iff
% 5.07/5.29 thf(fact_758_of__nat__le__0__iff,axiom,
% 5.07/5.29 ! [M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 5.07/5.29 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_0_iff
% 5.07/5.29 thf(fact_759_of__nat__le__0__iff,axiom,
% 5.07/5.29 ! [M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat )
% 5.07/5.29 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_0_iff
% 5.07/5.29 thf(fact_760_of__nat__le__0__iff,axiom,
% 5.07/5.29 ! [M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 5.07/5.29 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_0_iff
% 5.07/5.29 thf(fact_761_of__nat__le__0__iff,axiom,
% 5.07/5.29 ! [M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 5.07/5.29 = ( M2 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_le_0_iff
% 5.07/5.29 thf(fact_762_mod__minus1__right,axiom,
% 5.07/5.29 ! [A: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.07/5.29 = zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus1_right
% 5.07/5.29 thf(fact_763_mod__minus1__right,axiom,
% 5.07/5.29 ! [A: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus1_right
% 5.07/5.29 thf(fact_764_nat__1,axiom,
% 5.07/5.29 ( ( nat2 @ one_one_int )
% 5.07/5.29 = ( suc @ zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_1
% 5.07/5.29 thf(fact_765_zless__nat__conj,axiom,
% 5.07/5.29 ! [W: int,Z2: int] :
% 5.07/5.29 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 5.07/5.29 = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.07/5.29 & ( ord_less_int @ W @ Z2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zless_nat_conj
% 5.07/5.29 thf(fact_766_nat__zminus__int,axiom,
% 5.07/5.29 ! [N: nat] :
% 5.07/5.29 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.07/5.29 = zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % nat_zminus_int
% 5.07/5.29 thf(fact_767_le__divide__eq__1__pos,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.07/5.29 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_divide_eq_1_pos
% 5.07/5.29 thf(fact_768_le__divide__eq__1__pos,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.07/5.29 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_divide_eq_1_pos
% 5.07/5.29 thf(fact_769_le__divide__eq__1__neg,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_real @ A @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.07/5.29 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_divide_eq_1_neg
% 5.07/5.29 thf(fact_770_le__divide__eq__1__neg,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.07/5.29 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_divide_eq_1_neg
% 5.07/5.29 thf(fact_771_zero__less__nat__eq,axiom,
% 5.07/5.29 ! [Z2: int] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 5.07/5.29 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_less_nat_eq
% 5.07/5.29 thf(fact_772_verit__comp__simplify1_I2_J,axiom,
% 5.07/5.29 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(2)
% 5.07/5.29 thf(fact_773_verit__comp__simplify1_I2_J,axiom,
% 5.07/5.29 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(2)
% 5.07/5.29 thf(fact_774_verit__comp__simplify1_I2_J,axiom,
% 5.07/5.29 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(2)
% 5.07/5.29 thf(fact_775_verit__comp__simplify1_I2_J,axiom,
% 5.07/5.29 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(2)
% 5.07/5.29 thf(fact_776_verit__comp__simplify1_I2_J,axiom,
% 5.07/5.29 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(2)
% 5.07/5.29 thf(fact_777_verit__la__disequality,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( A = B )
% 5.07/5.29 | ~ ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_la_disequality
% 5.07/5.29 thf(fact_778_verit__la__disequality,axiom,
% 5.07/5.29 ! [A: num,B: num] :
% 5.07/5.29 ( ( A = B )
% 5.07/5.29 | ~ ( ord_less_eq_num @ A @ B )
% 5.07/5.29 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_la_disequality
% 5.07/5.29 thf(fact_779_verit__la__disequality,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( A = B )
% 5.07/5.29 | ~ ( ord_less_eq_nat @ A @ B )
% 5.07/5.29 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_la_disequality
% 5.07/5.29 thf(fact_780_verit__la__disequality,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( A = B )
% 5.07/5.29 | ~ ( ord_less_eq_int @ A @ B )
% 5.07/5.29 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_la_disequality
% 5.07/5.29 thf(fact_781_le__refl,axiom,
% 5.07/5.29 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.07/5.29
% 5.07/5.29 % le_refl
% 5.07/5.29 thf(fact_782_le__trans,axiom,
% 5.07/5.29 ! [I: nat,J2: nat,K: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ( ord_less_eq_nat @ J2 @ K )
% 5.07/5.29 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_trans
% 5.07/5.29 thf(fact_783_eq__imp__le,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( M2 = N )
% 5.07/5.29 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % eq_imp_le
% 5.07/5.29 thf(fact_784_le__antisym,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( M2 = N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_antisym
% 5.07/5.29 thf(fact_785_nat__le__linear,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_le_linear
% 5.07/5.29 thf(fact_786_Nat_Oex__has__greatest__nat,axiom,
% 5.07/5.29 ! [P: nat > $o,K: nat,B: nat] :
% 5.07/5.29 ( ( P @ K )
% 5.07/5.29 => ( ! [Y3: nat] :
% 5.07/5.29 ( ( P @ Y3 )
% 5.07/5.29 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.07/5.29 => ? [X3: nat] :
% 5.07/5.29 ( ( P @ X3 )
% 5.07/5.29 & ! [Y5: nat] :
% 5.07/5.29 ( ( P @ Y5 )
% 5.07/5.29 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Nat.ex_has_greatest_nat
% 5.07/5.29 thf(fact_787_nat__mono,axiom,
% 5.07/5.29 ! [X: int,Y: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ X @ Y )
% 5.07/5.29 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_mono
% 5.07/5.29 thf(fact_788_nat__le__iff,axiom,
% 5.07/5.29 ! [X: int,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.07/5.29 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_le_iff
% 5.07/5.29 thf(fact_789_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.07/5.29 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.07/5.29 thf(fact_790_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.07/5.29 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.07/5.29 thf(fact_791_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.07/5.29 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.07/5.29 thf(fact_792_of__nat__mod,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mod
% 5.07/5.29 thf(fact_793_of__nat__mod,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri3763490453095760265atural @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.07/5.29 = ( modulo8411746178871703098atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mod
% 5.07/5.29 thf(fact_794_of__nat__mod,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.07/5.29 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mod
% 5.07/5.29 thf(fact_795_of__nat__mod,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.07/5.29 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mod
% 5.07/5.29 thf(fact_796_eq__nat__nat__iff,axiom,
% 5.07/5.29 ! [Z2: int,Z3: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.07/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.07/5.29 => ( ( ( nat2 @ Z2 )
% 5.07/5.29 = ( nat2 @ Z3 ) )
% 5.07/5.29 = ( Z2 = Z3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % eq_nat_nat_iff
% 5.07/5.29 thf(fact_797_all__nat,axiom,
% 5.07/5.29 ( ( ^ [P2: nat > $o] :
% 5.07/5.29 ! [X5: nat] : ( P2 @ X5 ) )
% 5.07/5.29 = ( ^ [P3: nat > $o] :
% 5.07/5.29 ! [X2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.07/5.29 => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % all_nat
% 5.07/5.29 thf(fact_798_ex__nat,axiom,
% 5.07/5.29 ( ( ^ [P2: nat > $o] :
% 5.07/5.29 ? [X5: nat] : ( P2 @ X5 ) )
% 5.07/5.29 = ( ^ [P3: nat > $o] :
% 5.07/5.29 ? [X2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.07/5.29 & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % ex_nat
% 5.07/5.29 thf(fact_799_zmod__le__nonneg__dividend,axiom,
% 5.07/5.29 ! [M2: int,K: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 5.07/5.29 => ( ord_less_eq_int @ ( modulo_modulo_int @ M2 @ K ) @ M2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % zmod_le_nonneg_dividend
% 5.07/5.29 thf(fact_800_lift__Suc__mono__le,axiom,
% 5.07/5.29 ! [F: nat > set_nat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_mono_le
% 5.07/5.29 thf(fact_801_lift__Suc__mono__le,axiom,
% 5.07/5.29 ! [F: nat > rat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_mono_le
% 5.07/5.29 thf(fact_802_lift__Suc__mono__le,axiom,
% 5.07/5.29 ! [F: nat > num,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_mono_le
% 5.07/5.29 thf(fact_803_lift__Suc__mono__le,axiom,
% 5.07/5.29 ! [F: nat > nat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_mono_le
% 5.07/5.29 thf(fact_804_lift__Suc__mono__le,axiom,
% 5.07/5.29 ! [F: nat > int,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_mono_le
% 5.07/5.29 thf(fact_805_lift__Suc__antimono__le,axiom,
% 5.07/5.29 ! [F: nat > set_nat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_antimono_le
% 5.07/5.29 thf(fact_806_lift__Suc__antimono__le,axiom,
% 5.07/5.29 ! [F: nat > rat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_antimono_le
% 5.07/5.29 thf(fact_807_lift__Suc__antimono__le,axiom,
% 5.07/5.29 ! [F: nat > num,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_antimono_le
% 5.07/5.29 thf(fact_808_lift__Suc__antimono__le,axiom,
% 5.07/5.29 ! [F: nat > nat,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_antimono_le
% 5.07/5.29 thf(fact_809_lift__Suc__antimono__le,axiom,
% 5.07/5.29 ! [F: nat > int,N: nat,N3: nat] :
% 5.07/5.29 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.07/5.29 => ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % lift_Suc_antimono_le
% 5.07/5.29 thf(fact_810_of__nat__mono,axiom,
% 5.07/5.29 ! [I: nat,J2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mono
% 5.07/5.29 thf(fact_811_of__nat__mono,axiom,
% 5.07/5.29 ! [I: nat,J2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mono
% 5.07/5.29 thf(fact_812_of__nat__mono,axiom,
% 5.07/5.29 ! [I: nat,J2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mono
% 5.07/5.29 thf(fact_813_of__nat__mono,axiom,
% 5.07/5.29 ! [I: nat,J2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % of_nat_mono
% 5.07/5.29 thf(fact_814_zle__int,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % zle_int
% 5.07/5.29 thf(fact_815_nat__int__comparison_I3_J,axiom,
% 5.07/5.29 ( ord_less_eq_nat
% 5.07/5.29 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_int_comparison(3)
% 5.07/5.29 thf(fact_816_nat__le__eq__zle,axiom,
% 5.07/5.29 ! [W: int,Z2: int] :
% 5.07/5.29 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.07/5.29 | ( ord_less_eq_int @ zero_zero_int @ Z2 ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 5.07/5.29 = ( ord_less_eq_int @ W @ Z2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_le_eq_zle
% 5.07/5.29 thf(fact_817_le__nat__iff,axiom,
% 5.07/5.29 ! [K: int,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.07/5.29 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.07/5.29 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_nat_iff
% 5.07/5.29 thf(fact_818_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.07/5.29 ! [B: code_integer,A: code_integer] :
% 5.07/5.29 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.07/5.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.07/5.29 thf(fact_819_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.07/5.29 ! [B: nat,A: nat] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.07/5.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.07/5.29 thf(fact_820_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.07/5.29 thf(fact_821_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.07/5.29 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.07/5.29 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.07/5.29 = A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less
% 5.07/5.29 thf(fact_822_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.07/5.29 => ( ( ord_less_nat @ A @ B )
% 5.07/5.29 => ( ( modulo_modulo_nat @ A @ B )
% 5.07/5.29 = A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less
% 5.07/5.29 thf(fact_823_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.07/5.29 => ( ( ord_less_int @ A @ B )
% 5.07/5.29 => ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 = A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.mod_less
% 5.07/5.29 thf(fact_824_nat__0__le,axiom,
% 5.07/5.29 ! [Z2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.07/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 5.07/5.29 = Z2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_0_le
% 5.07/5.29 thf(fact_825_int__eq__iff,axiom,
% 5.07/5.29 ! [M2: nat,Z2: int] :
% 5.07/5.29 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.07/5.29 = Z2 )
% 5.07/5.29 = ( ( M2
% 5.07/5.29 = ( nat2 @ Z2 ) )
% 5.07/5.29 & ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % int_eq_iff
% 5.07/5.29 thf(fact_826_Euclidean__Division_Opos__mod__sign,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ L )
% 5.07/5.29 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Euclidean_Division.pos_mod_sign
% 5.07/5.29 thf(fact_827_neg__mod__sign,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ L @ zero_zero_int )
% 5.07/5.29 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_mod_sign
% 5.07/5.29 thf(fact_828_zmod__trivial__iff,axiom,
% 5.07/5.29 ! [I: int,K: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ I @ K )
% 5.07/5.29 = I )
% 5.07/5.29 = ( ( K = zero_zero_int )
% 5.07/5.29 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.07/5.29 & ( ord_less_int @ I @ K ) )
% 5.07/5.29 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.07/5.29 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zmod_trivial_iff
% 5.07/5.29 thf(fact_829_pos__mod__conj,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.07/5.29 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % pos_mod_conj
% 5.07/5.29 thf(fact_830_neg__mod__conj,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ B @ zero_zero_int )
% 5.07/5.29 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.07/5.29 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_mod_conj
% 5.07/5.29 thf(fact_831_mod__diff__right__eq,axiom,
% 5.07/5.29 ! [A: int,B: int,C: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.07/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_right_eq
% 5.07/5.29 thf(fact_832_mod__diff__right__eq,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_right_eq
% 5.07/5.29 thf(fact_833_mod__diff__left__eq,axiom,
% 5.07/5.29 ! [A: int,C: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.07/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_left_eq
% 5.07/5.29 thf(fact_834_mod__diff__left__eq,axiom,
% 5.07/5.29 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_left_eq
% 5.07/5.29 thf(fact_835_mod__diff__cong,axiom,
% 5.07/5.29 ! [A: int,C: int,A5: int,B: int,B4: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ A @ C )
% 5.07/5.29 = ( modulo_modulo_int @ A5 @ C ) )
% 5.07/5.29 => ( ( ( modulo_modulo_int @ B @ C )
% 5.07/5.29 = ( modulo_modulo_int @ B4 @ C ) )
% 5.07/5.29 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.07/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_cong
% 5.07/5.29 thf(fact_836_mod__diff__cong,axiom,
% 5.07/5.29 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B4: code_integer] :
% 5.07/5.29 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.07/5.29 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.07/5.29 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_cong
% 5.07/5.29 thf(fact_837_mod__diff__eq,axiom,
% 5.07/5.29 ! [A: int,C: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.07/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_eq
% 5.07/5.29 thf(fact_838_mod__diff__eq,axiom,
% 5.07/5.29 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_diff_eq
% 5.07/5.29 thf(fact_839_mod__minus__right,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_right
% 5.07/5.29 thf(fact_840_mod__minus__right,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.29 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_right
% 5.07/5.29 thf(fact_841_mod__minus__cong,axiom,
% 5.07/5.29 ! [A: int,B: int,A5: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 = ( modulo_modulo_int @ A5 @ B ) )
% 5.07/5.29 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.07/5.29 = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_cong
% 5.07/5.29 thf(fact_842_mod__minus__cong,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer,A5: code_integer] :
% 5.07/5.29 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.07/5.29 = ( modulo364778990260209775nteger @ A5 @ B ) )
% 5.07/5.29 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_cong
% 5.07/5.29 thf(fact_843_mod__minus__eq,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.07/5.29 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_eq
% 5.07/5.29 thf(fact_844_mod__minus__eq,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.07/5.29 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_minus_eq
% 5.07/5.29 thf(fact_845_zero__le,axiom,
% 5.07/5.29 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.07/5.29
% 5.07/5.29 % zero_le
% 5.07/5.29 thf(fact_846_le__numeral__extra_I3_J,axiom,
% 5.07/5.29 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(3)
% 5.07/5.29 thf(fact_847_le__numeral__extra_I3_J,axiom,
% 5.07/5.29 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(3)
% 5.07/5.29 thf(fact_848_le__numeral__extra_I3_J,axiom,
% 5.07/5.29 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(3)
% 5.07/5.29 thf(fact_849_le__numeral__extra_I3_J,axiom,
% 5.07/5.29 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(3)
% 5.07/5.29 thf(fact_850_verit__comp__simplify1_I3_J,axiom,
% 5.07/5.29 ! [B4: real,A5: real] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_real @ B4 @ A5 ) )
% 5.07/5.29 = ( ord_less_real @ A5 @ B4 ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(3)
% 5.07/5.29 thf(fact_851_verit__comp__simplify1_I3_J,axiom,
% 5.07/5.29 ! [B4: rat,A5: rat] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_rat @ B4 @ A5 ) )
% 5.07/5.29 = ( ord_less_rat @ A5 @ B4 ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(3)
% 5.07/5.29 thf(fact_852_verit__comp__simplify1_I3_J,axiom,
% 5.07/5.29 ! [B4: num,A5: num] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_num @ B4 @ A5 ) )
% 5.07/5.29 = ( ord_less_num @ A5 @ B4 ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(3)
% 5.07/5.29 thf(fact_853_verit__comp__simplify1_I3_J,axiom,
% 5.07/5.29 ! [B4: nat,A5: nat] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_nat @ B4 @ A5 ) )
% 5.07/5.29 = ( ord_less_nat @ A5 @ B4 ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(3)
% 5.07/5.29 thf(fact_854_verit__comp__simplify1_I3_J,axiom,
% 5.07/5.29 ! [B4: int,A5: int] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_int @ B4 @ A5 ) )
% 5.07/5.29 = ( ord_less_int @ A5 @ B4 ) ) ).
% 5.07/5.29
% 5.07/5.29 % verit_comp_simplify1(3)
% 5.07/5.29 thf(fact_855_le__numeral__extra_I4_J,axiom,
% 5.07/5.29 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(4)
% 5.07/5.29 thf(fact_856_le__numeral__extra_I4_J,axiom,
% 5.07/5.29 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(4)
% 5.07/5.29 thf(fact_857_le__numeral__extra_I4_J,axiom,
% 5.07/5.29 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(4)
% 5.07/5.29 thf(fact_858_le__numeral__extra_I4_J,axiom,
% 5.07/5.29 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.07/5.29
% 5.07/5.29 % le_numeral_extra(4)
% 5.07/5.29 thf(fact_859_diff__mono,axiom,
% 5.07/5.29 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 => ( ( ord_less_eq_rat @ D @ C )
% 5.07/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_mono
% 5.07/5.29 thf(fact_860_diff__mono,axiom,
% 5.07/5.29 ! [A: int,B: int,D: int,C: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.07/5.29 => ( ( ord_less_eq_int @ D @ C )
% 5.07/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_mono
% 5.07/5.29 thf(fact_861_diff__left__mono,axiom,
% 5.07/5.29 ! [B: rat,A: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ B @ A )
% 5.07/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_left_mono
% 5.07/5.29 thf(fact_862_diff__left__mono,axiom,
% 5.07/5.29 ! [B: int,A: int,C: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ B @ A )
% 5.07/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_left_mono
% 5.07/5.29 thf(fact_863_diff__right__mono,axiom,
% 5.07/5.29 ! [A: rat,B: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_right_mono
% 5.07/5.29 thf(fact_864_diff__right__mono,axiom,
% 5.07/5.29 ! [A: int,B: int,C: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.07/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_right_mono
% 5.07/5.29 thf(fact_865_diff__eq__diff__less__eq,axiom,
% 5.07/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.07/5.29 ( ( ( minus_minus_rat @ A @ B )
% 5.07/5.29 = ( minus_minus_rat @ C @ D ) )
% 5.07/5.29 => ( ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_eq_diff_less_eq
% 5.07/5.29 thf(fact_866_diff__eq__diff__less__eq,axiom,
% 5.07/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.07/5.29 ( ( ( minus_minus_int @ A @ B )
% 5.07/5.29 = ( minus_minus_int @ C @ D ) )
% 5.07/5.29 => ( ( ord_less_eq_int @ A @ B )
% 5.07/5.29 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_eq_diff_less_eq
% 5.07/5.29 thf(fact_867_le__minus__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.07/5.29 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_minus_iff
% 5.07/5.29 thf(fact_868_le__minus__iff,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_minus_iff
% 5.07/5.29 thf(fact_869_le__minus__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.07/5.29 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_minus_iff
% 5.07/5.29 thf(fact_870_le__minus__iff,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.07/5.29 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_minus_iff
% 5.07/5.29 thf(fact_871_minus__le__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.07/5.29 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_le_iff
% 5.07/5.29 thf(fact_872_minus__le__iff,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.07/5.29 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_le_iff
% 5.07/5.29 thf(fact_873_minus__le__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.07/5.29 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_le_iff
% 5.07/5.29 thf(fact_874_minus__le__iff,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.07/5.29 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_le_iff
% 5.07/5.29 thf(fact_875_le__imp__neg__le,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.07/5.29 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_imp_neg_le
% 5.07/5.29 thf(fact_876_le__imp__neg__le,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.07/5.29 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_imp_neg_le
% 5.07/5.29 thf(fact_877_le__imp__neg__le,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_imp_neg_le
% 5.07/5.29 thf(fact_878_le__imp__neg__le,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.07/5.29 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_imp_neg_le
% 5.07/5.29 thf(fact_879_compl__le__swap2,axiom,
% 5.07/5.29 ! [Y: set_nat,X: set_nat] :
% 5.07/5.29 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 5.07/5.29 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 5.07/5.29
% 5.07/5.29 % compl_le_swap2
% 5.07/5.29 thf(fact_880_compl__le__swap1,axiom,
% 5.07/5.29 ! [Y: set_nat,X: set_nat] :
% 5.07/5.29 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 5.07/5.29 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % compl_le_swap1
% 5.07/5.29 thf(fact_881_compl__mono,axiom,
% 5.07/5.29 ! [X: set_nat,Y: set_nat] :
% 5.07/5.29 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.07/5.29 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % compl_mono
% 5.07/5.29 thf(fact_882_Suc__leD,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % Suc_leD
% 5.07/5.29 thf(fact_883_le__SucE,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.07/5.29 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( M2
% 5.07/5.29 = ( suc @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_SucE
% 5.07/5.29 thf(fact_884_le__SucI,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_SucI
% 5.07/5.29 thf(fact_885_Suc__le__D,axiom,
% 5.07/5.29 ! [N: nat,M6: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 5.07/5.29 => ? [M3: nat] :
% 5.07/5.29 ( M6
% 5.07/5.29 = ( suc @ M3 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Suc_le_D
% 5.07/5.29 thf(fact_886_le__Suc__eq,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.07/5.29 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 | ( M2
% 5.07/5.29 = ( suc @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_Suc_eq
% 5.07/5.29 thf(fact_887_Suc__n__not__le__n,axiom,
% 5.07/5.29 ! [N: nat] :
% 5.07/5.29 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.07/5.29
% 5.07/5.29 % Suc_n_not_le_n
% 5.07/5.29 thf(fact_888_not__less__eq__eq,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 5.07/5.29 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % not_less_eq_eq
% 5.07/5.29 thf(fact_889_full__nat__induct,axiom,
% 5.07/5.29 ! [P: nat > $o,N: nat] :
% 5.07/5.29 ( ! [N2: nat] :
% 5.07/5.29 ( ! [M: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.07/5.29 => ( P @ M ) )
% 5.07/5.29 => ( P @ N2 ) )
% 5.07/5.29 => ( P @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % full_nat_induct
% 5.07/5.29 thf(fact_890_nat__induct__at__least,axiom,
% 5.07/5.29 ! [M2: nat,N: nat,P: nat > $o] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ( P @ M2 )
% 5.07/5.29 => ( ! [N2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.07/5.29 => ( ( P @ N2 )
% 5.07/5.29 => ( P @ ( suc @ N2 ) ) ) )
% 5.07/5.29 => ( P @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_induct_at_least
% 5.07/5.29 thf(fact_891_transitive__stepwise__le,axiom,
% 5.07/5.29 ! [M2: nat,N: nat,R2: nat > nat > $o] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 5.07/5.29 => ( ! [X3: nat,Y3: nat,Z4: nat] :
% 5.07/5.29 ( ( R2 @ X3 @ Y3 )
% 5.07/5.29 => ( ( R2 @ Y3 @ Z4 )
% 5.07/5.29 => ( R2 @ X3 @ Z4 ) ) )
% 5.07/5.29 => ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
% 5.07/5.29 => ( R2 @ M2 @ N ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % transitive_stepwise_le
% 5.07/5.29 thf(fact_892_le__0__eq,axiom,
% 5.07/5.29 ! [N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.07/5.29 = ( N = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_0_eq
% 5.07/5.29 thf(fact_893_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.07/5.29 => ( A = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % bot_nat_0.extremum_uniqueI
% 5.07/5.29 thf(fact_894_bot__nat__0_Oextremum__unique,axiom,
% 5.07/5.29 ! [A: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.07/5.29 = ( A = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % bot_nat_0.extremum_unique
% 5.07/5.29 thf(fact_895_less__eq__nat_Osimps_I1_J,axiom,
% 5.07/5.29 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.07/5.29
% 5.07/5.29 % less_eq_nat.simps(1)
% 5.07/5.29 thf(fact_896_real__arch__simple,axiom,
% 5.07/5.29 ! [X: real] :
% 5.07/5.29 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % real_arch_simple
% 5.07/5.29 thf(fact_897_real__arch__simple,axiom,
% 5.07/5.29 ! [X: rat] :
% 5.07/5.29 ? [N2: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.07/5.29
% 5.07/5.29 % real_arch_simple
% 5.07/5.29 thf(fact_898_less__mono__imp__le__mono,axiom,
% 5.07/5.29 ! [F: nat > nat,I: nat,J2: nat] :
% 5.07/5.29 ( ! [I3: nat,J: nat] :
% 5.07/5.29 ( ( ord_less_nat @ I3 @ J )
% 5.07/5.29 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J ) ) )
% 5.07/5.29 => ( ( ord_less_eq_nat @ I @ J2 )
% 5.07/5.29 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J2 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_mono_imp_le_mono
% 5.07/5.29 thf(fact_899_le__neq__implies__less,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ( M2 != N )
% 5.07/5.29 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_neq_implies_less
% 5.07/5.29 thf(fact_900_less__or__eq__imp__le,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ( ord_less_nat @ M2 @ N )
% 5.07/5.29 | ( M2 = N ) )
% 5.07/5.29 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_or_eq_imp_le
% 5.07/5.29 thf(fact_901_le__eq__less__or__eq,axiom,
% 5.07/5.29 ( ord_less_eq_nat
% 5.07/5.29 = ( ^ [M5: nat,N4: nat] :
% 5.07/5.29 ( ( ord_less_nat @ M5 @ N4 )
% 5.07/5.29 | ( M5 = N4 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_eq_less_or_eq
% 5.07/5.29 thf(fact_902_less__imp__le__nat,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_nat @ M2 @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.07/5.29
% 5.07/5.29 % less_imp_le_nat
% 5.07/5.29 thf(fact_903_nat__less__le,axiom,
% 5.07/5.29 ( ord_less_nat
% 5.07/5.29 = ( ^ [M5: nat,N4: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.07/5.29 & ( M5 != N4 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_less_le
% 5.07/5.29 thf(fact_904_less__eq__int__code_I1_J,axiom,
% 5.07/5.29 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.07/5.29
% 5.07/5.29 % less_eq_int_code(1)
% 5.07/5.29 thf(fact_905_eq__diff__iff,axiom,
% 5.07/5.29 ! [K: nat,M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ K @ M2 )
% 5.07/5.29 => ( ( ord_less_eq_nat @ K @ N )
% 5.07/5.29 => ( ( ( minus_minus_nat @ M2 @ K )
% 5.07/5.29 = ( minus_minus_nat @ N @ K ) )
% 5.07/5.29 = ( M2 = N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % eq_diff_iff
% 5.07/5.29 thf(fact_906_le__diff__iff,axiom,
% 5.07/5.29 ! [K: nat,M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ K @ M2 )
% 5.07/5.29 => ( ( ord_less_eq_nat @ K @ N )
% 5.07/5.29 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.07/5.29 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_diff_iff
% 5.07/5.29 thf(fact_907_Nat_Odiff__diff__eq,axiom,
% 5.07/5.29 ! [K: nat,M2: nat,N: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ K @ M2 )
% 5.07/5.29 => ( ( ord_less_eq_nat @ K @ N )
% 5.07/5.29 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.07/5.29 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % Nat.diff_diff_eq
% 5.07/5.29 thf(fact_908_diff__le__mono,axiom,
% 5.07/5.29 ! [M2: nat,N: nat,L: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_le_mono
% 5.07/5.29 thf(fact_909_diff__le__self,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 5.07/5.29
% 5.07/5.29 % diff_le_self
% 5.07/5.29 thf(fact_910_le__diff__iff_H,axiom,
% 5.07/5.29 ! [A: nat,C: nat,B: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ A @ C )
% 5.07/5.29 => ( ( ord_less_eq_nat @ B @ C )
% 5.07/5.29 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.07/5.29 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_diff_iff'
% 5.07/5.29 thf(fact_911_diff__le__mono2,axiom,
% 5.07/5.29 ! [M2: nat,N: nat,L: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % diff_le_mono2
% 5.07/5.29 thf(fact_912_div__le__dividend,axiom,
% 5.07/5.29 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ).
% 5.07/5.29
% 5.07/5.29 % div_le_dividend
% 5.07/5.29 thf(fact_913_div__le__mono,axiom,
% 5.07/5.29 ! [M2: nat,N: nat,K: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ M2 @ N )
% 5.07/5.29 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % div_le_mono
% 5.07/5.29 thf(fact_914_real__of__nat__div4,axiom,
% 5.07/5.29 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % real_of_nat_div4
% 5.07/5.29 thf(fact_915_real__of__nat__div3,axiom,
% 5.07/5.29 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 5.07/5.29
% 5.07/5.29 % real_of_nat_div3
% 5.07/5.29 thf(fact_916_real__of__nat__div2,axiom,
% 5.07/5.29 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % real_of_nat_div2
% 5.07/5.29 thf(fact_917_nat__less__eq__zless,axiom,
% 5.07/5.29 ! [W: int,Z2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 5.07/5.29 = ( ord_less_int @ W @ Z2 ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_less_eq_zless
% 5.07/5.29 thf(fact_918_nat__eq__iff,axiom,
% 5.07/5.29 ! [W: int,M2: nat] :
% 5.07/5.29 ( ( ( nat2 @ W )
% 5.07/5.29 = M2 )
% 5.07/5.29 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( W
% 5.07/5.29 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.07/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_eq_iff
% 5.07/5.29 thf(fact_919_nat__eq__iff2,axiom,
% 5.07/5.29 ! [M2: nat,W: int] :
% 5.07/5.29 ( ( M2
% 5.07/5.29 = ( nat2 @ W ) )
% 5.07/5.29 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( W
% 5.07/5.29 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.07/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_eq_iff2
% 5.07/5.29 thf(fact_920_nat__diff__distrib_H,axiom,
% 5.07/5.29 ! [X: int,Y: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.07/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.07/5.29 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 5.07/5.29 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_diff_distrib'
% 5.07/5.29 thf(fact_921_nat__diff__distrib,axiom,
% 5.07/5.29 ! [Z3: int,Z2: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.07/5.29 => ( ( ord_less_eq_int @ Z3 @ Z2 )
% 5.07/5.29 => ( ( nat2 @ ( minus_minus_int @ Z2 @ Z3 ) )
% 5.07/5.29 = ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z3 ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_diff_distrib
% 5.07/5.29 thf(fact_922_nat__div__distrib_H,axiom,
% 5.07/5.29 ! [Y: int,X: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.07/5.29 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.07/5.29 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_div_distrib'
% 5.07/5.29 thf(fact_923_nat__div__distrib,axiom,
% 5.07/5.29 ! [X: int,Y: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.07/5.29 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.07/5.29 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_div_distrib
% 5.07/5.29 thf(fact_924_mod__pos__geq,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ L )
% 5.07/5.29 => ( ( ord_less_eq_int @ L @ K )
% 5.07/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.07/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_pos_geq
% 5.07/5.29 thf(fact_925_old_Onat_Osimps_I5_J,axiom,
% 5.07/5.29 ! [F1: $o,F22: nat > $o,X23: nat] :
% 5.07/5.29 ( ( case_nat_o @ F1 @ F22 @ ( suc @ X23 ) )
% 5.07/5.29 = ( F22 @ X23 ) ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(5)
% 5.07/5.29 thf(fact_926_old_Onat_Osimps_I5_J,axiom,
% 5.07/5.29 ! [F1: nat,F22: nat > nat,X23: nat] :
% 5.07/5.29 ( ( case_nat_nat @ F1 @ F22 @ ( suc @ X23 ) )
% 5.07/5.29 = ( F22 @ X23 ) ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(5)
% 5.07/5.29 thf(fact_927_old_Onat_Osimps_I5_J,axiom,
% 5.07/5.29 ! [F1: option_num,F22: nat > option_num,X23: nat] :
% 5.07/5.29 ( ( case_nat_option_num @ F1 @ F22 @ ( suc @ X23 ) )
% 5.07/5.29 = ( F22 @ X23 ) ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(5)
% 5.07/5.29 thf(fact_928_old_Onat_Osimps_I4_J,axiom,
% 5.07/5.29 ! [F1: $o,F22: nat > $o] :
% 5.07/5.29 ( ( case_nat_o @ F1 @ F22 @ zero_zero_nat )
% 5.07/5.29 = F1 ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(4)
% 5.07/5.29 thf(fact_929_old_Onat_Osimps_I4_J,axiom,
% 5.07/5.29 ! [F1: nat,F22: nat > nat] :
% 5.07/5.29 ( ( case_nat_nat @ F1 @ F22 @ zero_zero_nat )
% 5.07/5.29 = F1 ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(4)
% 5.07/5.29 thf(fact_930_old_Onat_Osimps_I4_J,axiom,
% 5.07/5.29 ! [F1: option_num,F22: nat > option_num] :
% 5.07/5.29 ( ( case_nat_option_num @ F1 @ F22 @ zero_zero_nat )
% 5.07/5.29 = F1 ) ).
% 5.07/5.29
% 5.07/5.29 % old.nat.simps(4)
% 5.07/5.29 thf(fact_931_power__diff__power__eq,axiom,
% 5.07/5.29 ! [A: nat,N: nat,M2: nat] :
% 5.07/5.29 ( ( A != zero_zero_nat )
% 5.07/5.29 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.07/5.29 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 5.07/5.29 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.07/5.29 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % power_diff_power_eq
% 5.07/5.29 thf(fact_932_power__diff__power__eq,axiom,
% 5.07/5.29 ! [A: int,N: nat,M2: nat] :
% 5.07/5.29 ( ( A != zero_zero_int )
% 5.07/5.29 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.07/5.29 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 5.07/5.29 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.07/5.29 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % power_diff_power_eq
% 5.07/5.29 thf(fact_933_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.07/5.29 ! [B: int,A: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ B )
% 5.07/5.29 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.07/5.29 thf(fact_934_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.07/5.29 ! [B: nat,A: nat] :
% 5.07/5.29 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.07/5.29 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.07/5.29 thf(fact_935_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.07/5.29 ! [B: code_integer,A: code_integer] :
% 5.07/5.29 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.07/5.29 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.07/5.29
% 5.07/5.29 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.07/5.29 thf(fact_936_nat__less__iff,axiom,
% 5.07/5.29 ! [W: int,M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.07/5.29 => ( ( ord_less_nat @ ( nat2 @ W ) @ M2 )
% 5.07/5.29 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_less_iff
% 5.07/5.29 thf(fact_937_mod__eq__self__iff__div__eq__0,axiom,
% 5.07/5.29 ! [A: int,B: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ A @ B )
% 5.07/5.29 = A )
% 5.07/5.29 = ( ( divide_divide_int @ A @ B )
% 5.07/5.29 = zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_eq_self_iff_div_eq_0
% 5.07/5.29 thf(fact_938_mod__eq__self__iff__div__eq__0,axiom,
% 5.07/5.29 ! [A: nat,B: nat] :
% 5.07/5.29 ( ( ( modulo_modulo_nat @ A @ B )
% 5.07/5.29 = A )
% 5.07/5.29 = ( ( divide_divide_nat @ A @ B )
% 5.07/5.29 = zero_zero_nat ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_eq_self_iff_div_eq_0
% 5.07/5.29 thf(fact_939_mod__eq__self__iff__div__eq__0,axiom,
% 5.07/5.29 ! [A: code_integer,B: code_integer] :
% 5.07/5.29 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.07/5.29 = A )
% 5.07/5.29 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.07/5.29 = zero_z3403309356797280102nteger ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_eq_self_iff_div_eq_0
% 5.07/5.29 thf(fact_940_mod__eq__self__iff__div__eq__0,axiom,
% 5.07/5.29 ! [A: code_natural,B: code_natural] :
% 5.07/5.29 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.07/5.29 = A )
% 5.07/5.29 = ( ( divide5121882707175180666atural @ A @ B )
% 5.07/5.29 = zero_z2226904508553997617atural ) ) ).
% 5.07/5.29
% 5.07/5.29 % mod_eq_self_iff_div_eq_0
% 5.07/5.29 thf(fact_941_inverse__of__nat__le,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( N != zero_zero_nat )
% 5.07/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % inverse_of_nat_le
% 5.07/5.29 thf(fact_942_inverse__of__nat__le,axiom,
% 5.07/5.29 ! [N: nat,M2: nat] :
% 5.07/5.29 ( ( ord_less_eq_nat @ N @ M2 )
% 5.07/5.29 => ( ( N != zero_zero_nat )
% 5.07/5.29 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % inverse_of_nat_le
% 5.07/5.29 thf(fact_943_nat__zero__as__int,axiom,
% 5.07/5.29 ( zero_zero_nat
% 5.07/5.29 = ( nat2 @ zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_zero_as_int
% 5.07/5.29 thf(fact_944_minus__mod__int__eq,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.07/5.29 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.07/5.29 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % minus_mod_int_eq
% 5.07/5.29 thf(fact_945_nat__one__as__int,axiom,
% 5.07/5.29 ( one_one_nat
% 5.07/5.29 = ( nat2 @ one_one_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % nat_one_as_int
% 5.07/5.29 thf(fact_946_Euclidean__Division_Opos__mod__bound,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ zero_zero_int @ L )
% 5.07/5.29 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.07/5.29
% 5.07/5.29 % Euclidean_Division.pos_mod_bound
% 5.07/5.29 thf(fact_947_neg__mod__bound,axiom,
% 5.07/5.29 ! [L: int,K: int] :
% 5.07/5.29 ( ( ord_less_int @ L @ zero_zero_int )
% 5.07/5.29 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % neg_mod_bound
% 5.07/5.29 thf(fact_948_zmod__zminus1__not__zero,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.07/5.29 != zero_zero_int )
% 5.07/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.07/5.29 != zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % zmod_zminus1_not_zero
% 5.07/5.29 thf(fact_949_zmod__zminus2__not__zero,axiom,
% 5.07/5.29 ! [K: int,L: int] :
% 5.07/5.29 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.07/5.29 != zero_zero_int )
% 5.07/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.07/5.29 != zero_zero_int ) ) ).
% 5.07/5.29
% 5.07/5.29 % zmod_zminus2_not_zero
% 5.07/5.29 thf(fact_950_not__one__le__zero,axiom,
% 5.07/5.29 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.07/5.29
% 5.07/5.29 % not_one_le_zero
% 5.07/5.29 thf(fact_951_not__one__le__zero,axiom,
% 5.07/5.29 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.07/5.29
% 5.07/5.29 % not_one_le_zero
% 5.07/5.29 thf(fact_952_not__one__le__zero,axiom,
% 5.07/5.29 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.07/5.29
% 5.07/5.29 % not_one_le_zero
% 5.07/5.29 thf(fact_953_not__one__le__zero,axiom,
% 5.07/5.29 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.07/5.29
% 5.07/5.29 % not_one_le_zero
% 5.07/5.29 thf(fact_954_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.07/5.29
% 5.07/5.29 % linordered_nonzero_semiring_class.zero_le_one
% 5.07/5.29 thf(fact_955_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.07/5.29
% 5.07/5.29 % linordered_nonzero_semiring_class.zero_le_one
% 5.07/5.29 thf(fact_956_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.07/5.29
% 5.07/5.29 % linordered_nonzero_semiring_class.zero_le_one
% 5.07/5.29 thf(fact_957_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.07/5.29
% 5.07/5.29 % linordered_nonzero_semiring_class.zero_le_one
% 5.07/5.29 thf(fact_958_zero__less__one__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.07/5.29
% 5.07/5.29 % zero_less_one_class.zero_le_one
% 5.07/5.29 thf(fact_959_zero__less__one__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.07/5.29
% 5.07/5.29 % zero_less_one_class.zero_le_one
% 5.07/5.29 thf(fact_960_zero__less__one__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.07/5.29
% 5.07/5.29 % zero_less_one_class.zero_le_one
% 5.07/5.29 thf(fact_961_zero__less__one__class_Ozero__le__one,axiom,
% 5.07/5.29 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.07/5.29
% 5.07/5.29 % zero_less_one_class.zero_le_one
% 5.07/5.29 thf(fact_962_le__iff__diff__le__0,axiom,
% 5.07/5.29 ( ord_less_eq_real
% 5.07/5.29 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_iff_diff_le_0
% 5.07/5.29 thf(fact_963_le__iff__diff__le__0,axiom,
% 5.07/5.29 ( ord_less_eq_rat
% 5.07/5.29 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_iff_diff_le_0
% 5.07/5.29 thf(fact_964_le__iff__diff__le__0,axiom,
% 5.07/5.29 ( ord_less_eq_int
% 5.07/5.29 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % le_iff_diff_le_0
% 5.07/5.29 thf(fact_965_divide__le__0__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.07/5.29 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.07/5.29 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_0_iff
% 5.07/5.29 thf(fact_966_divide__le__0__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.07/5.29 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.07/5.29 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_le_0_iff
% 5.07/5.29 thf(fact_967_divide__right__mono,axiom,
% 5.07/5.29 ! [A: real,B: real,C: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.07/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.07/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_right_mono
% 5.07/5.29 thf(fact_968_divide__right__mono,axiom,
% 5.07/5.29 ! [A: rat,B: rat,C: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.07/5.29 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.07/5.29 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_right_mono
% 5.07/5.29 thf(fact_969_zero__le__divide__iff,axiom,
% 5.07/5.29 ! [A: real,B: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.07/5.29 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.07/5.29 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.07/5.29 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.07/5.29 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_le_divide_iff
% 5.07/5.29 thf(fact_970_zero__le__divide__iff,axiom,
% 5.07/5.29 ! [A: rat,B: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.07/5.29 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.07/5.29 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.07/5.29 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.07/5.29 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % zero_le_divide_iff
% 5.07/5.29 thf(fact_971_divide__nonneg__nonneg,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.07/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.07/5.29 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonneg_nonneg
% 5.07/5.29 thf(fact_972_divide__nonneg__nonneg,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.07/5.29 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.07/5.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonneg_nonneg
% 5.07/5.29 thf(fact_973_divide__nonneg__nonpos,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.07/5.29 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.07/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonneg_nonpos
% 5.07/5.29 thf(fact_974_divide__nonneg__nonpos,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.07/5.29 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.07/5.29 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonneg_nonpos
% 5.07/5.29 thf(fact_975_divide__nonpos__nonneg,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.07/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.07/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonpos_nonneg
% 5.07/5.29 thf(fact_976_divide__nonpos__nonneg,axiom,
% 5.07/5.29 ! [X: rat,Y: rat] :
% 5.07/5.29 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.07/5.29 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.07/5.29 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.07/5.29
% 5.07/5.29 % divide_nonpos_nonneg
% 5.07/5.29 thf(fact_977_divide__nonpos__nonpos,axiom,
% 5.07/5.29 ! [X: real,Y: real] :
% 5.07/5.29 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.29 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.12/5.29 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.29
% 5.12/5.29 % divide_nonpos_nonpos
% 5.12/5.29 thf(fact_978_divide__nonpos__nonpos,axiom,
% 5.12/5.29 ! [X: rat,Y: rat] :
% 5.12/5.29 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.29 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.12/5.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.29
% 5.12/5.29 % divide_nonpos_nonpos
% 5.12/5.29 thf(fact_979_divide__right__mono__neg,axiom,
% 5.12/5.29 ! [A: real,B: real,C: real] :
% 5.12/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.29 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.12/5.29
% 5.12/5.29 % divide_right_mono_neg
% 5.12/5.29 thf(fact_980_divide__right__mono__neg,axiom,
% 5.12/5.29 ! [A: rat,B: rat,C: rat] :
% 5.12/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.29 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.29 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.12/5.29
% 5.12/5.29 % divide_right_mono_neg
% 5.12/5.29 thf(fact_981_le__minus__one__simps_I2_J,axiom,
% 5.12/5.29 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(2)
% 5.12/5.29 thf(fact_982_le__minus__one__simps_I2_J,axiom,
% 5.12/5.29 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(2)
% 5.12/5.29 thf(fact_983_le__minus__one__simps_I2_J,axiom,
% 5.12/5.29 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(2)
% 5.12/5.29 thf(fact_984_le__minus__one__simps_I2_J,axiom,
% 5.12/5.29 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(2)
% 5.12/5.29 thf(fact_985_le__minus__one__simps_I4_J,axiom,
% 5.12/5.29 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(4)
% 5.12/5.29 thf(fact_986_le__minus__one__simps_I4_J,axiom,
% 5.12/5.29 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.29
% 5.12/5.29 % le_minus_one_simps(4)
% 5.12/5.29 thf(fact_987_le__minus__one__simps_I4_J,axiom,
% 5.12/5.30 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(4)
% 5.12/5.30 thf(fact_988_le__minus__one__simps_I4_J,axiom,
% 5.12/5.30 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(4)
% 5.12/5.30 thf(fact_989_of__nat__0__le__iff,axiom,
% 5.12/5.30 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_0_le_iff
% 5.12/5.30 thf(fact_990_of__nat__0__le__iff,axiom,
% 5.12/5.30 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_0_le_iff
% 5.12/5.30 thf(fact_991_of__nat__0__le__iff,axiom,
% 5.12/5.30 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_0_le_iff
% 5.12/5.30 thf(fact_992_of__nat__0__le__iff,axiom,
% 5.12/5.30 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_0_le_iff
% 5.12/5.30 thf(fact_993_Suc__leI,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ M2 @ N )
% 5.12/5.30 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % Suc_leI
% 5.12/5.30 thf(fact_994_Suc__le__eq,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.12/5.30 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % Suc_le_eq
% 5.12/5.30 thf(fact_995_dec__induct,axiom,
% 5.12/5.30 ! [I: nat,J2: nat,P: nat > $o] :
% 5.12/5.30 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.30 => ( ( P @ I )
% 5.12/5.30 => ( ! [N2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ I @ N2 )
% 5.12/5.30 => ( ( ord_less_nat @ N2 @ J2 )
% 5.12/5.30 => ( ( P @ N2 )
% 5.12/5.30 => ( P @ ( suc @ N2 ) ) ) ) )
% 5.12/5.30 => ( P @ J2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % dec_induct
% 5.12/5.30 thf(fact_996_inc__induct,axiom,
% 5.12/5.30 ! [I: nat,J2: nat,P: nat > $o] :
% 5.12/5.30 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.30 => ( ( P @ J2 )
% 5.12/5.30 => ( ! [N2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ I @ N2 )
% 5.12/5.30 => ( ( ord_less_nat @ N2 @ J2 )
% 5.12/5.30 => ( ( P @ ( suc @ N2 ) )
% 5.12/5.30 => ( P @ N2 ) ) ) )
% 5.12/5.30 => ( P @ I ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % inc_induct
% 5.12/5.30 thf(fact_997_Suc__le__lessD,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % Suc_le_lessD
% 5.12/5.30 thf(fact_998_le__less__Suc__eq,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.30 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.12/5.30 = ( N = M2 ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_less_Suc_eq
% 5.12/5.30 thf(fact_999_less__Suc__eq__le,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % less_Suc_eq_le
% 5.12/5.30 thf(fact_1000_less__eq__Suc__le,axiom,
% 5.12/5.30 ( ord_less_nat
% 5.12/5.30 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % less_eq_Suc_le
% 5.12/5.30 thf(fact_1001_le__imp__less__Suc,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.30 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_imp_less_Suc
% 5.12/5.30 thf(fact_1002_ex__least__nat__le,axiom,
% 5.12/5.30 ! [P: nat > $o,N: nat] :
% 5.12/5.30 ( ( P @ N )
% 5.12/5.30 => ( ~ ( P @ zero_zero_nat )
% 5.12/5.30 => ? [K2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ K2 @ N )
% 5.12/5.30 & ! [I4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ I4 @ K2 )
% 5.12/5.30 => ~ ( P @ I4 ) )
% 5.12/5.30 & ( P @ K2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ex_least_nat_le
% 5.12/5.30 thf(fact_1003_Suc__diff__le,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 5.12/5.30 = ( suc @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % Suc_diff_le
% 5.12/5.30 thf(fact_1004_less__diff__iff,axiom,
% 5.12/5.30 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ K @ M2 )
% 5.12/5.30 => ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.30 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.12/5.30 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % less_diff_iff
% 5.12/5.30 thf(fact_1005_diff__less__mono,axiom,
% 5.12/5.30 ! [A: nat,B: nat,C: nat] :
% 5.12/5.30 ( ( ord_less_nat @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_nat @ C @ A )
% 5.12/5.30 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % diff_less_mono
% 5.12/5.30 thf(fact_1006_Suc__div__le__mono,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % Suc_div_le_mono
% 5.12/5.30 thf(fact_1007_nonneg__int__cases,axiom,
% 5.12/5.30 ! [K: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.30 => ~ ! [N2: nat] :
% 5.12/5.30 ( K
% 5.12/5.30 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nonneg_int_cases
% 5.12/5.30 thf(fact_1008_zero__le__imp__eq__int,axiom,
% 5.12/5.30 ! [K: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.30 => ? [N2: nat] :
% 5.12/5.30 ( K
% 5.12/5.30 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_le_imp_eq_int
% 5.12/5.30 thf(fact_1009_int__le__induct,axiom,
% 5.12/5.30 ! [I: int,K: int,P: int > $o] :
% 5.12/5.30 ( ( ord_less_eq_int @ I @ K )
% 5.12/5.30 => ( ( P @ K )
% 5.12/5.30 => ( ! [I3: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ I3 @ K )
% 5.12/5.30 => ( ( P @ I3 )
% 5.12/5.30 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.12/5.30 => ( P @ I ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % int_le_induct
% 5.12/5.30 thf(fact_1010_nat__mono__iff,axiom,
% 5.12/5.30 ! [Z2: int,W: int] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.30 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 5.12/5.30 = ( ord_less_int @ W @ Z2 ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_mono_iff
% 5.12/5.30 thf(fact_1011_zless__nat__eq__int__zless,axiom,
% 5.12/5.30 ! [M2: nat,Z2: int] :
% 5.12/5.30 ( ( ord_less_nat @ M2 @ ( nat2 @ Z2 ) )
% 5.12/5.30 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ Z2 ) ) ).
% 5.12/5.30
% 5.12/5.30 % zless_nat_eq_int_zless
% 5.12/5.30 thf(fact_1012_int__minus,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.30 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % int_minus
% 5.12/5.30 thf(fact_1013_divide__nonpos__pos,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonpos_pos
% 5.12/5.30 thf(fact_1014_divide__nonpos__pos,axiom,
% 5.12/5.30 ! [X: rat,Y: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.30 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonpos_pos
% 5.12/5.30 thf(fact_1015_divide__nonpos__neg,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.30 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.12/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonpos_neg
% 5.12/5.30 thf(fact_1016_divide__nonpos__neg,axiom,
% 5.12/5.30 ! [X: rat,Y: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.30 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonpos_neg
% 5.12/5.30 thf(fact_1017_divide__nonneg__pos,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonneg_pos
% 5.12/5.30 thf(fact_1018_divide__nonneg__pos,axiom,
% 5.12/5.30 ! [X: rat,Y: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonneg_pos
% 5.12/5.30 thf(fact_1019_divide__nonneg__neg,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.12/5.30 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonneg_neg
% 5.12/5.30 thf(fact_1020_divide__nonneg__neg,axiom,
% 5.12/5.30 ! [X: rat,Y: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.30 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_nonneg_neg
% 5.12/5.30 thf(fact_1021_divide__le__cancel,axiom,
% 5.12/5.30 ! [A: real,C: real,B: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.12/5.30 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.30 => ( ord_less_eq_real @ A @ B ) )
% 5.12/5.30 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.30 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_le_cancel
% 5.12/5.30 thf(fact_1022_divide__le__cancel,axiom,
% 5.12/5.30 ! [A: rat,C: rat,B: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.30 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.30 => ( ord_less_eq_rat @ A @ B ) )
% 5.12/5.30 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_le_cancel
% 5.12/5.30 thf(fact_1023_frac__less2,axiom,
% 5.12/5.30 ! [X: real,Y: real,W: real,Z2: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.12/5.30 => ( ( ord_less_real @ W @ Z2 )
% 5.12/5.30 => ( ord_less_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_less2
% 5.12/5.30 thf(fact_1024_frac__less2,axiom,
% 5.12/5.30 ! [X: rat,Y: rat,W: rat,Z2: rat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.30 => ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.12/5.30 => ( ( ord_less_rat @ W @ Z2 )
% 5.12/5.30 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_less2
% 5.12/5.30 thf(fact_1025_frac__less,axiom,
% 5.12/5.30 ! [X: real,Y: real,W: real,Z2: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ X @ Y )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.12/5.30 => ( ( ord_less_eq_real @ W @ Z2 )
% 5.12/5.30 => ( ord_less_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_less
% 5.12/5.30 thf(fact_1026_frac__less,axiom,
% 5.12/5.30 ! [X: rat,Y: rat,W: rat,Z2: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.30 => ( ( ord_less_rat @ X @ Y )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.12/5.30 => ( ( ord_less_eq_rat @ W @ Z2 )
% 5.12/5.30 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_less
% 5.12/5.30 thf(fact_1027_frac__le,axiom,
% 5.12/5.30 ! [Y: real,X: real,W: real,Z2: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.12/5.30 => ( ( ord_less_eq_real @ W @ Z2 )
% 5.12/5.30 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z2 ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_le
% 5.12/5.30 thf(fact_1028_frac__le,axiom,
% 5.12/5.30 ! [Y: rat,X: rat,W: rat,Z2: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.30 => ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.12/5.30 => ( ( ord_less_eq_rat @ W @ Z2 )
% 5.12/5.30 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z2 ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % frac_le
% 5.12/5.30 thf(fact_1029_div__positive,axiom,
% 5.12/5.30 ! [B: nat,A: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ord_less_eq_nat @ B @ A )
% 5.12/5.30 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_positive
% 5.12/5.30 thf(fact_1030_div__positive,axiom,
% 5.12/5.30 ! [B: int,A: int] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_eq_int @ B @ A )
% 5.12/5.30 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_positive
% 5.12/5.30 thf(fact_1031_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.12/5.30 ! [A: nat,B: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ A @ B )
% 5.12/5.30 => ( ( divide_divide_nat @ A @ B )
% 5.12/5.30 = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % unique_euclidean_semiring_numeral_class.div_less
% 5.12/5.30 thf(fact_1032_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ A @ B )
% 5.12/5.30 => ( ( divide_divide_int @ A @ B )
% 5.12/5.30 = zero_zero_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % unique_euclidean_semiring_numeral_class.div_less
% 5.12/5.30 thf(fact_1033_le__minus__one__simps_I1_J,axiom,
% 5.12/5.30 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(1)
% 5.12/5.30 thf(fact_1034_le__minus__one__simps_I1_J,axiom,
% 5.12/5.30 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(1)
% 5.12/5.30 thf(fact_1035_le__minus__one__simps_I1_J,axiom,
% 5.12/5.30 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(1)
% 5.12/5.30 thf(fact_1036_le__minus__one__simps_I1_J,axiom,
% 5.12/5.30 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(1)
% 5.12/5.30 thf(fact_1037_le__minus__one__simps_I3_J,axiom,
% 5.12/5.30 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(3)
% 5.12/5.30 thf(fact_1038_le__minus__one__simps_I3_J,axiom,
% 5.12/5.30 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(3)
% 5.12/5.30 thf(fact_1039_le__minus__one__simps_I3_J,axiom,
% 5.12/5.30 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(3)
% 5.12/5.30 thf(fact_1040_le__minus__one__simps_I3_J,axiom,
% 5.12/5.30 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_minus_one_simps(3)
% 5.12/5.30 thf(fact_1041_zdiv__mono__strict,axiom,
% 5.12/5.30 ! [A2: int,B5: int,N: int] :
% 5.12/5.30 ( ( ord_less_int @ A2 @ B5 )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.12/5.30 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 => ( ( ( modulo_modulo_int @ B5 @ N )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B5 @ N ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_mono_strict
% 5.12/5.30 thf(fact_1042_zmod__zminus1__eq__if,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.30 = zero_zero_int ) )
% 5.12/5.30 & ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.30 != zero_zero_int )
% 5.12/5.30 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.30 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zmod_zminus1_eq_if
% 5.12/5.30 thf(fact_1043_zmod__zminus2__eq__if,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.12/5.30 = zero_zero_int ) )
% 5.12/5.30 & ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.30 != zero_zero_int )
% 5.12/5.30 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.12/5.30 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zmod_zminus2_eq_if
% 5.12/5.30 thf(fact_1044_ex__least__nat__less,axiom,
% 5.12/5.30 ! [P: nat > $o,N: nat] :
% 5.12/5.30 ( ( P @ N )
% 5.12/5.30 => ( ~ ( P @ zero_zero_nat )
% 5.12/5.30 => ? [K2: nat] :
% 5.12/5.30 ( ( ord_less_nat @ K2 @ N )
% 5.12/5.30 & ! [I4: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ I4 @ K2 )
% 5.12/5.30 => ~ ( P @ I4 ) )
% 5.12/5.30 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ex_least_nat_less
% 5.12/5.30 thf(fact_1045_of__nat__diff,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_diff
% 5.12/5.30 thf(fact_1046_of__nat__diff,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_diff
% 5.12/5.30 thf(fact_1047_of__nat__diff,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_diff
% 5.12/5.30 thf(fact_1048_of__nat__diff,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_diff
% 5.12/5.30 thf(fact_1049_of__nat__diff,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_diff
% 5.12/5.30 thf(fact_1050_div__greater__zero__iff,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.30 = ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_greater_zero_iff
% 5.12/5.30 thf(fact_1051_div__le__mono2,axiom,
% 5.12/5.30 ! [M2: nat,N: nat,K: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.30 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.30 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_le_mono2
% 5.12/5.30 thf(fact_1052_int__one__le__iff__zero__less,axiom,
% 5.12/5.30 ! [Z2: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ one_one_int @ Z2 )
% 5.12/5.30 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.30
% 5.12/5.30 % int_one_le_iff_zero_less
% 5.12/5.30 thf(fact_1053_int__zle__neg,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.12/5.30 = ( ( N = zero_zero_nat )
% 5.12/5.30 & ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % int_zle_neg
% 5.12/5.30 thf(fact_1054_negative__zle__0,axiom,
% 5.12/5.30 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.12/5.30
% 5.12/5.30 % negative_zle_0
% 5.12/5.30 thf(fact_1055_nonpos__int__cases,axiom,
% 5.12/5.30 ! [K: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.12/5.30 => ~ ! [N2: nat] :
% 5.12/5.30 ( K
% 5.12/5.30 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nonpos_int_cases
% 5.12/5.30 thf(fact_1056_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.12/5.30 = ( ( ord_less_eq_int @ B @ A )
% 5.12/5.30 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nonneg1_imp_zdiv_pos_iff
% 5.12/5.30 thf(fact_1057_pos__imp__zdiv__nonneg__iff,axiom,
% 5.12/5.30 ! [B: int,A: int] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.12/5.30 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pos_imp_zdiv_nonneg_iff
% 5.12/5.30 thf(fact_1058_neg__imp__zdiv__nonneg__iff,axiom,
% 5.12/5.30 ! [B: int,A: int] :
% 5.12/5.30 ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.12/5.30 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % neg_imp_zdiv_nonneg_iff
% 5.12/5.30 thf(fact_1059_pos__imp__zdiv__pos__iff,axiom,
% 5.12/5.30 ! [K: int,I: int] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.12/5.30 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pos_imp_zdiv_pos_iff
% 5.12/5.30 thf(fact_1060_div__nonpos__pos__le0,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_nonpos_pos_le0
% 5.12/5.30 thf(fact_1061_div__nonneg__neg__le0,axiom,
% 5.12/5.30 ! [A: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_nonneg_neg_le0
% 5.12/5.30 thf(fact_1062_div__positive__int,axiom,
% 5.12/5.30 ! [L: int,K: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ L @ K )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.12/5.30 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_positive_int
% 5.12/5.30 thf(fact_1063_div__int__pos__iff,axiom,
% 5.12/5.30 ! [K: int,L: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.12/5.30 = ( ( K = zero_zero_int )
% 5.12/5.30 | ( L = zero_zero_int )
% 5.12/5.30 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.30 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.12/5.30 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.30 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_int_pos_iff
% 5.12/5.30 thf(fact_1064_zdiv__mono2__neg,axiom,
% 5.12/5.30 ! [A: int,B4: int,B: int] :
% 5.12/5.30 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.12/5.30 => ( ( ord_less_eq_int @ B4 @ B )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_mono2_neg
% 5.12/5.30 thf(fact_1065_zdiv__mono1__neg,axiom,
% 5.12/5.30 ! [A: int,A5: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ A @ A5 )
% 5.12/5.30 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_mono1_neg
% 5.12/5.30 thf(fact_1066_zdiv__eq__0__iff,axiom,
% 5.12/5.30 ! [I: int,K: int] :
% 5.12/5.30 ( ( ( divide_divide_int @ I @ K )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 = ( ( K = zero_zero_int )
% 5.12/5.30 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.12/5.30 & ( ord_less_int @ I @ K ) )
% 5.12/5.30 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.12/5.30 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_eq_0_iff
% 5.12/5.30 thf(fact_1067_zdiv__mono2,axiom,
% 5.12/5.30 ! [A: int,B4: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.12/5.30 => ( ( ord_less_eq_int @ B4 @ B )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_mono2
% 5.12/5.30 thf(fact_1068_zdiv__mono1,axiom,
% 5.12/5.30 ! [A: int,A5: int,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ A @ A5 )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiv_mono1
% 5.12/5.30 thf(fact_1069_split__nat,axiom,
% 5.12/5.30 ! [P: nat > $o,I: int] :
% 5.12/5.30 ( ( P @ ( nat2 @ I ) )
% 5.12/5.30 = ( ! [N4: nat] :
% 5.12/5.30 ( ( I
% 5.12/5.30 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.12/5.30 => ( P @ N4 ) )
% 5.12/5.30 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.12/5.30 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % split_nat
% 5.12/5.30 thf(fact_1070_le__divide__eq__1,axiom,
% 5.12/5.30 ! [B: real,A: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.12/5.30 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 & ( ord_less_eq_real @ A @ B ) )
% 5.12/5.30 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.30 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_divide_eq_1
% 5.12/5.30 thf(fact_1071_le__divide__eq__1,axiom,
% 5.12/5.30 ! [B: rat,A: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.12/5.30 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.30 & ( ord_less_eq_rat @ A @ B ) )
% 5.12/5.30 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.30 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_divide_eq_1
% 5.12/5.30 thf(fact_1072_divide__le__eq__1,axiom,
% 5.12/5.30 ! [B: real,A: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.12/5.30 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 & ( ord_less_eq_real @ B @ A ) )
% 5.12/5.30 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.30 & ( ord_less_eq_real @ A @ B ) )
% 5.12/5.30 | ( A = zero_zero_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_le_eq_1
% 5.12/5.30 thf(fact_1073_divide__le__eq__1,axiom,
% 5.12/5.30 ! [B: rat,A: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.12/5.30 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.30 & ( ord_less_eq_rat @ B @ A ) )
% 5.12/5.30 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.30 & ( ord_less_eq_rat @ A @ B ) )
% 5.12/5.30 | ( A = zero_zero_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % divide_le_eq_1
% 5.12/5.30 thf(fact_1074_not__zle__0__negative,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % not_zle_0_negative
% 5.12/5.30 thf(fact_1075_verit__less__mono__div__int2,axiom,
% 5.12/5.30 ! [A2: int,B5: int,N: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ A2 @ B5 )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.12/5.30 => ( ord_less_eq_int @ ( divide_divide_int @ B5 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % verit_less_mono_div_int2
% 5.12/5.30 thf(fact_1076_of__nat__zero__less__power__iff,axiom,
% 5.12/5.30 ! [X: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.12/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.30 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_zero_less_power_iff
% 5.12/5.30 thf(fact_1077_of__nat__zero__less__power__iff,axiom,
% 5.12/5.30 ! [X: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.12/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.30 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_zero_less_power_iff
% 5.12/5.30 thf(fact_1078_of__nat__zero__less__power__iff,axiom,
% 5.12/5.30 ! [X: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.12/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.30 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_zero_less_power_iff
% 5.12/5.30 thf(fact_1079_of__nat__zero__less__power__iff,axiom,
% 5.12/5.30 ! [X: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.12/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.30 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_zero_less_power_iff
% 5.12/5.30 thf(fact_1080_power__decreasing__iff,axiom,
% 5.12/5.30 ! [B: real,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ( ord_less_real @ B @ one_one_real )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing_iff
% 5.12/5.30 thf(fact_1081_power__decreasing__iff,axiom,
% 5.12/5.30 ! [B: rat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.12/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing_iff
% 5.12/5.30 thf(fact_1082_power__decreasing__iff,axiom,
% 5.12/5.30 ! [B: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.12/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing_iff
% 5.12/5.30 thf(fact_1083_power__decreasing__iff,axiom,
% 5.12/5.30 ! [B: int,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_int @ B @ one_one_int )
% 5.12/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing_iff
% 5.12/5.30 thf(fact_1084_power__mono__iff,axiom,
% 5.12/5.30 ! [A: real,B: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono_iff
% 5.12/5.30 thf(fact_1085_power__mono__iff,axiom,
% 5.12/5.30 ! [A: rat,B: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono_iff
% 5.12/5.30 thf(fact_1086_power__mono__iff,axiom,
% 5.12/5.30 ! [A: nat,B: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono_iff
% 5.12/5.30 thf(fact_1087_power__mono__iff,axiom,
% 5.12/5.30 ! [A: int,B: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.12/5.30 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono_iff
% 5.12/5.30 thf(fact_1088_power__increasing__iff,axiom,
% 5.12/5.30 ! [B: real,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing_iff
% 5.12/5.30 thf(fact_1089_power__increasing__iff,axiom,
% 5.12/5.30 ! [B: rat,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ B )
% 5.12/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing_iff
% 5.12/5.30 thf(fact_1090_power__increasing__iff,axiom,
% 5.12/5.30 ! [B: nat,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ B )
% 5.12/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing_iff
% 5.12/5.30 thf(fact_1091_power__increasing__iff,axiom,
% 5.12/5.30 ! [B: int,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ B )
% 5.12/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing_iff
% 5.12/5.30 thf(fact_1092_power__strict__decreasing__iff,axiom,
% 5.12/5.30 ! [B: real,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ( ord_less_real @ B @ one_one_real )
% 5.12/5.30 => ( ( ord_less_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.12/5.30 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing_iff
% 5.12/5.30 thf(fact_1093_power__strict__decreasing__iff,axiom,
% 5.12/5.30 ! [B: rat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.12/5.30 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 5.12/5.30 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing_iff
% 5.12/5.30 thf(fact_1094_power__strict__decreasing__iff,axiom,
% 5.12/5.30 ! [B: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.12/5.30 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 5.12/5.30 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing_iff
% 5.12/5.30 thf(fact_1095_power__strict__decreasing__iff,axiom,
% 5.12/5.30 ! [B: int,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_int @ B @ one_one_int )
% 5.12/5.30 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 5.12/5.30 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing_iff
% 5.12/5.30 thf(fact_1096_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_le_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1097_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_le_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1098_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_le_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1099_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_le_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1100_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.12/5.30 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_le_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1101_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.12/5.30 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_le_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1102_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.12/5.30 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_le_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1103_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.12/5.30 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_le_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1104_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_less_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1105_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_less_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1106_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_less_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1107_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.12/5.30 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_less_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1108_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.12/5.30 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_less_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1109_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.12/5.30 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_less_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1110_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.12/5.30 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_less_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1111_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.12/5.30 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_less_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1112_power__eq__0__iff,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ( power_power_rat @ A @ N )
% 5.12/5.30 = zero_zero_rat )
% 5.12/5.30 = ( ( A = zero_zero_rat )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_0_iff
% 5.12/5.30 thf(fact_1113_power__eq__0__iff,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ( power_power_int @ A @ N )
% 5.12/5.30 = zero_zero_int )
% 5.12/5.30 = ( ( A = zero_zero_int )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_0_iff
% 5.12/5.30 thf(fact_1114_power__eq__0__iff,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ( power_power_nat @ A @ N )
% 5.12/5.30 = zero_zero_nat )
% 5.12/5.30 = ( ( A = zero_zero_nat )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_0_iff
% 5.12/5.30 thf(fact_1115_power__eq__0__iff,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ( power_power_real @ A @ N )
% 5.12/5.30 = zero_zero_real )
% 5.12/5.30 = ( ( A = zero_zero_real )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_0_iff
% 5.12/5.30 thf(fact_1116_power__eq__0__iff,axiom,
% 5.12/5.30 ! [A: complex,N: nat] :
% 5.12/5.30 ( ( ( power_power_complex @ A @ N )
% 5.12/5.30 = zero_zero_complex )
% 5.12/5.30 = ( ( A = zero_zero_complex )
% 5.12/5.30 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_0_iff
% 5.12/5.30 thf(fact_1117_power__strict__increasing__iff,axiom,
% 5.12/5.30 ! [B: real,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.30 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.12/5.30 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing_iff
% 5.12/5.30 thf(fact_1118_power__strict__increasing__iff,axiom,
% 5.12/5.30 ! [B: rat,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ B )
% 5.12/5.30 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.12/5.30 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing_iff
% 5.12/5.30 thf(fact_1119_power__strict__increasing__iff,axiom,
% 5.12/5.30 ! [B: nat,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.12/5.30 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing_iff
% 5.12/5.30 thf(fact_1120_power__strict__increasing__iff,axiom,
% 5.12/5.30 ! [B: int,X: nat,Y: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ B )
% 5.12/5.30 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.12/5.30 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing_iff
% 5.12/5.30 thf(fact_1121_ln__inj__iff,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ( ln_ln_real @ X )
% 5.12/5.30 = ( ln_ln_real @ Y ) )
% 5.12/5.30 = ( X = Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_inj_iff
% 5.12/5.30 thf(fact_1122_ln__less__cancel__iff,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.12/5.30 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_less_cancel_iff
% 5.12/5.30 thf(fact_1123_power__one,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_rat @ one_one_rat @ N )
% 5.12/5.30 = one_one_rat ) ).
% 5.12/5.30
% 5.12/5.30 % power_one
% 5.12/5.30 thf(fact_1124_power__one,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_int @ one_one_int @ N )
% 5.12/5.30 = one_one_int ) ).
% 5.12/5.30
% 5.12/5.30 % power_one
% 5.12/5.30 thf(fact_1125_power__one,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_nat @ one_one_nat @ N )
% 5.12/5.30 = one_one_nat ) ).
% 5.12/5.30
% 5.12/5.30 % power_one
% 5.12/5.30 thf(fact_1126_power__one,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_real @ one_one_real @ N )
% 5.12/5.30 = one_one_real ) ).
% 5.12/5.30
% 5.12/5.30 % power_one
% 5.12/5.30 thf(fact_1127_power__one,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_complex @ one_one_complex @ N )
% 5.12/5.30 = one_one_complex ) ).
% 5.12/5.30
% 5.12/5.30 % power_one
% 5.12/5.30 thf(fact_1128_ln__le__cancel__iff,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.12/5.30 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_le_cancel_iff
% 5.12/5.30 thf(fact_1129_ln__less__zero__iff,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.12/5.30 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_less_zero_iff
% 5.12/5.30 thf(fact_1130_ln__gt__zero__iff,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.12/5.30 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_gt_zero_iff
% 5.12/5.30 thf(fact_1131_ln__eq__zero__iff,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ( ln_ln_real @ X )
% 5.12/5.30 = zero_zero_real )
% 5.12/5.30 = ( X = one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_eq_zero_iff
% 5.12/5.30 thf(fact_1132_power__one__right,axiom,
% 5.12/5.30 ! [A: int] :
% 5.12/5.30 ( ( power_power_int @ A @ one_one_nat )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_right
% 5.12/5.30 thf(fact_1133_power__one__right,axiom,
% 5.12/5.30 ! [A: nat] :
% 5.12/5.30 ( ( power_power_nat @ A @ one_one_nat )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_right
% 5.12/5.30 thf(fact_1134_power__one__right,axiom,
% 5.12/5.30 ! [A: real] :
% 5.12/5.30 ( ( power_power_real @ A @ one_one_nat )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_right
% 5.12/5.30 thf(fact_1135_power__one__right,axiom,
% 5.12/5.30 ! [A: complex] :
% 5.12/5.30 ( ( power_power_complex @ A @ one_one_nat )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_right
% 5.12/5.30 thf(fact_1136_mod__less,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ M2 @ N )
% 5.12/5.30 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.12/5.30 = M2 ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_less
% 5.12/5.30 thf(fact_1137_power__inject__exp,axiom,
% 5.12/5.30 ! [A: real,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ( ( power_power_real @ A @ M2 )
% 5.12/5.30 = ( power_power_real @ A @ N ) )
% 5.12/5.30 = ( M2 = N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_exp
% 5.12/5.30 thf(fact_1138_power__inject__exp,axiom,
% 5.12/5.30 ! [A: rat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ( ( power_power_rat @ A @ M2 )
% 5.12/5.30 = ( power_power_rat @ A @ N ) )
% 5.12/5.30 = ( M2 = N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_exp
% 5.12/5.30 thf(fact_1139_power__inject__exp,axiom,
% 5.12/5.30 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ( ( power_power_nat @ A @ M2 )
% 5.12/5.30 = ( power_power_nat @ A @ N ) )
% 5.12/5.30 = ( M2 = N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_exp
% 5.12/5.30 thf(fact_1140_power__inject__exp,axiom,
% 5.12/5.30 ! [A: int,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ( ( power_power_int @ A @ M2 )
% 5.12/5.30 = ( power_power_int @ A @ N ) )
% 5.12/5.30 = ( M2 = N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_exp
% 5.12/5.30 thf(fact_1141_power__0__Suc,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.12/5.30 = zero_zero_rat ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_Suc
% 5.12/5.30 thf(fact_1142_power__0__Suc,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.12/5.30 = zero_zero_int ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_Suc
% 5.12/5.30 thf(fact_1143_power__0__Suc,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.12/5.30 = zero_zero_nat ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_Suc
% 5.12/5.30 thf(fact_1144_power__0__Suc,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.12/5.30 = zero_zero_real ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_Suc
% 5.12/5.30 thf(fact_1145_power__0__Suc,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.12/5.30 = zero_zero_complex ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_Suc
% 5.12/5.30 thf(fact_1146_power__Suc0__right,axiom,
% 5.12/5.30 ! [A: int] :
% 5.12/5.30 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc0_right
% 5.12/5.30 thf(fact_1147_power__Suc0__right,axiom,
% 5.12/5.30 ! [A: nat] :
% 5.12/5.30 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc0_right
% 5.12/5.30 thf(fact_1148_power__Suc0__right,axiom,
% 5.12/5.30 ! [A: real] :
% 5.12/5.30 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc0_right
% 5.12/5.30 thf(fact_1149_power__Suc0__right,axiom,
% 5.12/5.30 ! [A: complex] :
% 5.12/5.30 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.12/5.30 = A ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc0_right
% 5.12/5.30 thf(fact_1150_ln__ge__zero__iff,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.12/5.30 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_ge_zero_iff
% 5.12/5.30 thf(fact_1151_ln__le__zero__iff,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.12/5.30 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_le_zero_iff
% 5.12/5.30 thf(fact_1152_power__Suc__0,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.30 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_0
% 5.12/5.30 thf(fact_1153_nat__power__eq__Suc__0__iff,axiom,
% 5.12/5.30 ! [X: nat,M2: nat] :
% 5.12/5.30 ( ( ( power_power_nat @ X @ M2 )
% 5.12/5.30 = ( suc @ zero_zero_nat ) )
% 5.12/5.30 = ( ( M2 = zero_zero_nat )
% 5.12/5.30 | ( X
% 5.12/5.30 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_power_eq_Suc_0_iff
% 5.12/5.30 thf(fact_1154_nat__zero__less__power__iff,axiom,
% 5.12/5.30 ! [X: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.12/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.30 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_zero_less_power_iff
% 5.12/5.30 thf(fact_1155_of__nat__power,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M2 @ N ) )
% 5.12/5.30 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power
% 5.12/5.30 thf(fact_1156_of__nat__power,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M2 @ N ) )
% 5.12/5.30 = ( power_power_real @ ( semiri5074537144036343181t_real @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power
% 5.12/5.30 thf(fact_1157_of__nat__power,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M2 @ N ) )
% 5.12/5.30 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power
% 5.12/5.30 thf(fact_1158_of__nat__power,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M2 @ N ) )
% 5.12/5.30 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power
% 5.12/5.30 thf(fact_1159_of__nat__power,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M2 @ N ) )
% 5.12/5.30 = ( power_power_int @ ( semiri1314217659103216013at_int @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power
% 5.12/5.30 thf(fact_1160_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.12/5.30 = ( semiri8010041392384452111omplex @ X ) )
% 5.12/5.30 = ( ( power_power_nat @ B @ W )
% 5.12/5.30 = X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_eq_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1161_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.12/5.30 = ( semiri5074537144036343181t_real @ X ) )
% 5.12/5.30 = ( ( power_power_nat @ B @ W )
% 5.12/5.30 = X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_eq_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1162_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.12/5.30 = ( semiri681578069525770553at_rat @ X ) )
% 5.12/5.30 = ( ( power_power_nat @ B @ W )
% 5.12/5.30 = X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_eq_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1163_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.12/5.30 = ( semiri1316708129612266289at_nat @ X ) )
% 5.12/5.30 = ( ( power_power_nat @ B @ W )
% 5.12/5.30 = X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_eq_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1164_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.12/5.30 ! [B: nat,W: nat,X: nat] :
% 5.12/5.30 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.12/5.30 = ( semiri1314217659103216013at_int @ X ) )
% 5.12/5.30 = ( ( power_power_nat @ B @ W )
% 5.12/5.30 = X ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_eq_of_nat_power_cancel_iff
% 5.12/5.30 thf(fact_1165_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ( semiri8010041392384452111omplex @ X )
% 5.12/5.30 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.12/5.30 = ( X
% 5.12/5.30 = ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_eq_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1166_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ( semiri5074537144036343181t_real @ X )
% 5.12/5.30 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.12/5.30 = ( X
% 5.12/5.30 = ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_eq_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1167_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ( semiri681578069525770553at_rat @ X )
% 5.12/5.30 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.12/5.30 = ( X
% 5.12/5.30 = ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_eq_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1168_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.12/5.30 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.12/5.30 = ( X
% 5.12/5.30 = ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_eq_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1169_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.30 ! [X: nat,B: nat,W: nat] :
% 5.12/5.30 ( ( ( semiri1314217659103216013at_int @ X )
% 5.12/5.30 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.12/5.30 = ( X
% 5.12/5.30 = ( power_power_nat @ B @ W ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % of_nat_power_eq_of_nat_cancel_iff
% 5.12/5.30 thf(fact_1170_mod__by__Suc__0,axiom,
% 5.12/5.30 ! [M2: nat] :
% 5.12/5.30 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.12/5.30 = zero_zero_nat ) ).
% 5.12/5.30
% 5.12/5.30 % mod_by_Suc_0
% 5.12/5.30 thf(fact_1171_ln__diff__le,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_diff_le
% 5.12/5.30 thf(fact_1172_real__arch__pow,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.30 => ? [N2: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % real_arch_pow
% 5.12/5.30 thf(fact_1173_real__arch__pow__inv,axiom,
% 5.12/5.30 ! [Y: real,X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.30 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % real_arch_pow_inv
% 5.12/5.30 thf(fact_1174_ln__ge__zero,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_ge_zero
% 5.12/5.30 thf(fact_1175_ln__ge__zero__imp__ge__one,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_ge_zero_imp_ge_one
% 5.12/5.30 thf(fact_1176_ln__bound,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_bound
% 5.12/5.30 thf(fact_1177_verit__la__generic,axiom,
% 5.12/5.30 ! [A: int,X: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ A @ X )
% 5.12/5.30 | ( A = X )
% 5.12/5.30 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.12/5.30
% 5.12/5.30 % verit_la_generic
% 5.12/5.30 thf(fact_1178_complete__real,axiom,
% 5.12/5.30 ! [S3: set_real] :
% 5.12/5.30 ( ? [X4: real] : ( member_real @ X4 @ S3 )
% 5.12/5.30 => ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( member_real @ X3 @ S3 )
% 5.12/5.30 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 5.12/5.30 => ? [Y3: real] :
% 5.12/5.30 ( ! [X4: real] :
% 5.12/5.30 ( ( member_real @ X4 @ S3 )
% 5.12/5.30 => ( ord_less_eq_real @ X4 @ Y3 ) )
% 5.12/5.30 & ! [Z5: real] :
% 5.12/5.30 ( ! [X3: real] :
% 5.12/5.30 ( ( member_real @ X3 @ S3 )
% 5.12/5.30 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 5.12/5.30 => ( ord_less_eq_real @ Y3 @ Z5 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % complete_real
% 5.12/5.30 thf(fact_1179_less__eq__real__def,axiom,
% 5.12/5.30 ( ord_less_eq_real
% 5.12/5.30 = ( ^ [X2: real,Y6: real] :
% 5.12/5.30 ( ( ord_less_real @ X2 @ Y6 )
% 5.12/5.30 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % less_eq_real_def
% 5.12/5.30 thf(fact_1180_ln__one__minus__pos__upper__bound,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.30 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_one_minus_pos_upper_bound
% 5.12/5.30 thf(fact_1181_ln__le__minus__one,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_le_minus_one
% 5.12/5.30 thf(fact_1182_ln__eq__minus__one,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ( ln_ln_real @ X )
% 5.12/5.30 = ( minus_minus_real @ X @ one_one_real ) )
% 5.12/5.30 => ( X = one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_eq_minus_one
% 5.12/5.30 thf(fact_1183_ln__less__self,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_less_self
% 5.12/5.30 thf(fact_1184_ln__gt__zero__imp__gt__one,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_gt_zero_imp_gt_one
% 5.12/5.30 thf(fact_1185_ln__less__zero,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.30 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_less_zero
% 5.12/5.30 thf(fact_1186_ln__gt__zero,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.30 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_gt_zero
% 5.12/5.30 thf(fact_1187_ln__div,axiom,
% 5.12/5.30 ! [X: real,Y: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.30 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.30 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % ln_div
% 5.12/5.30 thf(fact_1188_mod__Suc__eq,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) @ N )
% 5.12/5.30 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_Suc_eq
% 5.12/5.30 thf(fact_1189_mod__Suc__Suc__eq,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ N )
% 5.12/5.30 = ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_Suc_Suc_eq
% 5.12/5.30 thf(fact_1190_nat__power__less__imp__less,axiom,
% 5.12/5.30 ! [I: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.12/5.30 => ( ( ord_less_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_power_less_imp_less
% 5.12/5.30 thf(fact_1191_mod__Suc,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.12/5.30 = N )
% 5.12/5.30 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 5.12/5.30 = zero_zero_nat ) )
% 5.12/5.30 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.12/5.30 != N )
% 5.12/5.30 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 5.12/5.30 = ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_Suc
% 5.12/5.30 thf(fact_1192_mod__induct,axiom,
% 5.12/5.30 ! [P: nat > $o,N: nat,P4: nat,M2: nat] :
% 5.12/5.30 ( ( P @ N )
% 5.12/5.30 => ( ( ord_less_nat @ N @ P4 )
% 5.12/5.30 => ( ( ord_less_nat @ M2 @ P4 )
% 5.12/5.30 => ( ! [N2: nat] :
% 5.12/5.30 ( ( ord_less_nat @ N2 @ P4 )
% 5.12/5.30 => ( ( P @ N2 )
% 5.12/5.30 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P4 ) ) ) )
% 5.12/5.30 => ( P @ M2 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_induct
% 5.12/5.30 thf(fact_1193_mod__less__divisor,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_less_divisor
% 5.12/5.30 thf(fact_1194_mod__Suc__le__divisor,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N ) ) @ N ) ).
% 5.12/5.30
% 5.12/5.30 % mod_Suc_le_divisor
% 5.12/5.30 thf(fact_1195_power__gt__expt,axiom,
% 5.12/5.30 ! [N: nat,K: nat] :
% 5.12/5.30 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.30 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_gt_expt
% 5.12/5.30 thf(fact_1196_mod__geq,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ~ ( ord_less_nat @ M2 @ N )
% 5.12/5.30 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.12/5.30 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_geq
% 5.12/5.30 thf(fact_1197_mod__if,axiom,
% 5.12/5.30 ( modulo_modulo_nat
% 5.12/5.30 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M5 @ N4 ) @ M5 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_if
% 5.12/5.30 thf(fact_1198_nat__one__le__power,axiom,
% 5.12/5.30 ! [I: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.12/5.30 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_one_le_power
% 5.12/5.30 thf(fact_1199_le__mod__geq,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.12/5.30 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % le_mod_geq
% 5.12/5.30 thf(fact_1200_zmod__int,axiom,
% 5.12/5.30 ! [A: nat,B: nat] :
% 5.12/5.30 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.30 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zmod_int
% 5.12/5.30 thf(fact_1201_mod__le__divisor,axiom,
% 5.12/5.30 ! [N: nat,M2: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 5.12/5.30
% 5.12/5.30 % mod_le_divisor
% 5.12/5.30 thf(fact_1202_div__less__mono,axiom,
% 5.12/5.30 ! [A2: nat,B5: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ A2 @ B5 )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.12/5.30 = zero_zero_nat )
% 5.12/5.30 => ( ( ( modulo_modulo_nat @ B5 @ N )
% 5.12/5.30 = zero_zero_nat )
% 5.12/5.30 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % div_less_mono
% 5.12/5.30 thf(fact_1203_nat__mod__distrib,axiom,
% 5.12/5.30 ! [X: int,Y: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.30 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.12/5.30 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_mod_distrib
% 5.12/5.30 thf(fact_1204_nat__power__eq,axiom,
% 5.12/5.30 ! [Z2: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.30 => ( ( nat2 @ ( power_power_int @ Z2 @ N ) )
% 5.12/5.30 = ( power_power_nat @ ( nat2 @ Z2 ) @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat_power_eq
% 5.12/5.30 thf(fact_1205_field__char__0__class_Oof__nat__div,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % field_char_0_class.of_nat_div
% 5.12/5.30 thf(fact_1206_field__char__0__class_Oof__nat__div,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % field_char_0_class.of_nat_div
% 5.12/5.30 thf(fact_1207_field__char__0__class_Oof__nat__div,axiom,
% 5.12/5.30 ! [M2: nat,N: nat] :
% 5.12/5.30 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % field_char_0_class.of_nat_div
% 5.12/5.30 thf(fact_1208_power__not__zero,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( A != zero_zero_rat )
% 5.12/5.30 => ( ( power_power_rat @ A @ N )
% 5.12/5.30 != zero_zero_rat ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_not_zero
% 5.12/5.30 thf(fact_1209_power__not__zero,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( A != zero_zero_int )
% 5.12/5.30 => ( ( power_power_int @ A @ N )
% 5.12/5.30 != zero_zero_int ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_not_zero
% 5.12/5.30 thf(fact_1210_power__not__zero,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( A != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_nat @ A @ N )
% 5.12/5.30 != zero_zero_nat ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_not_zero
% 5.12/5.30 thf(fact_1211_power__not__zero,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( A != zero_zero_real )
% 5.12/5.30 => ( ( power_power_real @ A @ N )
% 5.12/5.30 != zero_zero_real ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_not_zero
% 5.12/5.30 thf(fact_1212_power__not__zero,axiom,
% 5.12/5.30 ! [A: complex,N: nat] :
% 5.12/5.30 ( ( A != zero_zero_complex )
% 5.12/5.30 => ( ( power_power_complex @ A @ N )
% 5.12/5.30 != zero_zero_complex ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_not_zero
% 5.12/5.30 thf(fact_1213_power__divide,axiom,
% 5.12/5.30 ! [A: complex,B: complex,N: nat] :
% 5.12/5.30 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.12/5.30 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_divide
% 5.12/5.30 thf(fact_1214_power__divide,axiom,
% 5.12/5.30 ! [A: real,B: real,N: nat] :
% 5.12/5.30 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.12/5.30 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_divide
% 5.12/5.30 thf(fact_1215_power__divide,axiom,
% 5.12/5.30 ! [A: rat,B: rat,N: nat] :
% 5.12/5.30 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.12/5.30 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_divide
% 5.12/5.30 thf(fact_1216_zero__le__power,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_le_power
% 5.12/5.30 thf(fact_1217_zero__le__power,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_le_power
% 5.12/5.30 thf(fact_1218_zero__le__power,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_le_power
% 5.12/5.30 thf(fact_1219_zero__le__power,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_le_power
% 5.12/5.30 thf(fact_1220_power__mono,axiom,
% 5.12/5.30 ! [A: real,B: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono
% 5.12/5.30 thf(fact_1221_power__mono,axiom,
% 5.12/5.30 ! [A: rat,B: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono
% 5.12/5.30 thf(fact_1222_power__mono,axiom,
% 5.12/5.30 ! [A: nat,B: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono
% 5.12/5.30 thf(fact_1223_power__mono,axiom,
% 5.12/5.30 ! [A: int,B: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_mono
% 5.12/5.30 thf(fact_1224_zero__less__power,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_less_power
% 5.12/5.30 thf(fact_1225_zero__less__power,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_less_power
% 5.12/5.30 thf(fact_1226_zero__less__power,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_less_power
% 5.12/5.30 thf(fact_1227_zero__less__power,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_less_power
% 5.12/5.30 thf(fact_1228_one__le__power,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.12/5.30 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_le_power
% 5.12/5.30 thf(fact_1229_one__le__power,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_le_power
% 5.12/5.30 thf(fact_1230_one__le__power,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_le_power
% 5.12/5.30 thf(fact_1231_one__le__power,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.12/5.30 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_le_power
% 5.12/5.30 thf(fact_1232_power__one__over,axiom,
% 5.12/5.30 ! [A: complex,N: nat] :
% 5.12/5.30 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.12/5.30 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_over
% 5.12/5.30 thf(fact_1233_power__one__over,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.12/5.30 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_over
% 5.12/5.30 thf(fact_1234_power__one__over,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.12/5.30 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_one_over
% 5.12/5.30 thf(fact_1235_power__0,axiom,
% 5.12/5.30 ! [A: rat] :
% 5.12/5.30 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.12/5.30 = one_one_rat ) ).
% 5.12/5.30
% 5.12/5.30 % power_0
% 5.12/5.30 thf(fact_1236_power__0,axiom,
% 5.12/5.30 ! [A: int] :
% 5.12/5.30 ( ( power_power_int @ A @ zero_zero_nat )
% 5.12/5.30 = one_one_int ) ).
% 5.12/5.30
% 5.12/5.30 % power_0
% 5.12/5.30 thf(fact_1237_power__0,axiom,
% 5.12/5.30 ! [A: nat] :
% 5.12/5.30 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.12/5.30 = one_one_nat ) ).
% 5.12/5.30
% 5.12/5.30 % power_0
% 5.12/5.30 thf(fact_1238_power__0,axiom,
% 5.12/5.30 ! [A: real] :
% 5.12/5.30 ( ( power_power_real @ A @ zero_zero_nat )
% 5.12/5.30 = one_one_real ) ).
% 5.12/5.30
% 5.12/5.30 % power_0
% 5.12/5.30 thf(fact_1239_power__0,axiom,
% 5.12/5.30 ! [A: complex] :
% 5.12/5.30 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.12/5.30 = one_one_complex ) ).
% 5.12/5.30
% 5.12/5.30 % power_0
% 5.12/5.30 thf(fact_1240_power__less__imp__less__base,axiom,
% 5.12/5.30 ! [A: real,N: nat,B: real] :
% 5.12/5.30 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_base
% 5.12/5.30 thf(fact_1241_power__less__imp__less__base,axiom,
% 5.12/5.30 ! [A: rat,N: nat,B: rat] :
% 5.12/5.30 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_base
% 5.12/5.30 thf(fact_1242_power__less__imp__less__base,axiom,
% 5.12/5.30 ! [A: nat,N: nat,B: nat] :
% 5.12/5.30 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_base
% 5.12/5.30 thf(fact_1243_power__less__imp__less__base,axiom,
% 5.12/5.30 ! [A: int,N: nat,B: int] :
% 5.12/5.30 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_base
% 5.12/5.30 thf(fact_1244_power__le__one,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.12/5.30 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_one
% 5.12/5.30 thf(fact_1245_power__le__one,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_one
% 5.12/5.30 thf(fact_1246_power__le__one,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.12/5.30 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_one
% 5.12/5.30 thf(fact_1247_power__le__one,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.12/5.30 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_one
% 5.12/5.30 thf(fact_1248_power__inject__base,axiom,
% 5.12/5.30 ! [A: real,N: nat,B: real] :
% 5.12/5.30 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.12/5.30 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( A = B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_base
% 5.12/5.30 thf(fact_1249_power__inject__base,axiom,
% 5.12/5.30 ! [A: rat,N: nat,B: rat] :
% 5.12/5.30 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.12/5.30 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( A = B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_base
% 5.12/5.30 thf(fact_1250_power__inject__base,axiom,
% 5.12/5.30 ! [A: nat,N: nat,B: nat] :
% 5.12/5.30 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.12/5.30 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( A = B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_base
% 5.12/5.30 thf(fact_1251_power__inject__base,axiom,
% 5.12/5.30 ! [A: int,N: nat,B: int] :
% 5.12/5.30 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.12/5.30 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( A = B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_inject_base
% 5.12/5.30 thf(fact_1252_power__le__imp__le__base,axiom,
% 5.12/5.30 ! [A: real,N: nat,B: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_base
% 5.12/5.30 thf(fact_1253_power__le__imp__le__base,axiom,
% 5.12/5.30 ! [A: rat,N: nat,B: rat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_base
% 5.12/5.30 thf(fact_1254_power__le__imp__le__base,axiom,
% 5.12/5.30 ! [A: nat,N: nat,B: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_base
% 5.12/5.30 thf(fact_1255_power__le__imp__le__base,axiom,
% 5.12/5.30 ! [A: int,N: nat,B: int] :
% 5.12/5.30 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_base
% 5.12/5.30 thf(fact_1256_power__0__left,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ( N = zero_zero_nat )
% 5.12/5.30 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.12/5.30 = one_one_rat ) )
% 5.12/5.30 & ( ( N != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.12/5.30 = zero_zero_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_left
% 5.12/5.30 thf(fact_1257_power__0__left,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ( N = zero_zero_nat )
% 5.12/5.30 => ( ( power_power_int @ zero_zero_int @ N )
% 5.12/5.30 = one_one_int ) )
% 5.12/5.30 & ( ( N != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_int @ zero_zero_int @ N )
% 5.12/5.30 = zero_zero_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_left
% 5.12/5.30 thf(fact_1258_power__0__left,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ( N = zero_zero_nat )
% 5.12/5.30 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.12/5.30 = one_one_nat ) )
% 5.12/5.30 & ( ( N != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.12/5.30 = zero_zero_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_left
% 5.12/5.30 thf(fact_1259_power__0__left,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ( N = zero_zero_nat )
% 5.12/5.30 => ( ( power_power_real @ zero_zero_real @ N )
% 5.12/5.30 = one_one_real ) )
% 5.12/5.30 & ( ( N != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_real @ zero_zero_real @ N )
% 5.12/5.30 = zero_zero_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_left
% 5.12/5.30 thf(fact_1260_power__0__left,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ( N = zero_zero_nat )
% 5.12/5.30 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.12/5.30 = one_one_complex ) )
% 5.12/5.30 & ( ( N != zero_zero_nat )
% 5.12/5.30 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.12/5.30 = zero_zero_complex ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_0_left
% 5.12/5.30 thf(fact_1261_power__gt1,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_gt1
% 5.12/5.30 thf(fact_1262_power__gt1,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_gt1
% 5.12/5.30 thf(fact_1263_power__gt1,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_gt1
% 5.12/5.30 thf(fact_1264_power__gt1,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_gt1
% 5.12/5.30 thf(fact_1265_power__less__imp__less__exp,axiom,
% 5.12/5.30 ! [A: real,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ( ord_less_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_exp
% 5.12/5.30 thf(fact_1266_power__less__imp__less__exp,axiom,
% 5.12/5.30 ! [A: rat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ( ord_less_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_exp
% 5.12/5.30 thf(fact_1267_power__less__imp__less__exp,axiom,
% 5.12/5.30 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_exp
% 5.12/5.30 thf(fact_1268_power__less__imp__less__exp,axiom,
% 5.12/5.30 ! [A: int,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.12/5.30 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_less_imp_less_exp
% 5.12/5.30 thf(fact_1269_power__strict__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: real] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing
% 5.12/5.30 thf(fact_1270_power__strict__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: rat] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing
% 5.12/5.30 thf(fact_1271_power__strict__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: nat] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing
% 5.12/5.30 thf(fact_1272_power__strict__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: int] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_increasing
% 5.12/5.30 thf(fact_1273_power__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: real] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.12/5.30 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing
% 5.12/5.30 thf(fact_1274_power__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: rat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing
% 5.12/5.30 thf(fact_1275_power__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing
% 5.12/5.30 thf(fact_1276_power__increasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: int] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.12/5.30 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_increasing
% 5.12/5.30 thf(fact_1277_zero__power,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.12/5.30 = zero_zero_rat ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_power
% 5.12/5.30 thf(fact_1278_zero__power,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( power_power_int @ zero_zero_int @ N )
% 5.12/5.30 = zero_zero_int ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_power
% 5.12/5.30 thf(fact_1279_zero__power,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.12/5.30 = zero_zero_nat ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_power
% 5.12/5.30 thf(fact_1280_zero__power,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( power_power_real @ zero_zero_real @ N )
% 5.12/5.30 = zero_zero_real ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_power
% 5.12/5.30 thf(fact_1281_zero__power,axiom,
% 5.12/5.30 ! [N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.12/5.30 = zero_zero_complex ) ) ).
% 5.12/5.30
% 5.12/5.30 % zero_power
% 5.12/5.30 thf(fact_1282_power__Suc__le__self,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.12/5.30 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_le_self
% 5.12/5.30 thf(fact_1283_power__Suc__le__self,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_le_self
% 5.12/5.30 thf(fact_1284_power__Suc__le__self,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.12/5.30 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_le_self
% 5.12/5.30 thf(fact_1285_power__Suc__le__self,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.12/5.30 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_le_self
% 5.12/5.30 thf(fact_1286_power__Suc__less__one,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_real @ A @ one_one_real )
% 5.12/5.30 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_less_one
% 5.12/5.30 thf(fact_1287_power__Suc__less__one,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.12/5.30 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_less_one
% 5.12/5.30 thf(fact_1288_power__Suc__less__one,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.12/5.30 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_less_one
% 5.12/5.30 thf(fact_1289_power__Suc__less__one,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ A @ one_one_int )
% 5.12/5.30 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_Suc_less_one
% 5.12/5.30 thf(fact_1290_power__strict__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: real] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_real @ A @ one_one_real )
% 5.12/5.30 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing
% 5.12/5.30 thf(fact_1291_power__strict__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: rat] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.12/5.30 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing
% 5.12/5.30 thf(fact_1292_power__strict__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: nat] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.12/5.30 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing
% 5.12/5.30 thf(fact_1293_power__strict__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: int] :
% 5.12/5.30 ( ( ord_less_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_int @ A @ one_one_int )
% 5.12/5.30 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_decreasing
% 5.12/5.30 thf(fact_1294_power__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: real] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.12/5.30 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing
% 5.12/5.30 thf(fact_1295_power__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: rat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.12/5.30 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing
% 5.12/5.30 thf(fact_1296_power__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.12/5.30 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing
% 5.12/5.30 thf(fact_1297_power__decreasing,axiom,
% 5.12/5.30 ! [N: nat,N5: nat,A: int] :
% 5.12/5.30 ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.12/5.30 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_decreasing
% 5.12/5.30 thf(fact_1298_power__le__imp__le__exp,axiom,
% 5.12/5.30 ! [A: real,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 5.12/5.30 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_exp
% 5.12/5.30 thf(fact_1299_power__le__imp__le__exp,axiom,
% 5.12/5.30 ! [A: rat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 5.12/5.30 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_exp
% 5.12/5.30 thf(fact_1300_power__le__imp__le__exp,axiom,
% 5.12/5.30 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 5.12/5.30 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_exp
% 5.12/5.30 thf(fact_1301_power__le__imp__le__exp,axiom,
% 5.12/5.30 ! [A: int,M2: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 5.12/5.30 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_le_imp_le_exp
% 5.12/5.30 thf(fact_1302_power__eq__iff__eq__base,axiom,
% 5.12/5.30 ! [N: nat,A: real,B: real] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ( ( power_power_real @ A @ N )
% 5.12/5.30 = ( power_power_real @ B @ N ) )
% 5.12/5.30 = ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_iff_eq_base
% 5.12/5.30 thf(fact_1303_power__eq__iff__eq__base,axiom,
% 5.12/5.30 ! [N: nat,A: rat,B: rat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ( ( power_power_rat @ A @ N )
% 5.12/5.30 = ( power_power_rat @ B @ N ) )
% 5.12/5.30 = ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_iff_eq_base
% 5.12/5.30 thf(fact_1304_power__eq__iff__eq__base,axiom,
% 5.12/5.30 ! [N: nat,A: nat,B: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ( power_power_nat @ A @ N )
% 5.12/5.30 = ( power_power_nat @ B @ N ) )
% 5.12/5.30 = ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_iff_eq_base
% 5.12/5.30 thf(fact_1305_power__eq__iff__eq__base,axiom,
% 5.12/5.30 ! [N: nat,A: int,B: int] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ( power_power_int @ A @ N )
% 5.12/5.30 = ( power_power_int @ B @ N ) )
% 5.12/5.30 = ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_iff_eq_base
% 5.12/5.30 thf(fact_1306_power__eq__imp__eq__base,axiom,
% 5.12/5.30 ! [A: real,N: nat,B: real] :
% 5.12/5.30 ( ( ( power_power_real @ A @ N )
% 5.12/5.30 = ( power_power_real @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_imp_eq_base
% 5.12/5.30 thf(fact_1307_power__eq__imp__eq__base,axiom,
% 5.12/5.30 ! [A: rat,N: nat,B: rat] :
% 5.12/5.30 ( ( ( power_power_rat @ A @ N )
% 5.12/5.30 = ( power_power_rat @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_imp_eq_base
% 5.12/5.30 thf(fact_1308_power__eq__imp__eq__base,axiom,
% 5.12/5.30 ! [A: nat,N: nat,B: nat] :
% 5.12/5.30 ( ( ( power_power_nat @ A @ N )
% 5.12/5.30 = ( power_power_nat @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_imp_eq_base
% 5.12/5.30 thf(fact_1309_power__eq__imp__eq__base,axiom,
% 5.12/5.30 ! [A: int,N: nat,B: int] :
% 5.12/5.30 ( ( ( power_power_int @ A @ N )
% 5.12/5.30 = ( power_power_int @ B @ N ) )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( A = B ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_eq_imp_eq_base
% 5.12/5.30 thf(fact_1310_self__le__power,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % self_le_power
% 5.12/5.30 thf(fact_1311_self__le__power,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % self_le_power
% 5.12/5.30 thf(fact_1312_self__le__power,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % self_le_power
% 5.12/5.30 thf(fact_1313_self__le__power,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % self_le_power
% 5.12/5.30 thf(fact_1314_one__less__power,axiom,
% 5.12/5.30 ! [A: real,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_less_power
% 5.12/5.30 thf(fact_1315_one__less__power,axiom,
% 5.12/5.30 ! [A: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_less_power
% 5.12/5.30 thf(fact_1316_one__less__power,axiom,
% 5.12/5.30 ! [A: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_less_power
% 5.12/5.30 thf(fact_1317_one__less__power,axiom,
% 5.12/5.30 ! [A: int,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % one_less_power
% 5.12/5.30 thf(fact_1318_power__diff,axiom,
% 5.12/5.30 ! [A: complex,N: nat,M2: nat] :
% 5.12/5.30 ( ( A != zero_zero_complex )
% 5.12/5.30 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_diff
% 5.12/5.30 thf(fact_1319_power__diff,axiom,
% 5.12/5.30 ! [A: real,N: nat,M2: nat] :
% 5.12/5.30 ( ( A != zero_zero_real )
% 5.12/5.30 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_diff
% 5.12/5.30 thf(fact_1320_power__diff,axiom,
% 5.12/5.30 ! [A: rat,N: nat,M2: nat] :
% 5.12/5.30 ( ( A != zero_zero_rat )
% 5.12/5.30 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_diff
% 5.12/5.30 thf(fact_1321_power__diff,axiom,
% 5.12/5.30 ! [A: nat,N: nat,M2: nat] :
% 5.12/5.30 ( ( A != zero_zero_nat )
% 5.12/5.30 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_diff
% 5.12/5.30 thf(fact_1322_power__diff,axiom,
% 5.12/5.30 ! [A: int,N: nat,M2: nat] :
% 5.12/5.30 ( ( A != zero_zero_int )
% 5.12/5.30 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.30 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.30 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_diff
% 5.12/5.30 thf(fact_1323_power__strict__mono,axiom,
% 5.12/5.30 ! [A: real,B: real,N: nat] :
% 5.12/5.30 ( ( ord_less_real @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_mono
% 5.12/5.30 thf(fact_1324_power__strict__mono,axiom,
% 5.12/5.30 ! [A: rat,B: rat,N: nat] :
% 5.12/5.30 ( ( ord_less_rat @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_mono
% 5.12/5.30 thf(fact_1325_power__strict__mono,axiom,
% 5.12/5.30 ! [A: nat,B: nat,N: nat] :
% 5.12/5.30 ( ( ord_less_nat @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_mono
% 5.12/5.30 thf(fact_1326_power__strict__mono,axiom,
% 5.12/5.30 ! [A: int,B: int,N: nat] :
% 5.12/5.30 ( ( ord_less_int @ A @ B )
% 5.12/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % power_strict_mono
% 5.12/5.30 thf(fact_1327_zdiff__int__split,axiom,
% 5.12/5.30 ! [P: int > $o,X: nat,Y: nat] :
% 5.12/5.30 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.12/5.30 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.12/5.30 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.12/5.30 & ( ( ord_less_nat @ X @ Y )
% 5.12/5.30 => ( P @ zero_zero_int ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % zdiff_int_split
% 5.12/5.30 thf(fact_1328_Bolzano,axiom,
% 5.12/5.30 ! [A: real,B: real,P: real > real > $o] :
% 5.12/5.30 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.30 => ( ! [A4: real,B3: real,C2: real] :
% 5.12/5.30 ( ( P @ A4 @ B3 )
% 5.12/5.30 => ( ( P @ B3 @ C2 )
% 5.12/5.30 => ( ( ord_less_eq_real @ A4 @ B3 )
% 5.12/5.30 => ( ( ord_less_eq_real @ B3 @ C2 )
% 5.12/5.30 => ( P @ A4 @ C2 ) ) ) ) )
% 5.12/5.30 => ( ! [X3: real] :
% 5.12/5.30 ( ( ord_less_eq_real @ A @ X3 )
% 5.12/5.30 => ( ( ord_less_eq_real @ X3 @ B )
% 5.12/5.30 => ? [D3: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.12/5.30 & ! [A4: real,B3: real] :
% 5.12/5.30 ( ( ( ord_less_eq_real @ A4 @ X3 )
% 5.12/5.30 & ( ord_less_eq_real @ X3 @ B3 )
% 5.12/5.30 & ( ord_less_real @ ( minus_minus_real @ B3 @ A4 ) @ D3 ) )
% 5.12/5.30 => ( P @ A4 @ B3 ) ) ) ) )
% 5.12/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % Bolzano
% 5.12/5.30 thf(fact_1329_gcd__nat__induct,axiom,
% 5.12/5.30 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 5.12/5.30 ( ! [M3: nat] : ( P @ M3 @ zero_zero_nat )
% 5.12/5.30 => ( ! [M3: nat,N2: nat] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.12/5.30 => ( ( P @ N2 @ ( modulo_modulo_nat @ M3 @ N2 ) )
% 5.12/5.30 => ( P @ M3 @ N2 ) ) )
% 5.12/5.30 => ( P @ M2 @ N ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % gcd_nat_induct
% 5.12/5.30 thf(fact_1330_realpow__pos__nth,axiom,
% 5.12/5.30 ! [N: nat,A: real] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 => ? [R3: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.12/5.30 & ( ( power_power_real @ R3 @ N )
% 5.12/5.30 = A ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % realpow_pos_nth
% 5.12/5.30 thf(fact_1331_realpow__pos__nth__unique,axiom,
% 5.12/5.30 ! [N: nat,A: real] :
% 5.12/5.30 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.30 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.30 => ? [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.12/5.30 & ( ( power_power_real @ X3 @ N )
% 5.12/5.30 = A )
% 5.12/5.30 & ! [Y5: real] :
% 5.12/5.30 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.12/5.30 & ( ( power_power_real @ Y5 @ N )
% 5.12/5.30 = A ) )
% 5.12/5.30 => ( Y5 = X3 ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % realpow_pos_nth_unique
% 5.12/5.30 thf(fact_1332_nat_Osplit__sels_I1_J,axiom,
% 5.12/5.30 ! [P: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 => ( P @ F1 ) )
% 5.12/5.30 & ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 => ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(1)
% 5.12/5.30 thf(fact_1333_nat_Osplit__sels_I1_J,axiom,
% 5.12/5.30 ! [P: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 => ( P @ F1 ) )
% 5.12/5.30 & ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 => ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(1)
% 5.12/5.30 thf(fact_1334_nat_Osplit__sels_I1_J,axiom,
% 5.12/5.30 ! [P: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 => ( P @ F1 ) )
% 5.12/5.30 & ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 => ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(1)
% 5.12/5.30 thf(fact_1335_nat_Osplit__sels_I2_J,axiom,
% 5.12/5.30 ! [P: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ~ ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 & ~ ( P @ F1 ) )
% 5.12/5.30 | ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 & ~ ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(2)
% 5.12/5.30 thf(fact_1336_nat_Osplit__sels_I2_J,axiom,
% 5.12/5.30 ! [P: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ~ ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 & ~ ( P @ F1 ) )
% 5.12/5.30 | ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 & ~ ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(2)
% 5.12/5.30 thf(fact_1337_nat_Osplit__sels_I2_J,axiom,
% 5.12/5.30 ! [P: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.12/5.30 ( ( P @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.12/5.30 = ( ~ ( ( ( Nat = zero_zero_nat )
% 5.12/5.30 & ~ ( P @ F1 ) )
% 5.12/5.30 | ( ( Nat
% 5.12/5.30 = ( suc @ ( pred @ Nat ) ) )
% 5.12/5.30 & ~ ( P @ ( F22 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % nat.split_sels(2)
% 5.12/5.30 thf(fact_1338_imp__le__cong,axiom,
% 5.12/5.30 ! [X: int,X6: int,P: $o,P5: $o] :
% 5.12/5.30 ( ( X = X6 )
% 5.12/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.12/5.30 => ( P = P5 ) )
% 5.12/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.30 => P )
% 5.12/5.30 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.12/5.30 => P5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % imp_le_cong
% 5.12/5.30 thf(fact_1339_conj__le__cong,axiom,
% 5.12/5.30 ! [X: int,X6: int,P: $o,P5: $o] :
% 5.12/5.30 ( ( X = X6 )
% 5.12/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.12/5.30 => ( P = P5 ) )
% 5.12/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.30 & P )
% 5.12/5.30 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.12/5.30 & P5 ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % conj_le_cong
% 5.12/5.30 thf(fact_1340_arsinh__minus__real,axiom,
% 5.12/5.30 ! [X: real] :
% 5.12/5.30 ( ( arsinh_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.30 = ( uminus_uminus_real @ ( arsinh_real @ X ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % arsinh_minus_real
% 5.12/5.30 thf(fact_1341_pinf_I1_J,axiom,
% 5.12/5.30 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.12/5.30 ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(1)
% 5.12/5.30 thf(fact_1342_pinf_I1_J,axiom,
% 5.12/5.30 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.12/5.30 ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(1)
% 5.12/5.30 thf(fact_1343_pinf_I1_J,axiom,
% 5.12/5.30 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.12/5.30 ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(1)
% 5.12/5.30 thf(fact_1344_pinf_I1_J,axiom,
% 5.12/5.30 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.12/5.30 ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(1)
% 5.12/5.30 thf(fact_1345_pinf_I1_J,axiom,
% 5.12/5.30 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.12/5.30 ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(1)
% 5.12/5.30 thf(fact_1346_pinf_I2_J,axiom,
% 5.12/5.30 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.12/5.30 ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(2)
% 5.12/5.30 thf(fact_1347_pinf_I2_J,axiom,
% 5.12/5.30 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.12/5.30 ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(2)
% 5.12/5.30 thf(fact_1348_pinf_I2_J,axiom,
% 5.12/5.30 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.12/5.30 ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(2)
% 5.12/5.30 thf(fact_1349_pinf_I2_J,axiom,
% 5.12/5.30 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.12/5.30 ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(2)
% 5.12/5.30 thf(fact_1350_pinf_I2_J,axiom,
% 5.12/5.30 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.12/5.30 ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(2)
% 5.12/5.30 thf(fact_1351_pinf_I3_J,axiom,
% 5.12/5.30 ! [T: real] :
% 5.12/5.30 ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(3)
% 5.12/5.30 thf(fact_1352_pinf_I3_J,axiom,
% 5.12/5.30 ! [T: rat] :
% 5.12/5.30 ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(3)
% 5.12/5.30 thf(fact_1353_pinf_I3_J,axiom,
% 5.12/5.30 ! [T: num] :
% 5.12/5.30 ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(3)
% 5.12/5.30 thf(fact_1354_pinf_I3_J,axiom,
% 5.12/5.30 ! [T: nat] :
% 5.12/5.30 ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(3)
% 5.12/5.30 thf(fact_1355_pinf_I3_J,axiom,
% 5.12/5.30 ! [T: int] :
% 5.12/5.30 ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(3)
% 5.12/5.30 thf(fact_1356_pinf_I4_J,axiom,
% 5.12/5.30 ! [T: real] :
% 5.12/5.30 ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(4)
% 5.12/5.30 thf(fact_1357_pinf_I4_J,axiom,
% 5.12/5.30 ! [T: rat] :
% 5.12/5.30 ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(4)
% 5.12/5.30 thf(fact_1358_pinf_I4_J,axiom,
% 5.12/5.30 ! [T: num] :
% 5.12/5.30 ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(4)
% 5.12/5.30 thf(fact_1359_pinf_I4_J,axiom,
% 5.12/5.30 ! [T: nat] :
% 5.12/5.30 ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(4)
% 5.12/5.30 thf(fact_1360_pinf_I4_J,axiom,
% 5.12/5.30 ! [T: int] :
% 5.12/5.30 ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ( X4 != T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(4)
% 5.12/5.30 thf(fact_1361_pinf_I5_J,axiom,
% 5.12/5.30 ! [T: real] :
% 5.12/5.30 ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ~ ( ord_less_real @ X4 @ T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(5)
% 5.12/5.30 thf(fact_1362_pinf_I5_J,axiom,
% 5.12/5.30 ! [T: rat] :
% 5.12/5.30 ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(5)
% 5.12/5.30 thf(fact_1363_pinf_I5_J,axiom,
% 5.12/5.30 ! [T: num] :
% 5.12/5.30 ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ~ ( ord_less_num @ X4 @ T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(5)
% 5.12/5.30 thf(fact_1364_pinf_I5_J,axiom,
% 5.12/5.30 ! [T: nat] :
% 5.12/5.30 ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(5)
% 5.12/5.30 thf(fact_1365_pinf_I5_J,axiom,
% 5.12/5.30 ! [T: int] :
% 5.12/5.30 ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ~ ( ord_less_int @ X4 @ T ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(5)
% 5.12/5.30 thf(fact_1366_pinf_I7_J,axiom,
% 5.12/5.30 ! [T: real] :
% 5.12/5.30 ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.30 => ( ord_less_real @ T @ X4 ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(7)
% 5.12/5.30 thf(fact_1367_pinf_I7_J,axiom,
% 5.12/5.30 ! [T: rat] :
% 5.12/5.30 ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.30 => ( ord_less_rat @ T @ X4 ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(7)
% 5.12/5.30 thf(fact_1368_pinf_I7_J,axiom,
% 5.12/5.30 ! [T: num] :
% 5.12/5.30 ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.30 => ( ord_less_num @ T @ X4 ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(7)
% 5.12/5.30 thf(fact_1369_pinf_I7_J,axiom,
% 5.12/5.30 ! [T: nat] :
% 5.12/5.30 ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.30 => ( ord_less_nat @ T @ X4 ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(7)
% 5.12/5.30 thf(fact_1370_pinf_I7_J,axiom,
% 5.12/5.30 ! [T: int] :
% 5.12/5.30 ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.30 => ( ord_less_int @ T @ X4 ) ) ).
% 5.12/5.30
% 5.12/5.30 % pinf(7)
% 5.12/5.30 thf(fact_1371_minf_I1_J,axiom,
% 5.12/5.30 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.12/5.30 ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(1)
% 5.12/5.30 thf(fact_1372_minf_I1_J,axiom,
% 5.12/5.30 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.12/5.30 ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(1)
% 5.12/5.30 thf(fact_1373_minf_I1_J,axiom,
% 5.12/5.30 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.12/5.30 ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: num] :
% 5.12/5.30 ! [X3: num] :
% 5.12/5.30 ( ( ord_less_num @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: num] :
% 5.12/5.30 ! [X4: num] :
% 5.12/5.30 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(1)
% 5.12/5.30 thf(fact_1374_minf_I1_J,axiom,
% 5.12/5.30 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.12/5.30 ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: nat] :
% 5.12/5.30 ! [X3: nat] :
% 5.12/5.30 ( ( ord_less_nat @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: nat] :
% 5.12/5.30 ! [X4: nat] :
% 5.12/5.30 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(1)
% 5.12/5.30 thf(fact_1375_minf_I1_J,axiom,
% 5.12/5.30 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.12/5.30 ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: int] :
% 5.12/5.30 ! [X3: int] :
% 5.12/5.30 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: int] :
% 5.12/5.30 ! [X4: int] :
% 5.12/5.30 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 & ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 & ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(1)
% 5.12/5.30 thf(fact_1376_minf_I2_J,axiom,
% 5.12/5.30 ! [P: real > $o,P5: real > $o,Q: real > $o,Q2: real > $o] :
% 5.12/5.30 ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: real] :
% 5.12/5.30 ! [X3: real] :
% 5.12/5.30 ( ( ord_less_real @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: real] :
% 5.12/5.30 ! [X4: real] :
% 5.12/5.30 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(2)
% 5.12/5.30 thf(fact_1377_minf_I2_J,axiom,
% 5.12/5.30 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 5.12/5.30 ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X3 @ Z5 )
% 5.12/5.30 => ( ( P @ X3 )
% 5.12/5.30 = ( P5 @ X3 ) ) )
% 5.12/5.30 => ( ? [Z5: rat] :
% 5.12/5.30 ! [X3: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X3 @ Z5 )
% 5.12/5.30 => ( ( Q @ X3 )
% 5.12/5.30 = ( Q2 @ X3 ) ) )
% 5.12/5.30 => ? [Z4: rat] :
% 5.12/5.30 ! [X4: rat] :
% 5.12/5.30 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.30 => ( ( ( P @ X4 )
% 5.12/5.30 | ( Q @ X4 ) )
% 5.12/5.30 = ( ( P5 @ X4 )
% 5.12/5.30 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.30
% 5.12/5.30 % minf(2)
% 5.12/5.30 thf(fact_1378_minf_I2_J,axiom,
% 5.12/5.31 ! [P: num > $o,P5: num > $o,Q: num > $o,Q2: num > $o] :
% 5.12/5.31 ( ? [Z5: num] :
% 5.12/5.31 ! [X3: num] :
% 5.12/5.31 ( ( ord_less_num @ X3 @ Z5 )
% 5.12/5.31 => ( ( P @ X3 )
% 5.12/5.31 = ( P5 @ X3 ) ) )
% 5.12/5.31 => ( ? [Z5: num] :
% 5.12/5.31 ! [X3: num] :
% 5.12/5.31 ( ( ord_less_num @ X3 @ Z5 )
% 5.12/5.31 => ( ( Q @ X3 )
% 5.12/5.31 = ( Q2 @ X3 ) ) )
% 5.12/5.31 => ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ( ( ( P @ X4 )
% 5.12/5.31 | ( Q @ X4 ) )
% 5.12/5.31 = ( ( P5 @ X4 )
% 5.12/5.31 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(2)
% 5.12/5.31 thf(fact_1379_minf_I2_J,axiom,
% 5.12/5.31 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 5.12/5.31 ( ? [Z5: nat] :
% 5.12/5.31 ! [X3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X3 @ Z5 )
% 5.12/5.31 => ( ( P @ X3 )
% 5.12/5.31 = ( P5 @ X3 ) ) )
% 5.12/5.31 => ( ? [Z5: nat] :
% 5.12/5.31 ! [X3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X3 @ Z5 )
% 5.12/5.31 => ( ( Q @ X3 )
% 5.12/5.31 = ( Q2 @ X3 ) ) )
% 5.12/5.31 => ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ( ( ( P @ X4 )
% 5.12/5.31 | ( Q @ X4 ) )
% 5.12/5.31 = ( ( P5 @ X4 )
% 5.12/5.31 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(2)
% 5.12/5.31 thf(fact_1380_minf_I2_J,axiom,
% 5.12/5.31 ! [P: int > $o,P5: int > $o,Q: int > $o,Q2: int > $o] :
% 5.12/5.31 ( ? [Z5: int] :
% 5.12/5.31 ! [X3: int] :
% 5.12/5.31 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.31 => ( ( P @ X3 )
% 5.12/5.31 = ( P5 @ X3 ) ) )
% 5.12/5.31 => ( ? [Z5: int] :
% 5.12/5.31 ! [X3: int] :
% 5.12/5.31 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.31 => ( ( Q @ X3 )
% 5.12/5.31 = ( Q2 @ X3 ) ) )
% 5.12/5.31 => ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ( ( ( P @ X4 )
% 5.12/5.31 | ( Q @ X4 ) )
% 5.12/5.31 = ( ( P5 @ X4 )
% 5.12/5.31 | ( Q2 @ X4 ) ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(2)
% 5.12/5.31 thf(fact_1381_minf_I3_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(3)
% 5.12/5.31 thf(fact_1382_minf_I3_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(3)
% 5.12/5.31 thf(fact_1383_minf_I3_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(3)
% 5.12/5.31 thf(fact_1384_minf_I3_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(3)
% 5.12/5.31 thf(fact_1385_minf_I3_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(3)
% 5.12/5.31 thf(fact_1386_minf_I4_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(4)
% 5.12/5.31 thf(fact_1387_minf_I4_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(4)
% 5.12/5.31 thf(fact_1388_minf_I4_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(4)
% 5.12/5.31 thf(fact_1389_minf_I4_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(4)
% 5.12/5.31 thf(fact_1390_minf_I4_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ( X4 != T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(4)
% 5.12/5.31 thf(fact_1391_minf_I5_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_real @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(5)
% 5.12/5.31 thf(fact_1392_minf_I5_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_rat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(5)
% 5.12/5.31 thf(fact_1393_minf_I5_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_num @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(5)
% 5.12/5.31 thf(fact_1394_minf_I5_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_nat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(5)
% 5.12/5.31 thf(fact_1395_minf_I5_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_int @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(5)
% 5.12/5.31 thf(fact_1396_minf_I7_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_real @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(7)
% 5.12/5.31 thf(fact_1397_minf_I7_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(7)
% 5.12/5.31 thf(fact_1398_minf_I7_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_num @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(7)
% 5.12/5.31 thf(fact_1399_minf_I7_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(7)
% 5.12/5.31 thf(fact_1400_minf_I7_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_int @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(7)
% 5.12/5.31 thf(fact_1401_pinf_I6_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.31 => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(6)
% 5.12/5.31 thf(fact_1402_pinf_I6_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.31 => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(6)
% 5.12/5.31 thf(fact_1403_pinf_I6_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.31 => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(6)
% 5.12/5.31 thf(fact_1404_pinf_I6_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.31 => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(6)
% 5.12/5.31 thf(fact_1405_pinf_I6_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.31 => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(6)
% 5.12/5.31 thf(fact_1406_pinf_I8_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.31 => ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(8)
% 5.12/5.31 thf(fact_1407_pinf_I8_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.31 => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(8)
% 5.12/5.31 thf(fact_1408_pinf_I8_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ Z4 @ X4 )
% 5.12/5.31 => ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(8)
% 5.12/5.31 thf(fact_1409_pinf_I8_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.31 => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(8)
% 5.12/5.31 thf(fact_1410_pinf_I8_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.31 => ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % pinf(8)
% 5.12/5.31 thf(fact_1411_minf_I6_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(6)
% 5.12/5.31 thf(fact_1412_minf_I6_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(6)
% 5.12/5.31 thf(fact_1413_minf_I6_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(6)
% 5.12/5.31 thf(fact_1414_minf_I6_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(6)
% 5.12/5.31 thf(fact_1415_minf_I6_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(6)
% 5.12/5.31 thf(fact_1416_minf_I8_J,axiom,
% 5.12/5.31 ! [T: real] :
% 5.12/5.31 ? [Z4: real] :
% 5.12/5.31 ! [X4: real] :
% 5.12/5.31 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(8)
% 5.12/5.31 thf(fact_1417_minf_I8_J,axiom,
% 5.12/5.31 ! [T: rat] :
% 5.12/5.31 ? [Z4: rat] :
% 5.12/5.31 ! [X4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(8)
% 5.12/5.31 thf(fact_1418_minf_I8_J,axiom,
% 5.12/5.31 ! [T: num] :
% 5.12/5.31 ? [Z4: num] :
% 5.12/5.31 ! [X4: num] :
% 5.12/5.31 ( ( ord_less_num @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(8)
% 5.12/5.31 thf(fact_1419_minf_I8_J,axiom,
% 5.12/5.31 ! [T: nat] :
% 5.12/5.31 ? [Z4: nat] :
% 5.12/5.31 ! [X4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(8)
% 5.12/5.31 thf(fact_1420_minf_I8_J,axiom,
% 5.12/5.31 ! [T: int] :
% 5.12/5.31 ? [Z4: int] :
% 5.12/5.31 ! [X4: int] :
% 5.12/5.31 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.31 => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.12/5.31
% 5.12/5.31 % minf(8)
% 5.12/5.31 thf(fact_1421_realpow__pos__nth2,axiom,
% 5.12/5.31 ! [A: real,N: nat] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.31 => ? [R3: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.12/5.31 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.12/5.31 = A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % realpow_pos_nth2
% 5.12/5.31 thf(fact_1422_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.12/5.31 ! [X: real,N: nat] :
% 5.12/5.31 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_ge_one_minus_x_over_n_power_n
% 5.12/5.31 thf(fact_1423_nat__descend__induct,axiom,
% 5.12/5.31 ! [N: nat,P: nat > $o,M2: nat] :
% 5.12/5.31 ( ! [K2: nat] :
% 5.12/5.31 ( ( ord_less_nat @ N @ K2 )
% 5.12/5.31 => ( P @ K2 ) )
% 5.12/5.31 => ( ! [K2: nat] :
% 5.12/5.31 ( ( ord_less_eq_nat @ K2 @ N )
% 5.12/5.31 => ( ! [I4: nat] :
% 5.12/5.31 ( ( ord_less_nat @ K2 @ I4 )
% 5.12/5.31 => ( P @ I4 ) )
% 5.12/5.31 => ( P @ K2 ) ) )
% 5.12/5.31 => ( P @ M2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % nat_descend_induct
% 5.12/5.31 thf(fact_1424_nat__ivt__aux,axiom,
% 5.12/5.31 ! [N: nat,F: nat > int,K: int] :
% 5.12/5.31 ( ! [I3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ I3 @ N )
% 5.12/5.31 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.12/5.31 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.12/5.31 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.12/5.31 => ? [I3: nat] :
% 5.12/5.31 ( ( ord_less_eq_nat @ I3 @ N )
% 5.12/5.31 & ( ( F @ I3 )
% 5.12/5.31 = K ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % nat_ivt_aux
% 5.12/5.31 thf(fact_1425_ln__root,axiom,
% 5.12/5.31 ! [N: nat,B: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.31 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.12/5.31 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ln_root
% 5.12/5.31 thf(fact_1426_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.31 => ( ( ord_less_real @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1427_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: set_nat,Y: set_nat] :
% 5.12/5.31 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.12/5.31 => ( ( ord_less_set_nat @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1428_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.31 => ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1429_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X @ Y )
% 5.12/5.31 => ( ( ord_less_num @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1430_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( ord_less_eq_nat @ X @ Y )
% 5.12/5.31 => ( ( ord_less_nat @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1431_order__le__imp__less__or__eq,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ X @ Y )
% 5.12/5.31 => ( ( ord_less_int @ X @ Y )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_imp_less_or_eq
% 5.12/5.31 thf(fact_1432_linorder__le__less__linear,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.31 | ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_le_less_linear
% 5.12/5.31 thf(fact_1433_linorder__le__less__linear,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.31 | ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_le_less_linear
% 5.12/5.31 thf(fact_1434_linorder__le__less__linear,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X @ Y )
% 5.12/5.31 | ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_le_less_linear
% 5.12/5.31 thf(fact_1435_linorder__le__less__linear,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( ord_less_eq_nat @ X @ Y )
% 5.12/5.31 | ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_le_less_linear
% 5.12/5.31 thf(fact_1436_linorder__le__less__linear,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ X @ Y )
% 5.12/5.31 | ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_le_less_linear
% 5.12/5.31 thf(fact_1437_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > real,C: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1438_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1439_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > real,C: real] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1440_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1441_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: int,B: int,F: int > real,C: real] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: int,Y3: int] :
% 5.12/5.31 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1442_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1443_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1444_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1445_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1446_order__less__le__subst2,axiom,
% 5.12/5.31 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: int,Y3: int] :
% 5.12/5.31 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst2
% 5.12/5.31 thf(fact_1447_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1448_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1449_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1450_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1451_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1452_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: real,F: num > real,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1453_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1454_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: num,F: num > num,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1455_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1456_order__less__le__subst1,axiom,
% 5.12/5.31 ! [A: int,F: num > int,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_le_subst1
% 5.12/5.31 thf(fact_1457_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1458_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1459_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1460_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1461_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1462_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > real,C: real] :
% 5.12/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1463_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1464_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > num,C: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1465_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.12/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1466_order__le__less__subst2,axiom,
% 5.12/5.31 ! [A: num,B: num,F: num > int,C: int] :
% 5.12/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.12/5.31 => ( ! [X3: num,Y3: num] :
% 5.12/5.31 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_le_less_subst2
% 5.12/5.31 thf(fact_1467_abs__abs,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.12/5.31 = ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_abs
% 5.12/5.31 thf(fact_1468_abs__abs,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.12/5.31 = ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_abs
% 5.12/5.31 thf(fact_1469_abs__abs,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_abs
% 5.12/5.31 thf(fact_1470_abs__abs,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.12/5.31 = ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_abs
% 5.12/5.31 thf(fact_1471_abs__idempotent,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.12/5.31 = ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_idempotent
% 5.12/5.31 thf(fact_1472_abs__idempotent,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.12/5.31 = ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_idempotent
% 5.12/5.31 thf(fact_1473_abs__idempotent,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_idempotent
% 5.12/5.31 thf(fact_1474_abs__idempotent,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.12/5.31 = ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_idempotent
% 5.12/5.31 thf(fact_1475_exp__inj__iff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ( exp_real @ X )
% 5.12/5.31 = ( exp_real @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_inj_iff
% 5.12/5.31 thf(fact_1476_abs__0__eq,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( zero_z3403309356797280102nteger
% 5.12/5.31 = ( abs_abs_Code_integer @ A ) )
% 5.12/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0_eq
% 5.12/5.31 thf(fact_1477_abs__0__eq,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( zero_zero_real
% 5.12/5.31 = ( abs_abs_real @ A ) )
% 5.12/5.31 = ( A = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0_eq
% 5.12/5.31 thf(fact_1478_abs__0__eq,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( zero_zero_rat
% 5.12/5.31 = ( abs_abs_rat @ A ) )
% 5.12/5.31 = ( A = zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0_eq
% 5.12/5.31 thf(fact_1479_abs__0__eq,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( zero_zero_int
% 5.12/5.31 = ( abs_abs_int @ A ) )
% 5.12/5.31 = ( A = zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0_eq
% 5.12/5.31 thf(fact_1480_abs__eq__0,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = zero_z3403309356797280102nteger )
% 5.12/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0
% 5.12/5.31 thf(fact_1481_abs__eq__0,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ( abs_abs_real @ A )
% 5.12/5.31 = zero_zero_real )
% 5.12/5.31 = ( A = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0
% 5.12/5.31 thf(fact_1482_abs__eq__0,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ( abs_abs_rat @ A )
% 5.12/5.31 = zero_zero_rat )
% 5.12/5.31 = ( A = zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0
% 5.12/5.31 thf(fact_1483_abs__eq__0,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ( abs_abs_int @ A )
% 5.12/5.31 = zero_zero_int )
% 5.12/5.31 = ( A = zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0
% 5.12/5.31 thf(fact_1484_abs__zero,axiom,
% 5.12/5.31 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.12/5.31 = zero_z3403309356797280102nteger ) ).
% 5.12/5.31
% 5.12/5.31 % abs_zero
% 5.12/5.31 thf(fact_1485_abs__zero,axiom,
% 5.12/5.31 ( ( abs_abs_real @ zero_zero_real )
% 5.12/5.31 = zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_zero
% 5.12/5.31 thf(fact_1486_abs__zero,axiom,
% 5.12/5.31 ( ( abs_abs_rat @ zero_zero_rat )
% 5.12/5.31 = zero_zero_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_zero
% 5.12/5.31 thf(fact_1487_abs__zero,axiom,
% 5.12/5.31 ( ( abs_abs_int @ zero_zero_int )
% 5.12/5.31 = zero_zero_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_zero
% 5.12/5.31 thf(fact_1488_abs__0,axiom,
% 5.12/5.31 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.12/5.31 = zero_z3403309356797280102nteger ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0
% 5.12/5.31 thf(fact_1489_abs__0,axiom,
% 5.12/5.31 ( ( abs_abs_real @ zero_zero_real )
% 5.12/5.31 = zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0
% 5.12/5.31 thf(fact_1490_abs__0,axiom,
% 5.12/5.31 ( ( abs_abs_rat @ zero_zero_rat )
% 5.12/5.31 = zero_zero_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0
% 5.12/5.31 thf(fact_1491_abs__0,axiom,
% 5.12/5.31 ( ( abs_abs_int @ zero_zero_int )
% 5.12/5.31 = zero_zero_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_0
% 5.12/5.31 thf(fact_1492_abs__1,axiom,
% 5.12/5.31 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.12/5.31 = one_one_Code_integer ) ).
% 5.12/5.31
% 5.12/5.31 % abs_1
% 5.12/5.31 thf(fact_1493_abs__1,axiom,
% 5.12/5.31 ( ( abs_abs_complex @ one_one_complex )
% 5.12/5.31 = one_one_complex ) ).
% 5.12/5.31
% 5.12/5.31 % abs_1
% 5.12/5.31 thf(fact_1494_abs__1,axiom,
% 5.12/5.31 ( ( abs_abs_real @ one_one_real )
% 5.12/5.31 = one_one_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_1
% 5.12/5.31 thf(fact_1495_abs__1,axiom,
% 5.12/5.31 ( ( abs_abs_rat @ one_one_rat )
% 5.12/5.31 = one_one_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_1
% 5.12/5.31 thf(fact_1496_abs__1,axiom,
% 5.12/5.31 ( ( abs_abs_int @ one_one_int )
% 5.12/5.31 = one_one_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_1
% 5.12/5.31 thf(fact_1497_abs__divide,axiom,
% 5.12/5.31 ! [A: complex,B: complex] :
% 5.12/5.31 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.31 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_divide
% 5.12/5.31 thf(fact_1498_abs__divide,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.31 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_divide
% 5.12/5.31 thf(fact_1499_abs__divide,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.12/5.31 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_divide
% 5.12/5.31 thf(fact_1500_abs__minus,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.12/5.31 = ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus
% 5.12/5.31 thf(fact_1501_abs__minus,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.12/5.31 = ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus
% 5.12/5.31 thf(fact_1502_abs__minus,axiom,
% 5.12/5.31 ! [A: complex] :
% 5.12/5.31 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.12/5.31 = ( abs_abs_complex @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus
% 5.12/5.31 thf(fact_1503_abs__minus,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus
% 5.12/5.31 thf(fact_1504_abs__minus,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.12/5.31 = ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus
% 5.12/5.31 thf(fact_1505_abs__minus__cancel,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.12/5.31 = ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_cancel
% 5.12/5.31 thf(fact_1506_abs__minus__cancel,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.12/5.31 = ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_cancel
% 5.12/5.31 thf(fact_1507_abs__minus__cancel,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_cancel
% 5.12/5.31 thf(fact_1508_abs__minus__cancel,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.12/5.31 = ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_cancel
% 5.12/5.31 thf(fact_1509_abs__of__nat,axiom,
% 5.12/5.31 ! [N: nat] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.12/5.31 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nat
% 5.12/5.31 thf(fact_1510_abs__of__nat,axiom,
% 5.12/5.31 ! [N: nat] :
% 5.12/5.31 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.31 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nat
% 5.12/5.31 thf(fact_1511_abs__of__nat,axiom,
% 5.12/5.31 ! [N: nat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.12/5.31 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nat
% 5.12/5.31 thf(fact_1512_abs__of__nat,axiom,
% 5.12/5.31 ! [N: nat] :
% 5.12/5.31 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.31 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nat
% 5.12/5.31 thf(fact_1513_exp__less__cancel__iff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.12/5.31 = ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_less_cancel_iff
% 5.12/5.31 thf(fact_1514_exp__less__mono,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_less_mono
% 5.12/5.31 thf(fact_1515_exp__le__cancel__iff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.12/5.31 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_le_cancel_iff
% 5.12/5.31 thf(fact_1516_ln__exp,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ln_ln_real @ ( exp_real @ X ) )
% 5.12/5.31 = X ) ).
% 5.12/5.31
% 5.12/5.31 % ln_exp
% 5.12/5.31 thf(fact_1517_abs__le__zero__iff,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.12/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_zero_iff
% 5.12/5.31 thf(fact_1518_abs__le__zero__iff,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.12/5.31 = ( A = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_zero_iff
% 5.12/5.31 thf(fact_1519_abs__le__zero__iff,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.12/5.31 = ( A = zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_zero_iff
% 5.12/5.31 thf(fact_1520_abs__le__zero__iff,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.12/5.31 = ( A = zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_zero_iff
% 5.12/5.31 thf(fact_1521_abs__le__self__iff,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.12/5.31 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_self_iff
% 5.12/5.31 thf(fact_1522_abs__le__self__iff,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.12/5.31 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_self_iff
% 5.12/5.31 thf(fact_1523_abs__le__self__iff,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.12/5.31 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_self_iff
% 5.12/5.31 thf(fact_1524_abs__le__self__iff,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.12/5.31 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_self_iff
% 5.12/5.31 thf(fact_1525_abs__of__nonneg,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.31 => ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonneg
% 5.12/5.31 thf(fact_1526_abs__of__nonneg,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.31 => ( ( abs_abs_real @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonneg
% 5.12/5.31 thf(fact_1527_abs__of__nonneg,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.31 => ( ( abs_abs_rat @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonneg
% 5.12/5.31 thf(fact_1528_abs__of__nonneg,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.31 => ( ( abs_abs_int @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonneg
% 5.12/5.31 thf(fact_1529_zero__less__abs__iff,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.31 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_abs_iff
% 5.12/5.31 thf(fact_1530_zero__less__abs__iff,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.12/5.31 = ( A != zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_abs_iff
% 5.12/5.31 thf(fact_1531_zero__less__abs__iff,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.12/5.31 = ( A != zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_abs_iff
% 5.12/5.31 thf(fact_1532_zero__less__abs__iff,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.12/5.31 = ( A != zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_abs_iff
% 5.12/5.31 thf(fact_1533_abs__neg__one,axiom,
% 5.12/5.31 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.31 = one_one_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_neg_one
% 5.12/5.31 thf(fact_1534_abs__neg__one,axiom,
% 5.12/5.31 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.31 = one_one_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_neg_one
% 5.12/5.31 thf(fact_1535_abs__neg__one,axiom,
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.31 = one_one_Code_integer ) ).
% 5.12/5.31
% 5.12/5.31 % abs_neg_one
% 5.12/5.31 thf(fact_1536_abs__neg__one,axiom,
% 5.12/5.31 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.31 = one_one_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_neg_one
% 5.12/5.31 thf(fact_1537_abs__power__minus,axiom,
% 5.12/5.31 ! [A: int,N: nat] :
% 5.12/5.31 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.12/5.31 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_power_minus
% 5.12/5.31 thf(fact_1538_abs__power__minus,axiom,
% 5.12/5.31 ! [A: real,N: nat] :
% 5.12/5.31 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.12/5.31 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_power_minus
% 5.12/5.31 thf(fact_1539_abs__power__minus,axiom,
% 5.12/5.31 ! [A: code_integer,N: nat] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_power_minus
% 5.12/5.31 thf(fact_1540_abs__power__minus,axiom,
% 5.12/5.31 ! [A: rat,N: nat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.12/5.31 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_power_minus
% 5.12/5.31 thf(fact_1541_exp__zero,axiom,
% 5.12/5.31 ( ( exp_complex @ zero_zero_complex )
% 5.12/5.31 = one_one_complex ) ).
% 5.12/5.31
% 5.12/5.31 % exp_zero
% 5.12/5.31 thf(fact_1542_exp__zero,axiom,
% 5.12/5.31 ( ( exp_real @ zero_zero_real )
% 5.12/5.31 = one_one_real ) ).
% 5.12/5.31
% 5.12/5.31 % exp_zero
% 5.12/5.31 thf(fact_1543_real__root__Suc__0,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.12/5.31 = X ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_Suc_0
% 5.12/5.31 thf(fact_1544_root__0,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( root @ zero_zero_nat @ X )
% 5.12/5.31 = zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % root_0
% 5.12/5.31 thf(fact_1545_real__root__eq__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ( root @ N @ X )
% 5.12/5.31 = ( root @ N @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_eq_iff
% 5.12/5.31 thf(fact_1546_exp__eq__one__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ( exp_real @ X )
% 5.12/5.31 = one_one_real )
% 5.12/5.31 = ( X = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_eq_one_iff
% 5.12/5.31 thf(fact_1547_zero__le__divide__abs__iff,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.12/5.31 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.31 | ( B = zero_zero_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_divide_abs_iff
% 5.12/5.31 thf(fact_1548_zero__le__divide__abs__iff,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.12/5.31 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.31 | ( B = zero_zero_rat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_divide_abs_iff
% 5.12/5.31 thf(fact_1549_divide__le__0__abs__iff,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.12/5.31 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.31 | ( B = zero_zero_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % divide_le_0_abs_iff
% 5.12/5.31 thf(fact_1550_divide__le__0__abs__iff,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.12/5.31 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.31 | ( B = zero_zero_rat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % divide_le_0_abs_iff
% 5.12/5.31 thf(fact_1551_abs__of__nonpos,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.31 => ( ( abs_abs_real @ A )
% 5.12/5.31 = ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonpos
% 5.12/5.31 thf(fact_1552_abs__of__nonpos,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.12/5.31 => ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonpos
% 5.12/5.31 thf(fact_1553_abs__of__nonpos,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.31 => ( ( abs_abs_rat @ A )
% 5.12/5.31 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonpos
% 5.12/5.31 thf(fact_1554_abs__of__nonpos,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.31 => ( ( abs_abs_int @ A )
% 5.12/5.31 = ( uminus_uminus_int @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_nonpos
% 5.12/5.31 thf(fact_1555_real__root__eq__0__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ( root @ N @ X )
% 5.12/5.31 = zero_zero_real )
% 5.12/5.31 = ( X = zero_zero_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_eq_0_iff
% 5.12/5.31 thf(fact_1556_real__root__less__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_less_iff
% 5.12/5.31 thf(fact_1557_real__root__le__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_le_iff
% 5.12/5.31 thf(fact_1558_real__root__one,axiom,
% 5.12/5.31 ! [N: nat] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( root @ N @ one_one_real )
% 5.12/5.31 = one_one_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_one
% 5.12/5.31 thf(fact_1559_real__root__eq__1__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ( root @ N @ X )
% 5.12/5.31 = one_one_real )
% 5.12/5.31 = ( X = one_one_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_eq_1_iff
% 5.12/5.31 thf(fact_1560_one__less__exp__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.12/5.31 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % one_less_exp_iff
% 5.12/5.31 thf(fact_1561_exp__less__one__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.12/5.31 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_less_one_iff
% 5.12/5.31 thf(fact_1562_exp__le__one__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.12/5.31 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_le_one_iff
% 5.12/5.31 thf(fact_1563_one__le__exp__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.12/5.31 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % one_le_exp_iff
% 5.12/5.31 thf(fact_1564_zabs__less__one__iff,axiom,
% 5.12/5.31 ! [Z2: int] :
% 5.12/5.31 ( ( ord_less_int @ ( abs_abs_int @ Z2 ) @ one_one_int )
% 5.12/5.31 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % zabs_less_one_iff
% 5.12/5.31 thf(fact_1565_exp__ln,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.31 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.12/5.31 = X ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_ln
% 5.12/5.31 thf(fact_1566_exp__ln__iff,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.12/5.31 = X )
% 5.12/5.31 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_ln_iff
% 5.12/5.31 thf(fact_1567_zero__less__power__abs__iff,axiom,
% 5.12/5.31 ! [A: code_integer,N: nat] :
% 5.12/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.12/5.31 = ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.31 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_power_abs_iff
% 5.12/5.31 thf(fact_1568_zero__less__power__abs__iff,axiom,
% 5.12/5.31 ! [A: real,N: nat] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.12/5.31 = ( ( A != zero_zero_real )
% 5.12/5.31 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_power_abs_iff
% 5.12/5.31 thf(fact_1569_zero__less__power__abs__iff,axiom,
% 5.12/5.31 ! [A: rat,N: nat] :
% 5.12/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.12/5.31 = ( ( A != zero_zero_rat )
% 5.12/5.31 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_power_abs_iff
% 5.12/5.31 thf(fact_1570_zero__less__power__abs__iff,axiom,
% 5.12/5.31 ! [A: int,N: nat] :
% 5.12/5.31 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.12/5.31 = ( ( A != zero_zero_int )
% 5.12/5.31 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_less_power_abs_iff
% 5.12/5.31 thf(fact_1571_real__root__gt__0__iff,axiom,
% 5.12/5.31 ! [N: nat,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_gt_0_iff
% 5.12/5.31 thf(fact_1572_real__root__lt__0__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.12/5.31 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_lt_0_iff
% 5.12/5.31 thf(fact_1573_real__root__ge__0__iff,axiom,
% 5.12/5.31 ! [N: nat,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_ge_0_iff
% 5.12/5.31 thf(fact_1574_real__root__le__0__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.12/5.31 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_le_0_iff
% 5.12/5.31 thf(fact_1575_real__root__gt__1__iff,axiom,
% 5.12/5.31 ! [N: nat,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_gt_1_iff
% 5.12/5.31 thf(fact_1576_real__root__lt__1__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.12/5.31 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_lt_1_iff
% 5.12/5.31 thf(fact_1577_real__root__ge__1__iff,axiom,
% 5.12/5.31 ! [N: nat,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 5.12/5.31 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_ge_1_iff
% 5.12/5.31 thf(fact_1578_real__root__le__1__iff,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.12/5.31 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_le_1_iff
% 5.12/5.31 thf(fact_1579_real__root__pow__pos2,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.31 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.12/5.31 = X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_pow_pos2
% 5.12/5.31 thf(fact_1580_abs__ge__self,axiom,
% 5.12/5.31 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_self
% 5.12/5.31 thf(fact_1581_abs__ge__self,axiom,
% 5.12/5.31 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_self
% 5.12/5.31 thf(fact_1582_abs__ge__self,axiom,
% 5.12/5.31 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_self
% 5.12/5.31 thf(fact_1583_abs__ge__self,axiom,
% 5.12/5.31 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_self
% 5.12/5.31 thf(fact_1584_abs__le__D1,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D1
% 5.12/5.31 thf(fact_1585_abs__le__D1,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.12/5.31 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D1
% 5.12/5.31 thf(fact_1586_abs__le__D1,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D1
% 5.12/5.31 thf(fact_1587_abs__le__D1,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D1
% 5.12/5.31 thf(fact_1588_abs__eq__0__iff,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = zero_z3403309356797280102nteger )
% 5.12/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0_iff
% 5.12/5.31 thf(fact_1589_abs__eq__0__iff,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ( abs_abs_real @ A )
% 5.12/5.31 = zero_zero_real )
% 5.12/5.31 = ( A = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0_iff
% 5.12/5.31 thf(fact_1590_abs__eq__0__iff,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ( abs_abs_rat @ A )
% 5.12/5.31 = zero_zero_rat )
% 5.12/5.31 = ( A = zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0_iff
% 5.12/5.31 thf(fact_1591_abs__eq__0__iff,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ( abs_abs_int @ A )
% 5.12/5.31 = zero_zero_int )
% 5.12/5.31 = ( A = zero_zero_int ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_0_iff
% 5.12/5.31 thf(fact_1592_abs__one,axiom,
% 5.12/5.31 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.12/5.31 = one_one_Code_integer ) ).
% 5.12/5.31
% 5.12/5.31 % abs_one
% 5.12/5.31 thf(fact_1593_abs__one,axiom,
% 5.12/5.31 ( ( abs_abs_real @ one_one_real )
% 5.12/5.31 = one_one_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_one
% 5.12/5.31 thf(fact_1594_abs__one,axiom,
% 5.12/5.31 ( ( abs_abs_rat @ one_one_rat )
% 5.12/5.31 = one_one_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_one
% 5.12/5.31 thf(fact_1595_abs__one,axiom,
% 5.12/5.31 ( ( abs_abs_int @ one_one_int )
% 5.12/5.31 = one_one_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_one
% 5.12/5.31 thf(fact_1596_abs__minus__commute,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.12/5.31 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_commute
% 5.12/5.31 thf(fact_1597_abs__minus__commute,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.12/5.31 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_commute
% 5.12/5.31 thf(fact_1598_abs__minus__commute,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.12/5.31 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_commute
% 5.12/5.31 thf(fact_1599_abs__minus__commute,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.12/5.31 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_commute
% 5.12/5.31 thf(fact_1600_exp__less__cancel,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.12/5.31 => ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_less_cancel
% 5.12/5.31 thf(fact_1601_abs__eq__iff,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ( abs_abs_int @ X )
% 5.12/5.31 = ( abs_abs_int @ Y ) )
% 5.12/5.31 = ( ( X = Y )
% 5.12/5.31 | ( X
% 5.12/5.31 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff
% 5.12/5.31 thf(fact_1602_abs__eq__iff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ( abs_abs_real @ X )
% 5.12/5.31 = ( abs_abs_real @ Y ) )
% 5.12/5.31 = ( ( X = Y )
% 5.12/5.31 | ( X
% 5.12/5.31 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff
% 5.12/5.31 thf(fact_1603_abs__eq__iff,axiom,
% 5.12/5.31 ! [X: code_integer,Y: code_integer] :
% 5.12/5.31 ( ( ( abs_abs_Code_integer @ X )
% 5.12/5.31 = ( abs_abs_Code_integer @ Y ) )
% 5.12/5.31 = ( ( X = Y )
% 5.12/5.31 | ( X
% 5.12/5.31 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff
% 5.12/5.31 thf(fact_1604_abs__eq__iff,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ( abs_abs_rat @ X )
% 5.12/5.31 = ( abs_abs_rat @ Y ) )
% 5.12/5.31 = ( ( X = Y )
% 5.12/5.31 | ( X
% 5.12/5.31 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff
% 5.12/5.31 thf(fact_1605_real__root__divide,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( root @ N @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.31 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_divide
% 5.12/5.31 thf(fact_1606_real__root__minus,axiom,
% 5.12/5.31 ! [N: nat,X: real] :
% 5.12/5.31 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 5.12/5.31 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_minus
% 5.12/5.31 thf(fact_1607_exp__not__eq__zero,axiom,
% 5.12/5.31 ! [X: complex] :
% 5.12/5.31 ( ( exp_complex @ X )
% 5.12/5.31 != zero_zero_complex ) ).
% 5.12/5.31
% 5.12/5.31 % exp_not_eq_zero
% 5.12/5.31 thf(fact_1608_exp__not__eq__zero,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( exp_real @ X )
% 5.12/5.31 != zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % exp_not_eq_zero
% 5.12/5.31 thf(fact_1609_ln__unique,axiom,
% 5.12/5.31 ! [Y: real,X: real] :
% 5.12/5.31 ( ( ( exp_real @ Y )
% 5.12/5.31 = X )
% 5.12/5.31 => ( ( ln_ln_real @ X )
% 5.12/5.31 = Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % ln_unique
% 5.12/5.31 thf(fact_1610_abs__ge__zero,axiom,
% 5.12/5.31 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_zero
% 5.12/5.31 thf(fact_1611_abs__ge__zero,axiom,
% 5.12/5.31 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_zero
% 5.12/5.31 thf(fact_1612_abs__ge__zero,axiom,
% 5.12/5.31 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_zero
% 5.12/5.31 thf(fact_1613_abs__ge__zero,axiom,
% 5.12/5.31 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_zero
% 5.12/5.31 thf(fact_1614_abs__of__pos,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.31 => ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_pos
% 5.12/5.31 thf(fact_1615_abs__of__pos,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.31 => ( ( abs_abs_real @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_pos
% 5.12/5.31 thf(fact_1616_abs__of__pos,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.31 => ( ( abs_abs_rat @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_pos
% 5.12/5.31 thf(fact_1617_abs__of__pos,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.31 => ( ( abs_abs_int @ A )
% 5.12/5.31 = A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_pos
% 5.12/5.31 thf(fact_1618_abs__not__less__zero,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.12/5.31
% 5.12/5.31 % abs_not_less_zero
% 5.12/5.31 thf(fact_1619_abs__not__less__zero,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_not_less_zero
% 5.12/5.31 thf(fact_1620_abs__not__less__zero,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_not_less_zero
% 5.12/5.31 thf(fact_1621_abs__not__less__zero,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_not_less_zero
% 5.12/5.31 thf(fact_1622_abs__triangle__ineq2__sym,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2_sym
% 5.12/5.31 thf(fact_1623_abs__triangle__ineq2__sym,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2_sym
% 5.12/5.31 thf(fact_1624_abs__triangle__ineq2__sym,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2_sym
% 5.12/5.31 thf(fact_1625_abs__triangle__ineq2__sym,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2_sym
% 5.12/5.31 thf(fact_1626_abs__triangle__ineq3,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq3
% 5.12/5.31 thf(fact_1627_abs__triangle__ineq3,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq3
% 5.12/5.31 thf(fact_1628_abs__triangle__ineq3,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq3
% 5.12/5.31 thf(fact_1629_abs__triangle__ineq3,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq3
% 5.12/5.31 thf(fact_1630_abs__triangle__ineq2,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2
% 5.12/5.31 thf(fact_1631_abs__triangle__ineq2,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2
% 5.12/5.31 thf(fact_1632_abs__triangle__ineq2,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2
% 5.12/5.31 thf(fact_1633_abs__triangle__ineq2,axiom,
% 5.12/5.31 ! [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 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_triangle_ineq2
% 5.12/5.31 thf(fact_1634_nonzero__abs__divide,axiom,
% 5.12/5.31 ! [B: real,A: real] :
% 5.12/5.31 ( ( B != zero_zero_real )
% 5.12/5.31 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.31 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % nonzero_abs_divide
% 5.12/5.31 thf(fact_1635_nonzero__abs__divide,axiom,
% 5.12/5.31 ! [B: rat,A: rat] :
% 5.12/5.31 ( ( B != zero_zero_rat )
% 5.12/5.31 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.12/5.31 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % nonzero_abs_divide
% 5.12/5.31 thf(fact_1636_abs__ge__minus__self,axiom,
% 5.12/5.31 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_minus_self
% 5.12/5.31 thf(fact_1637_abs__ge__minus__self,axiom,
% 5.12/5.31 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_minus_self
% 5.12/5.31 thf(fact_1638_abs__ge__minus__self,axiom,
% 5.12/5.31 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_minus_self
% 5.12/5.31 thf(fact_1639_abs__ge__minus__self,axiom,
% 5.12/5.31 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_ge_minus_self
% 5.12/5.31 thf(fact_1640_abs__le__iff,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_eq_real @ A @ B )
% 5.12/5.31 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_iff
% 5.12/5.31 thf(fact_1641_abs__le__iff,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.12/5.31 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.12/5.31 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_iff
% 5.12/5.31 thf(fact_1642_abs__le__iff,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_iff
% 5.12/5.31 thf(fact_1643_abs__le__iff,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_eq_int @ A @ B )
% 5.12/5.31 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_iff
% 5.12/5.31 thf(fact_1644_abs__le__D2,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D2
% 5.12/5.31 thf(fact_1645_abs__le__D2,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.12/5.31 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D2
% 5.12/5.31 thf(fact_1646_abs__le__D2,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D2
% 5.12/5.31 thf(fact_1647_abs__le__D2,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_le_D2
% 5.12/5.31 thf(fact_1648_abs__leI,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_leI
% 5.12/5.31 thf(fact_1649_abs__leI,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.12/5.31 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.12/5.31 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_leI
% 5.12/5.31 thf(fact_1650_abs__leI,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_leI
% 5.12/5.31 thf(fact_1651_abs__leI,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.31 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.31 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_leI
% 5.12/5.31 thf(fact_1652_abs__less__iff,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_int @ A @ B )
% 5.12/5.31 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_less_iff
% 5.12/5.31 thf(fact_1653_abs__less__iff,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_real @ A @ B )
% 5.12/5.31 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_less_iff
% 5.12/5.31 thf(fact_1654_abs__less__iff,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.12/5.31 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.12/5.31 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_less_iff
% 5.12/5.31 thf(fact_1655_abs__less__iff,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.12/5.31 = ( ( ord_less_rat @ A @ B )
% 5.12/5.31 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_less_iff
% 5.12/5.31 thf(fact_1656_not__exp__less__zero,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % not_exp_less_zero
% 5.12/5.31 thf(fact_1657_exp__gt__zero,axiom,
% 5.12/5.31 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_gt_zero
% 5.12/5.31 thf(fact_1658_exp__total,axiom,
% 5.12/5.31 ! [Y: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.31 => ? [X3: real] :
% 5.12/5.31 ( ( exp_real @ X3 )
% 5.12/5.31 = Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_total
% 5.12/5.31 thf(fact_1659_exp__ge__zero,axiom,
% 5.12/5.31 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_ge_zero
% 5.12/5.31 thf(fact_1660_not__exp__le__zero,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % not_exp_le_zero
% 5.12/5.31 thf(fact_1661_exp__diff,axiom,
% 5.12/5.31 ! [X: complex,Y: complex] :
% 5.12/5.31 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.31 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_diff
% 5.12/5.31 thf(fact_1662_exp__diff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.31 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_diff
% 5.12/5.31 thf(fact_1663_dense__eq0__I,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ! [E: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ E )
% 5.12/5.31 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E ) )
% 5.12/5.31 => ( X = zero_zero_real ) ) ).
% 5.12/5.31
% 5.12/5.31 % dense_eq0_I
% 5.12/5.31 thf(fact_1664_dense__eq0__I,axiom,
% 5.12/5.31 ! [X: rat] :
% 5.12/5.31 ( ! [E: rat] :
% 5.12/5.31 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.12/5.31 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E ) )
% 5.12/5.31 => ( X = zero_zero_rat ) ) ).
% 5.12/5.31
% 5.12/5.31 % dense_eq0_I
% 5.12/5.31 thf(fact_1665_abs__minus__le__zero,axiom,
% 5.12/5.31 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_le_zero
% 5.12/5.31 thf(fact_1666_abs__minus__le__zero,axiom,
% 5.12/5.31 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_le_zero
% 5.12/5.31 thf(fact_1667_abs__minus__le__zero,axiom,
% 5.12/5.31 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_le_zero
% 5.12/5.31 thf(fact_1668_abs__minus__le__zero,axiom,
% 5.12/5.31 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.12/5.31
% 5.12/5.31 % abs_minus_le_zero
% 5.12/5.31 thf(fact_1669_eq__abs__iff_H,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( abs_abs_real @ B ) )
% 5.12/5.31 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.31 & ( ( B = A )
% 5.12/5.31 | ( B
% 5.12/5.31 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % eq_abs_iff'
% 5.12/5.31 thf(fact_1670_eq__abs__iff_H,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( abs_abs_Code_integer @ B ) )
% 5.12/5.31 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.31 & ( ( B = A )
% 5.12/5.31 | ( B
% 5.12/5.31 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % eq_abs_iff'
% 5.12/5.31 thf(fact_1671_eq__abs__iff_H,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( abs_abs_rat @ B ) )
% 5.12/5.31 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.31 & ( ( B = A )
% 5.12/5.31 | ( B
% 5.12/5.31 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % eq_abs_iff'
% 5.12/5.31 thf(fact_1672_eq__abs__iff_H,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( abs_abs_int @ B ) )
% 5.12/5.31 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.31 & ( ( B = A )
% 5.12/5.31 | ( B
% 5.12/5.31 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % eq_abs_iff'
% 5.12/5.31 thf(fact_1673_abs__eq__iff_H,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ( abs_abs_real @ A )
% 5.12/5.31 = B )
% 5.12/5.31 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.31 & ( ( A = B )
% 5.12/5.31 | ( A
% 5.12/5.31 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff'
% 5.12/5.31 thf(fact_1674_abs__eq__iff_H,axiom,
% 5.12/5.31 ! [A: code_integer,B: code_integer] :
% 5.12/5.31 ( ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = B )
% 5.12/5.31 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.31 & ( ( A = B )
% 5.12/5.31 | ( A
% 5.12/5.31 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff'
% 5.12/5.31 thf(fact_1675_abs__eq__iff_H,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ( abs_abs_rat @ A )
% 5.12/5.31 = B )
% 5.12/5.31 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.31 & ( ( A = B )
% 5.12/5.31 | ( A
% 5.12/5.31 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff'
% 5.12/5.31 thf(fact_1676_abs__eq__iff_H,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ( abs_abs_int @ A )
% 5.12/5.31 = B )
% 5.12/5.31 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.31 & ( ( A = B )
% 5.12/5.31 | ( A
% 5.12/5.31 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_eq_iff'
% 5.12/5.31 thf(fact_1677_zero__le__power__abs,axiom,
% 5.12/5.31 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_power_abs
% 5.12/5.31 thf(fact_1678_zero__le__power__abs,axiom,
% 5.12/5.31 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_power_abs
% 5.12/5.31 thf(fact_1679_zero__le__power__abs,axiom,
% 5.12/5.31 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_power_abs
% 5.12/5.31 thf(fact_1680_zero__le__power__abs,axiom,
% 5.12/5.31 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.12/5.31
% 5.12/5.31 % zero_le_power_abs
% 5.12/5.31 thf(fact_1681_abs__div__pos,axiom,
% 5.12/5.31 ! [Y: real,X: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.31 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.12/5.31 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_div_pos
% 5.12/5.31 thf(fact_1682_abs__div__pos,axiom,
% 5.12/5.31 ! [Y: rat,X: rat] :
% 5.12/5.31 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.31 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.12/5.31 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_div_pos
% 5.12/5.31 thf(fact_1683_abs__if__raw,axiom,
% 5.12/5.31 ( abs_abs_int
% 5.12/5.31 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if_raw
% 5.12/5.31 thf(fact_1684_abs__if__raw,axiom,
% 5.12/5.31 ( abs_abs_real
% 5.12/5.31 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if_raw
% 5.12/5.31 thf(fact_1685_abs__if__raw,axiom,
% 5.12/5.31 ( abs_abs_Code_integer
% 5.12/5.31 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if_raw
% 5.12/5.31 thf(fact_1686_abs__if__raw,axiom,
% 5.12/5.31 ( abs_abs_rat
% 5.12/5.31 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if_raw
% 5.12/5.31 thf(fact_1687_abs__of__neg,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.31 => ( ( abs_abs_int @ A )
% 5.12/5.31 = ( uminus_uminus_int @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_neg
% 5.12/5.31 thf(fact_1688_abs__of__neg,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.31 => ( ( abs_abs_real @ A )
% 5.12/5.31 = ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_neg
% 5.12/5.31 thf(fact_1689_abs__of__neg,axiom,
% 5.12/5.31 ! [A: code_integer] :
% 5.12/5.31 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.12/5.31 => ( ( abs_abs_Code_integer @ A )
% 5.12/5.31 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_neg
% 5.12/5.31 thf(fact_1690_abs__of__neg,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.31 => ( ( abs_abs_rat @ A )
% 5.12/5.31 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_of_neg
% 5.12/5.31 thf(fact_1691_abs__if,axiom,
% 5.12/5.31 ( abs_abs_int
% 5.12/5.31 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if
% 5.12/5.31 thf(fact_1692_abs__if,axiom,
% 5.12/5.31 ( abs_abs_real
% 5.12/5.31 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if
% 5.12/5.31 thf(fact_1693_abs__if,axiom,
% 5.12/5.31 ( abs_abs_Code_integer
% 5.12/5.31 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if
% 5.12/5.31 thf(fact_1694_abs__if,axiom,
% 5.12/5.31 ( abs_abs_rat
% 5.12/5.31 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_if
% 5.12/5.31 thf(fact_1695_real__root__less__mono,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_less_mono
% 5.12/5.31 thf(fact_1696_real__root__le__mono,axiom,
% 5.12/5.31 ! [N: nat,X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.31 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_le_mono
% 5.12/5.31 thf(fact_1697_real__root__power,axiom,
% 5.12/5.31 ! [N: nat,X: real,K: nat] :
% 5.12/5.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.31 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 5.12/5.31 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % real_root_power
% 5.12/5.31 thf(fact_1698_exp__gt__one,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.31 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exp_gt_one
% 5.12/5.31 thf(fact_1699_zabs__def,axiom,
% 5.12/5.31 ( abs_abs_int
% 5.12/5.31 = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % zabs_def
% 5.12/5.31 thf(fact_1700_abs__mod__less,axiom,
% 5.12/5.31 ! [L: int,K: int] :
% 5.12/5.31 ( ( L != zero_zero_int )
% 5.12/5.31 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % abs_mod_less
% 5.12/5.31 thf(fact_1701_lt__ex,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 5.12/5.31
% 5.12/5.31 % lt_ex
% 5.12/5.31 thf(fact_1702_lt__ex,axiom,
% 5.12/5.31 ! [X: rat] :
% 5.12/5.31 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.12/5.31
% 5.12/5.31 % lt_ex
% 5.12/5.31 thf(fact_1703_lt__ex,axiom,
% 5.12/5.31 ! [X: int] :
% 5.12/5.31 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 5.12/5.31
% 5.12/5.31 % lt_ex
% 5.12/5.31 thf(fact_1704_gt__ex,axiom,
% 5.12/5.31 ! [X: real] :
% 5.12/5.31 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.12/5.31
% 5.12/5.31 % gt_ex
% 5.12/5.31 thf(fact_1705_gt__ex,axiom,
% 5.12/5.31 ! [X: rat] :
% 5.12/5.31 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.12/5.31
% 5.12/5.31 % gt_ex
% 5.12/5.31 thf(fact_1706_gt__ex,axiom,
% 5.12/5.31 ! [X: nat] :
% 5.12/5.31 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.12/5.31
% 5.12/5.31 % gt_ex
% 5.12/5.31 thf(fact_1707_gt__ex,axiom,
% 5.12/5.31 ! [X: int] :
% 5.12/5.31 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.12/5.31
% 5.12/5.31 % gt_ex
% 5.12/5.31 thf(fact_1708_dense,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ? [Z4: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Z4 )
% 5.12/5.31 & ( ord_less_real @ Z4 @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dense
% 5.12/5.31 thf(fact_1709_dense,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ? [Z4: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X @ Z4 )
% 5.12/5.31 & ( ord_less_rat @ Z4 @ Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dense
% 5.12/5.31 thf(fact_1710_less__imp__neq,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( X != Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_imp_neq
% 5.12/5.31 thf(fact_1711_less__imp__neq,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ( X != Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_imp_neq
% 5.12/5.31 thf(fact_1712_less__imp__neq,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( ord_less_num @ X @ Y )
% 5.12/5.31 => ( X != Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_imp_neq
% 5.12/5.31 thf(fact_1713_less__imp__neq,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X @ Y )
% 5.12/5.31 => ( X != Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_imp_neq
% 5.12/5.31 thf(fact_1714_less__imp__neq,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ord_less_int @ X @ Y )
% 5.12/5.31 => ( X != Y ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_imp_neq
% 5.12/5.31 thf(fact_1715_order_Oasym,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.asym
% 5.12/5.31 thf(fact_1716_order_Oasym,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.asym
% 5.12/5.31 thf(fact_1717_order_Oasym,axiom,
% 5.12/5.31 ! [A: num,B: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.asym
% 5.12/5.31 thf(fact_1718_order_Oasym,axiom,
% 5.12/5.31 ! [A: nat,B: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.asym
% 5.12/5.31 thf(fact_1719_order_Oasym,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.asym
% 5.12/5.31 thf(fact_1720_ord__eq__less__trans,axiom,
% 5.12/5.31 ! [A: real,B: real,C: real] :
% 5.12/5.31 ( ( A = B )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ord_less_real @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_trans
% 5.12/5.31 thf(fact_1721_ord__eq__less__trans,axiom,
% 5.12/5.31 ! [A: rat,B: rat,C: rat] :
% 5.12/5.31 ( ( A = B )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_trans
% 5.12/5.31 thf(fact_1722_ord__eq__less__trans,axiom,
% 5.12/5.31 ! [A: num,B: num,C: num] :
% 5.12/5.31 ( ( A = B )
% 5.12/5.31 => ( ( ord_less_num @ B @ C )
% 5.12/5.31 => ( ord_less_num @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_trans
% 5.12/5.31 thf(fact_1723_ord__eq__less__trans,axiom,
% 5.12/5.31 ! [A: nat,B: nat,C: nat] :
% 5.12/5.31 ( ( A = B )
% 5.12/5.31 => ( ( ord_less_nat @ B @ C )
% 5.12/5.31 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_trans
% 5.12/5.31 thf(fact_1724_ord__eq__less__trans,axiom,
% 5.12/5.31 ! [A: int,B: int,C: int] :
% 5.12/5.31 ( ( A = B )
% 5.12/5.31 => ( ( ord_less_int @ B @ C )
% 5.12/5.31 => ( ord_less_int @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_trans
% 5.12/5.31 thf(fact_1725_ord__less__eq__trans,axiom,
% 5.12/5.31 ! [A: real,B: real,C: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( B = C )
% 5.12/5.31 => ( ord_less_real @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_trans
% 5.12/5.31 thf(fact_1726_ord__less__eq__trans,axiom,
% 5.12/5.31 ! [A: rat,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( B = C )
% 5.12/5.31 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_trans
% 5.12/5.31 thf(fact_1727_ord__less__eq__trans,axiom,
% 5.12/5.31 ! [A: num,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ( ( B = C )
% 5.12/5.31 => ( ord_less_num @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_trans
% 5.12/5.31 thf(fact_1728_ord__less__eq__trans,axiom,
% 5.12/5.31 ! [A: nat,B: nat,C: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ( ( B = C )
% 5.12/5.31 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_trans
% 5.12/5.31 thf(fact_1729_ord__less__eq__trans,axiom,
% 5.12/5.31 ! [A: int,B: int,C: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ( ( B = C )
% 5.12/5.31 => ( ord_less_int @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_trans
% 5.12/5.31 thf(fact_1730_less__induct,axiom,
% 5.12/5.31 ! [P: nat > $o,A: nat] :
% 5.12/5.31 ( ! [X3: nat] :
% 5.12/5.31 ( ! [Y5: nat] :
% 5.12/5.31 ( ( ord_less_nat @ Y5 @ X3 )
% 5.12/5.31 => ( P @ Y5 ) )
% 5.12/5.31 => ( P @ X3 ) )
% 5.12/5.31 => ( P @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % less_induct
% 5.12/5.31 thf(fact_1731_antisym__conv3,axiom,
% 5.12/5.31 ! [Y: real,X: real] :
% 5.12/5.31 ( ~ ( ord_less_real @ Y @ X )
% 5.12/5.31 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % antisym_conv3
% 5.12/5.31 thf(fact_1732_antisym__conv3,axiom,
% 5.12/5.31 ! [Y: rat,X: rat] :
% 5.12/5.31 ( ~ ( ord_less_rat @ Y @ X )
% 5.12/5.31 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % antisym_conv3
% 5.12/5.31 thf(fact_1733_antisym__conv3,axiom,
% 5.12/5.31 ! [Y: num,X: num] :
% 5.12/5.31 ( ~ ( ord_less_num @ Y @ X )
% 5.12/5.31 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % antisym_conv3
% 5.12/5.31 thf(fact_1734_antisym__conv3,axiom,
% 5.12/5.31 ! [Y: nat,X: nat] :
% 5.12/5.31 ( ~ ( ord_less_nat @ Y @ X )
% 5.12/5.31 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % antisym_conv3
% 5.12/5.31 thf(fact_1735_antisym__conv3,axiom,
% 5.12/5.31 ! [Y: int,X: int] :
% 5.12/5.31 ( ~ ( ord_less_int @ Y @ X )
% 5.12/5.31 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.12/5.31 = ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % antisym_conv3
% 5.12/5.31 thf(fact_1736_linorder__cases,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ~ ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( ( X != Y )
% 5.12/5.31 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_cases
% 5.12/5.31 thf(fact_1737_linorder__cases,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ~ ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ( ( X != Y )
% 5.12/5.31 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_cases
% 5.12/5.31 thf(fact_1738_linorder__cases,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ~ ( ord_less_num @ X @ Y )
% 5.12/5.31 => ( ( X != Y )
% 5.12/5.31 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_cases
% 5.12/5.31 thf(fact_1739_linorder__cases,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ~ ( ord_less_nat @ X @ Y )
% 5.12/5.31 => ( ( X != Y )
% 5.12/5.31 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_cases
% 5.12/5.31 thf(fact_1740_linorder__cases,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ~ ( ord_less_int @ X @ Y )
% 5.12/5.31 => ( ( X != Y )
% 5.12/5.31 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_cases
% 5.12/5.31 thf(fact_1741_dual__order_Oasym,axiom,
% 5.12/5.31 ! [B: real,A: real] :
% 5.12/5.31 ( ( ord_less_real @ B @ A )
% 5.12/5.31 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.asym
% 5.12/5.31 thf(fact_1742_dual__order_Oasym,axiom,
% 5.12/5.31 ! [B: rat,A: rat] :
% 5.12/5.31 ( ( ord_less_rat @ B @ A )
% 5.12/5.31 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.asym
% 5.12/5.31 thf(fact_1743_dual__order_Oasym,axiom,
% 5.12/5.31 ! [B: num,A: num] :
% 5.12/5.31 ( ( ord_less_num @ B @ A )
% 5.12/5.31 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.asym
% 5.12/5.31 thf(fact_1744_dual__order_Oasym,axiom,
% 5.12/5.31 ! [B: nat,A: nat] :
% 5.12/5.31 ( ( ord_less_nat @ B @ A )
% 5.12/5.31 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.asym
% 5.12/5.31 thf(fact_1745_dual__order_Oasym,axiom,
% 5.12/5.31 ! [B: int,A: int] :
% 5.12/5.31 ( ( ord_less_int @ B @ A )
% 5.12/5.31 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.asym
% 5.12/5.31 thf(fact_1746_dual__order_Oirrefl,axiom,
% 5.12/5.31 ! [A: real] :
% 5.12/5.31 ~ ( ord_less_real @ A @ A ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.irrefl
% 5.12/5.31 thf(fact_1747_dual__order_Oirrefl,axiom,
% 5.12/5.31 ! [A: rat] :
% 5.12/5.31 ~ ( ord_less_rat @ A @ A ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.irrefl
% 5.12/5.31 thf(fact_1748_dual__order_Oirrefl,axiom,
% 5.12/5.31 ! [A: num] :
% 5.12/5.31 ~ ( ord_less_num @ A @ A ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.irrefl
% 5.12/5.31 thf(fact_1749_dual__order_Oirrefl,axiom,
% 5.12/5.31 ! [A: nat] :
% 5.12/5.31 ~ ( ord_less_nat @ A @ A ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.irrefl
% 5.12/5.31 thf(fact_1750_dual__order_Oirrefl,axiom,
% 5.12/5.31 ! [A: int] :
% 5.12/5.31 ~ ( ord_less_int @ A @ A ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.irrefl
% 5.12/5.31 thf(fact_1751_exists__least__iff,axiom,
% 5.12/5.31 ( ( ^ [P2: nat > $o] :
% 5.12/5.31 ? [X5: nat] : ( P2 @ X5 ) )
% 5.12/5.31 = ( ^ [P3: nat > $o] :
% 5.12/5.31 ? [N4: nat] :
% 5.12/5.31 ( ( P3 @ N4 )
% 5.12/5.31 & ! [M5: nat] :
% 5.12/5.31 ( ( ord_less_nat @ M5 @ N4 )
% 5.12/5.31 => ~ ( P3 @ M5 ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % exists_least_iff
% 5.12/5.31 thf(fact_1752_linorder__less__wlog,axiom,
% 5.12/5.31 ! [P: real > real > $o,A: real,B: real] :
% 5.12/5.31 ( ! [A4: real,B3: real] :
% 5.12/5.31 ( ( ord_less_real @ A4 @ B3 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( ! [A4: real] : ( P @ A4 @ A4 )
% 5.12/5.31 => ( ! [A4: real,B3: real] :
% 5.12/5.31 ( ( P @ B3 @ A4 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_less_wlog
% 5.12/5.31 thf(fact_1753_linorder__less__wlog,axiom,
% 5.12/5.31 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.12/5.31 ( ! [A4: rat,B3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A4 @ B3 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 5.12/5.31 => ( ! [A4: rat,B3: rat] :
% 5.12/5.31 ( ( P @ B3 @ A4 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_less_wlog
% 5.12/5.31 thf(fact_1754_linorder__less__wlog,axiom,
% 5.12/5.31 ! [P: num > num > $o,A: num,B: num] :
% 5.12/5.31 ( ! [A4: num,B3: num] :
% 5.12/5.31 ( ( ord_less_num @ A4 @ B3 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( ! [A4: num] : ( P @ A4 @ A4 )
% 5.12/5.31 => ( ! [A4: num,B3: num] :
% 5.12/5.31 ( ( P @ B3 @ A4 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_less_wlog
% 5.12/5.31 thf(fact_1755_linorder__less__wlog,axiom,
% 5.12/5.31 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.12/5.31 ( ! [A4: nat,B3: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A4 @ B3 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 5.12/5.31 => ( ! [A4: nat,B3: nat] :
% 5.12/5.31 ( ( P @ B3 @ A4 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_less_wlog
% 5.12/5.31 thf(fact_1756_linorder__less__wlog,axiom,
% 5.12/5.31 ! [P: int > int > $o,A: int,B: int] :
% 5.12/5.31 ( ! [A4: int,B3: int] :
% 5.12/5.31 ( ( ord_less_int @ A4 @ B3 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 5.12/5.31 => ( ! [A4: int,B3: int] :
% 5.12/5.31 ( ( P @ B3 @ A4 )
% 5.12/5.31 => ( P @ A4 @ B3 ) )
% 5.12/5.31 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_less_wlog
% 5.12/5.31 thf(fact_1757_order_Ostrict__trans,axiom,
% 5.12/5.31 ! [A: real,B: real,C: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ord_less_real @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_trans
% 5.12/5.31 thf(fact_1758_order_Ostrict__trans,axiom,
% 5.12/5.31 ! [A: rat,B: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_trans
% 5.12/5.31 thf(fact_1759_order_Ostrict__trans,axiom,
% 5.12/5.31 ! [A: num,B: num,C: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ( ( ord_less_num @ B @ C )
% 5.12/5.31 => ( ord_less_num @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_trans
% 5.12/5.31 thf(fact_1760_order_Ostrict__trans,axiom,
% 5.12/5.31 ! [A: nat,B: nat,C: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ( ( ord_less_nat @ B @ C )
% 5.12/5.31 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_trans
% 5.12/5.31 thf(fact_1761_order_Ostrict__trans,axiom,
% 5.12/5.31 ! [A: int,B: int,C: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ( ( ord_less_int @ B @ C )
% 5.12/5.31 => ( ord_less_int @ A @ C ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_trans
% 5.12/5.31 thf(fact_1762_not__less__iff__gr__or__eq,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.12/5.31 = ( ( ord_less_real @ Y @ X )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % not_less_iff_gr_or_eq
% 5.12/5.31 thf(fact_1763_not__less__iff__gr__or__eq,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.12/5.31 = ( ( ord_less_rat @ Y @ X )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % not_less_iff_gr_or_eq
% 5.12/5.31 thf(fact_1764_not__less__iff__gr__or__eq,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.12/5.31 = ( ( ord_less_num @ Y @ X )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % not_less_iff_gr_or_eq
% 5.12/5.31 thf(fact_1765_not__less__iff__gr__or__eq,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.12/5.31 = ( ( ord_less_nat @ Y @ X )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % not_less_iff_gr_or_eq
% 5.12/5.31 thf(fact_1766_not__less__iff__gr__or__eq,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.12/5.31 = ( ( ord_less_int @ Y @ X )
% 5.12/5.31 | ( X = Y ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % not_less_iff_gr_or_eq
% 5.12/5.31 thf(fact_1767_dual__order_Ostrict__trans,axiom,
% 5.12/5.31 ! [B: real,A: real,C: real] :
% 5.12/5.31 ( ( ord_less_real @ B @ A )
% 5.12/5.31 => ( ( ord_less_real @ C @ B )
% 5.12/5.31 => ( ord_less_real @ C @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_trans
% 5.12/5.31 thf(fact_1768_dual__order_Ostrict__trans,axiom,
% 5.12/5.31 ! [B: rat,A: rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ B @ A )
% 5.12/5.31 => ( ( ord_less_rat @ C @ B )
% 5.12/5.31 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_trans
% 5.12/5.31 thf(fact_1769_dual__order_Ostrict__trans,axiom,
% 5.12/5.31 ! [B: num,A: num,C: num] :
% 5.12/5.31 ( ( ord_less_num @ B @ A )
% 5.12/5.31 => ( ( ord_less_num @ C @ B )
% 5.12/5.31 => ( ord_less_num @ C @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_trans
% 5.12/5.31 thf(fact_1770_dual__order_Ostrict__trans,axiom,
% 5.12/5.31 ! [B: nat,A: nat,C: nat] :
% 5.12/5.31 ( ( ord_less_nat @ B @ A )
% 5.12/5.31 => ( ( ord_less_nat @ C @ B )
% 5.12/5.31 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_trans
% 5.12/5.31 thf(fact_1771_dual__order_Ostrict__trans,axiom,
% 5.12/5.31 ! [B: int,A: int,C: int] :
% 5.12/5.31 ( ( ord_less_int @ B @ A )
% 5.12/5.31 => ( ( ord_less_int @ C @ B )
% 5.12/5.31 => ( ord_less_int @ C @ A ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_trans
% 5.12/5.31 thf(fact_1772_order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1773_order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1774_order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [A: num,B: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1775_order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [A: nat,B: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1776_order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1777_dual__order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [B: real,A: real] :
% 5.12/5.31 ( ( ord_less_real @ B @ A )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1778_dual__order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [B: rat,A: rat] :
% 5.12/5.31 ( ( ord_less_rat @ B @ A )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1779_dual__order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [B: num,A: num] :
% 5.12/5.31 ( ( ord_less_num @ B @ A )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1780_dual__order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [B: nat,A: nat] :
% 5.12/5.31 ( ( ord_less_nat @ B @ A )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1781_dual__order_Ostrict__implies__not__eq,axiom,
% 5.12/5.31 ! [B: int,A: int] :
% 5.12/5.31 ( ( ord_less_int @ B @ A )
% 5.12/5.31 => ( A != B ) ) ).
% 5.12/5.31
% 5.12/5.31 % dual_order.strict_implies_not_eq
% 5.12/5.31 thf(fact_1782_linorder__neqE,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 => ( ~ ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neqE
% 5.12/5.31 thf(fact_1783_linorder__neqE,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 => ( ~ ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neqE
% 5.12/5.31 thf(fact_1784_linorder__neqE,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 => ( ~ ( ord_less_num @ X @ Y )
% 5.12/5.31 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neqE
% 5.12/5.31 thf(fact_1785_linorder__neqE,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 => ( ~ ( ord_less_nat @ X @ Y )
% 5.12/5.31 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neqE
% 5.12/5.31 thf(fact_1786_linorder__neqE,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 => ( ~ ( ord_less_int @ X @ Y )
% 5.12/5.31 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neqE
% 5.12/5.31 thf(fact_1787_order__less__asym,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym
% 5.12/5.31 thf(fact_1788_order__less__asym,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym
% 5.12/5.31 thf(fact_1789_order__less__asym,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( ord_less_num @ X @ Y )
% 5.12/5.31 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym
% 5.12/5.31 thf(fact_1790_order__less__asym,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X @ Y )
% 5.12/5.31 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym
% 5.12/5.31 thf(fact_1791_order__less__asym,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( ord_less_int @ X @ Y )
% 5.12/5.31 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym
% 5.12/5.31 thf(fact_1792_linorder__neq__iff,axiom,
% 5.12/5.31 ! [X: real,Y: real] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 = ( ( ord_less_real @ X @ Y )
% 5.12/5.31 | ( ord_less_real @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neq_iff
% 5.12/5.31 thf(fact_1793_linorder__neq__iff,axiom,
% 5.12/5.31 ! [X: rat,Y: rat] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 = ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 | ( ord_less_rat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neq_iff
% 5.12/5.31 thf(fact_1794_linorder__neq__iff,axiom,
% 5.12/5.31 ! [X: num,Y: num] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 = ( ( ord_less_num @ X @ Y )
% 5.12/5.31 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neq_iff
% 5.12/5.31 thf(fact_1795_linorder__neq__iff,axiom,
% 5.12/5.31 ! [X: nat,Y: nat] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 = ( ( ord_less_nat @ X @ Y )
% 5.12/5.31 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neq_iff
% 5.12/5.31 thf(fact_1796_linorder__neq__iff,axiom,
% 5.12/5.31 ! [X: int,Y: int] :
% 5.12/5.31 ( ( X != Y )
% 5.12/5.31 = ( ( ord_less_int @ X @ Y )
% 5.12/5.31 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % linorder_neq_iff
% 5.12/5.31 thf(fact_1797_order__less__asym_H,axiom,
% 5.12/5.31 ! [A: real,B: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym'
% 5.12/5.31 thf(fact_1798_order__less__asym_H,axiom,
% 5.12/5.31 ! [A: rat,B: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym'
% 5.12/5.31 thf(fact_1799_order__less__asym_H,axiom,
% 5.12/5.31 ! [A: num,B: num] :
% 5.12/5.31 ( ( ord_less_num @ A @ B )
% 5.12/5.31 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym'
% 5.12/5.31 thf(fact_1800_order__less__asym_H,axiom,
% 5.12/5.31 ! [A: nat,B: nat] :
% 5.12/5.31 ( ( ord_less_nat @ A @ B )
% 5.12/5.31 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym'
% 5.12/5.31 thf(fact_1801_order__less__asym_H,axiom,
% 5.12/5.31 ! [A: int,B: int] :
% 5.12/5.31 ( ( ord_less_int @ A @ B )
% 5.12/5.31 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_asym'
% 5.12/5.31 thf(fact_1802_order__less__trans,axiom,
% 5.12/5.31 ! [X: real,Y: real,Z2: real] :
% 5.12/5.31 ( ( ord_less_real @ X @ Y )
% 5.12/5.31 => ( ( ord_less_real @ Y @ Z2 )
% 5.12/5.31 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_trans
% 5.12/5.31 thf(fact_1803_order__less__trans,axiom,
% 5.12/5.31 ! [X: rat,Y: rat,Z2: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X @ Y )
% 5.12/5.31 => ( ( ord_less_rat @ Y @ Z2 )
% 5.12/5.31 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_trans
% 5.12/5.31 thf(fact_1804_order__less__trans,axiom,
% 5.12/5.31 ! [X: num,Y: num,Z2: num] :
% 5.12/5.31 ( ( ord_less_num @ X @ Y )
% 5.12/5.31 => ( ( ord_less_num @ Y @ Z2 )
% 5.12/5.31 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_trans
% 5.12/5.31 thf(fact_1805_order__less__trans,axiom,
% 5.12/5.31 ! [X: nat,Y: nat,Z2: nat] :
% 5.12/5.31 ( ( ord_less_nat @ X @ Y )
% 5.12/5.31 => ( ( ord_less_nat @ Y @ Z2 )
% 5.12/5.31 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_trans
% 5.12/5.31 thf(fact_1806_order__less__trans,axiom,
% 5.12/5.31 ! [X: int,Y: int,Z2: int] :
% 5.12/5.31 ( ( ord_less_int @ X @ Y )
% 5.12/5.31 => ( ( ord_less_int @ Y @ Z2 )
% 5.12/5.31 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % order_less_trans
% 5.12/5.31 thf(fact_1807_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: real,F: real > real,B: real,C: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1808_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1809_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: num,F: real > num,B: real,C: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1810_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1811_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: int,F: real > int,B: real,C: real] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_real @ B @ C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1812_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1813_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1814_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1815_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1816_ord__eq__less__subst,axiom,
% 5.12/5.31 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.12/5.31 ( ( A
% 5.12/5.31 = ( F @ B ) )
% 5.12/5.31 => ( ( ord_less_rat @ B @ C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_eq_less_subst
% 5.12/5.31 thf(fact_1817_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > real,C: real] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1818_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1819_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > num,C: num] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1820_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1821_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: real,B: real,F: real > int,C: int] :
% 5.12/5.31 ( ( ord_less_real @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: real,Y3: real] :
% 5.12/5.31 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1822_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1823_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.31 thf(fact_1824_ord__less__eq__subst,axiom,
% 5.12/5.31 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.12/5.31 ( ( ord_less_rat @ A @ B )
% 5.12/5.31 => ( ( ( F @ B )
% 5.12/5.31 = C )
% 5.12/5.31 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.31 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.31 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.31 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.31
% 5.12/5.31 % ord_less_eq_subst
% 5.12/5.32 thf(fact_1825_ord__less__eq__subst,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ( F @ B )
% 5.12/5.32 = C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % ord_less_eq_subst
% 5.12/5.32 thf(fact_1826_ord__less__eq__subst,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ( F @ B )
% 5.12/5.32 = C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % ord_less_eq_subst
% 5.12/5.32 thf(fact_1827_order__less__irrefl,axiom,
% 5.12/5.32 ! [X: real] :
% 5.12/5.32 ~ ( ord_less_real @ X @ X ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_irrefl
% 5.12/5.32 thf(fact_1828_order__less__irrefl,axiom,
% 5.12/5.32 ! [X: rat] :
% 5.12/5.32 ~ ( ord_less_rat @ X @ X ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_irrefl
% 5.12/5.32 thf(fact_1829_order__less__irrefl,axiom,
% 5.12/5.32 ! [X: num] :
% 5.12/5.32 ~ ( ord_less_num @ X @ X ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_irrefl
% 5.12/5.32 thf(fact_1830_order__less__irrefl,axiom,
% 5.12/5.32 ! [X: nat] :
% 5.12/5.32 ~ ( ord_less_nat @ X @ X ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_irrefl
% 5.12/5.32 thf(fact_1831_order__less__irrefl,axiom,
% 5.12/5.32 ! [X: int] :
% 5.12/5.32 ~ ( ord_less_int @ X @ X ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_irrefl
% 5.12/5.32 thf(fact_1832_order__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: real > real,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_real @ B @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1833_order__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_rat @ B @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1834_order__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: num > real,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_num @ B @ C )
% 5.12/5.32 => ( ! [X3: num,Y3: num] :
% 5.12/5.32 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1835_order__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_nat @ B @ C )
% 5.12/5.32 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1836_order__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: int > real,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_int @ B @ C )
% 5.12/5.32 => ( ! [X3: int,Y3: int] :
% 5.12/5.32 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1837_order__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_real @ B @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1838_order__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_rat @ B @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1839_order__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_num @ B @ C )
% 5.12/5.32 => ( ! [X3: num,Y3: num] :
% 5.12/5.32 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1840_order__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_nat @ B @ C )
% 5.12/5.32 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1841_order__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_int @ B @ C )
% 5.12/5.32 => ( ! [X3: int,Y3: int] :
% 5.12/5.32 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst1
% 5.12/5.32 thf(fact_1842_order__less__subst2,axiom,
% 5.12/5.32 ! [A: real,B: real,F: real > real,C: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1843_order__less__subst2,axiom,
% 5.12/5.32 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1844_order__less__subst2,axiom,
% 5.12/5.32 ! [A: real,B: real,F: real > num,C: num] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1845_order__less__subst2,axiom,
% 5.12/5.32 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1846_order__less__subst2,axiom,
% 5.12/5.32 ! [A: real,B: real,F: real > int,C: int] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1847_order__less__subst2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1848_order__less__subst2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1849_order__less__subst2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1850_order__less__subst2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1851_order__less__subst2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_subst2
% 5.12/5.32 thf(fact_1852_order__less__not__sym,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_not_sym
% 5.12/5.32 thf(fact_1853_order__less__not__sym,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_not_sym
% 5.12/5.32 thf(fact_1854_order__less__not__sym,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_not_sym
% 5.12/5.32 thf(fact_1855_order__less__not__sym,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_not_sym
% 5.12/5.32 thf(fact_1856_order__less__not__sym,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_not_sym
% 5.12/5.32 thf(fact_1857_order__less__imp__triv,axiom,
% 5.12/5.32 ! [X: real,Y: real,P: $o] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ( ord_less_real @ Y @ X )
% 5.12/5.32 => P ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_triv
% 5.12/5.32 thf(fact_1858_order__less__imp__triv,axiom,
% 5.12/5.32 ! [X: rat,Y: rat,P: $o] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_rat @ Y @ X )
% 5.12/5.32 => P ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_triv
% 5.12/5.32 thf(fact_1859_order__less__imp__triv,axiom,
% 5.12/5.32 ! [X: num,Y: num,P: $o] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( ( ord_less_num @ Y @ X )
% 5.12/5.32 => P ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_triv
% 5.12/5.32 thf(fact_1860_order__less__imp__triv,axiom,
% 5.12/5.32 ! [X: nat,Y: nat,P: $o] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_nat @ Y @ X )
% 5.12/5.32 => P ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_triv
% 5.12/5.32 thf(fact_1861_order__less__imp__triv,axiom,
% 5.12/5.32 ! [X: int,Y: int,P: $o] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( ( ord_less_int @ Y @ X )
% 5.12/5.32 => P ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_triv
% 5.12/5.32 thf(fact_1862_linorder__less__linear,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 | ( X = Y )
% 5.12/5.32 | ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_less_linear
% 5.12/5.32 thf(fact_1863_linorder__less__linear,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 | ( X = Y )
% 5.12/5.32 | ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_less_linear
% 5.12/5.32 thf(fact_1864_linorder__less__linear,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 | ( X = Y )
% 5.12/5.32 | ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_less_linear
% 5.12/5.32 thf(fact_1865_linorder__less__linear,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 | ( X = Y )
% 5.12/5.32 | ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_less_linear
% 5.12/5.32 thf(fact_1866_linorder__less__linear,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 | ( X = Y )
% 5.12/5.32 | ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_less_linear
% 5.12/5.32 thf(fact_1867_order__less__imp__not__eq,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( X != Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq
% 5.12/5.32 thf(fact_1868_order__less__imp__not__eq,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( X != Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq
% 5.12/5.32 thf(fact_1869_order__less__imp__not__eq,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( X != Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq
% 5.12/5.32 thf(fact_1870_order__less__imp__not__eq,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( X != Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq
% 5.12/5.32 thf(fact_1871_order__less__imp__not__eq,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( X != Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq
% 5.12/5.32 thf(fact_1872_order__less__imp__not__eq2,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( Y != X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq2
% 5.12/5.32 thf(fact_1873_order__less__imp__not__eq2,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( Y != X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq2
% 5.12/5.32 thf(fact_1874_order__less__imp__not__eq2,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( Y != X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq2
% 5.12/5.32 thf(fact_1875_order__less__imp__not__eq2,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( Y != X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq2
% 5.12/5.32 thf(fact_1876_order__less__imp__not__eq2,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( Y != X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_eq2
% 5.12/5.32 thf(fact_1877_order__less__imp__not__less,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_less
% 5.12/5.32 thf(fact_1878_order__less__imp__not__less,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_less
% 5.12/5.32 thf(fact_1879_order__less__imp__not__less,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_less
% 5.12/5.32 thf(fact_1880_order__less__imp__not__less,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_less
% 5.12/5.32 thf(fact_1881_order__less__imp__not__less,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_not_less
% 5.12/5.32 thf(fact_1882_real__root__gt__zero,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_gt_zero
% 5.12/5.32 thf(fact_1883_real__root__strict__decreasing,axiom,
% 5.12/5.32 ! [N: nat,N5: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_nat @ N @ N5 )
% 5.12/5.32 => ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.32 => ( ord_less_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_strict_decreasing
% 5.12/5.32 thf(fact_1884_lemma__exp__total,axiom,
% 5.12/5.32 ! [Y: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.12/5.32 => ? [X3: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.12/5.32 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.12/5.32 & ( ( exp_real @ X3 )
% 5.12/5.32 = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % lemma_exp_total
% 5.12/5.32 thf(fact_1885_ln__ge__iff,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 5.12/5.32 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % ln_ge_iff
% 5.12/5.32 thf(fact_1886_ln__x__over__x__mono,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.12/5.32 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % ln_x_over_x_mono
% 5.12/5.32 thf(fact_1887_div__abs__eq__div__nat,axiom,
% 5.12/5.32 ! [K: int,L: int] :
% 5.12/5.32 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.12/5.32 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % div_abs_eq_div_nat
% 5.12/5.32 thf(fact_1888_mod__abs__eq__div__nat,axiom,
% 5.12/5.32 ! [K: int,L: int] :
% 5.12/5.32 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.12/5.32 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % mod_abs_eq_div_nat
% 5.12/5.32 thf(fact_1889_real__root__pos__pos,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_pos_pos
% 5.12/5.32 thf(fact_1890_real__root__strict__increasing,axiom,
% 5.12/5.32 ! [N: nat,N5: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_nat @ N @ N5 )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.32 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_strict_increasing
% 5.12/5.32 thf(fact_1891_real__root__decreasing,axiom,
% 5.12/5.32 ! [N: nat,N5: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.32 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.32 => ( ord_less_eq_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_decreasing
% 5.12/5.32 thf(fact_1892_real__root__pow__pos,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.12/5.32 = X ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_pow_pos
% 5.12/5.32 thf(fact_1893_real__root__pos__unique,axiom,
% 5.12/5.32 ! [N: nat,Y: real,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.32 => ( ( ( power_power_real @ Y @ N )
% 5.12/5.32 = X )
% 5.12/5.32 => ( ( root @ N @ X )
% 5.12/5.32 = Y ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_pos_unique
% 5.12/5.32 thf(fact_1894_real__root__power__cancel,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.12/5.32 = X ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_power_cancel
% 5.12/5.32 thf(fact_1895_exp__divide__power__eq,axiom,
% 5.12/5.32 ! [N: nat,X: complex] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.12/5.32 = ( exp_complex @ X ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % exp_divide_power_eq
% 5.12/5.32 thf(fact_1896_exp__divide__power__eq,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.12/5.32 = ( exp_real @ X ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % exp_divide_power_eq
% 5.12/5.32 thf(fact_1897_nat__abs__int__diff,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.12/5.32 = ( minus_minus_nat @ B @ A ) ) )
% 5.12/5.32 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.12/5.32 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nat_abs_int_diff
% 5.12/5.32 thf(fact_1898_real__root__increasing,axiom,
% 5.12/5.32 ! [N: nat,N5: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.12/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.32 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % real_root_increasing
% 5.12/5.32 thf(fact_1899_nat__intermed__int__val,axiom,
% 5.12/5.32 ! [M2: nat,N: nat,F: nat > int,K: int] :
% 5.12/5.32 ( ! [I3: nat] :
% 5.12/5.32 ( ( ( ord_less_eq_nat @ M2 @ I3 )
% 5.12/5.32 & ( ord_less_nat @ I3 @ N ) )
% 5.12/5.32 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.12/5.32 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.32 => ( ( ord_less_eq_int @ ( F @ M2 ) @ K )
% 5.12/5.32 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.12/5.32 => ? [I3: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ M2 @ I3 )
% 5.12/5.32 & ( ord_less_eq_nat @ I3 @ N )
% 5.12/5.32 & ( ( F @ I3 )
% 5.12/5.32 = K ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nat_intermed_int_val
% 5.12/5.32 thf(fact_1900_leD,axiom,
% 5.12/5.32 ! [Y: real,X: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1901_leD,axiom,
% 5.12/5.32 ! [Y: set_nat,X: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1902_leD,axiom,
% 5.12/5.32 ! [Y: rat,X: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1903_leD,axiom,
% 5.12/5.32 ! [Y: num,X: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1904_leD,axiom,
% 5.12/5.32 ! [Y: nat,X: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1905_leD,axiom,
% 5.12/5.32 ! [Y: int,X: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ Y @ X )
% 5.12/5.32 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % leD
% 5.12/5.32 thf(fact_1906_leI,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ~ ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % leI
% 5.12/5.32 thf(fact_1907_leI,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ~ ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % leI
% 5.12/5.32 thf(fact_1908_leI,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ~ ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % leI
% 5.12/5.32 thf(fact_1909_leI,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ~ ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % leI
% 5.12/5.32 thf(fact_1910_leI,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ~ ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % leI
% 5.12/5.32 thf(fact_1911_nless__le,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1912_nless__le,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat] :
% 5.12/5.32 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1913_nless__le,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1914_nless__le,axiom,
% 5.12/5.32 ! [A: num,B: num] :
% 5.12/5.32 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1915_nless__le,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1916_nless__le,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.12/5.32 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.12/5.32 | ( A = B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nless_le
% 5.12/5.32 thf(fact_1917_antisym__conv1,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ~ ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1918_antisym__conv1,axiom,
% 5.12/5.32 ! [X: set_nat,Y: set_nat] :
% 5.12/5.32 ( ~ ( ord_less_set_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_set_nat @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1919_antisym__conv1,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ~ ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1920_antisym__conv1,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ~ ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_num @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1921_antisym__conv1,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ~ ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_nat @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1922_antisym__conv1,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ~ ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_int @ X @ Y )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv1
% 5.12/5.32 thf(fact_1923_antisym__conv2,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1924_antisym__conv2,axiom,
% 5.12/5.32 ! [X: set_nat,Y: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1925_antisym__conv2,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1926_antisym__conv2,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1927_antisym__conv2,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1928_antisym__conv2,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ X @ Y )
% 5.12/5.32 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.12/5.32 = ( X = Y ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % antisym_conv2
% 5.12/5.32 thf(fact_1929_dense__ge,axiom,
% 5.12/5.32 ! [Z2: real,Y: real] :
% 5.12/5.32 ( ! [X3: real] :
% 5.12/5.32 ( ( ord_less_real @ Z2 @ X3 )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ X3 ) )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_ge
% 5.12/5.32 thf(fact_1930_dense__ge,axiom,
% 5.12/5.32 ! [Z2: rat,Y: rat] :
% 5.12/5.32 ( ! [X3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ Z2 @ X3 )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ X3 ) )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_ge
% 5.12/5.32 thf(fact_1931_dense__le,axiom,
% 5.12/5.32 ! [Y: real,Z2: real] :
% 5.12/5.32 ( ! [X3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y )
% 5.12/5.32 => ( ord_less_eq_real @ X3 @ Z2 ) )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ Z2 ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_le
% 5.12/5.32 thf(fact_1932_dense__le,axiom,
% 5.12/5.32 ! [Y: rat,Z2: rat] :
% 5.12/5.32 ( ! [X3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y )
% 5.12/5.32 => ( ord_less_eq_rat @ X3 @ Z2 ) )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ Z2 ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_le
% 5.12/5.32 thf(fact_1933_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [X2: real,Y6: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_real @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1934_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [X2: set_nat,Y6: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_set_nat @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1935_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [X2: rat,Y6: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_rat @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1936_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [X2: num,Y6: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_num @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1937_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [X2: nat,Y6: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_nat @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1938_less__le__not__le,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [X2: int,Y6: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ X2 @ Y6 )
% 5.12/5.32 & ~ ( ord_less_eq_int @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_le_not_le
% 5.12/5.32 thf(fact_1939_not__le__imp__less,axiom,
% 5.12/5.32 ! [Y: real,X: real] :
% 5.12/5.32 ( ~ ( ord_less_eq_real @ Y @ X )
% 5.12/5.32 => ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % not_le_imp_less
% 5.12/5.32 thf(fact_1940_not__le__imp__less,axiom,
% 5.12/5.32 ! [Y: rat,X: rat] :
% 5.12/5.32 ( ~ ( ord_less_eq_rat @ Y @ X )
% 5.12/5.32 => ( ord_less_rat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % not_le_imp_less
% 5.12/5.32 thf(fact_1941_not__le__imp__less,axiom,
% 5.12/5.32 ! [Y: num,X: num] :
% 5.12/5.32 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.12/5.32 => ( ord_less_num @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % not_le_imp_less
% 5.12/5.32 thf(fact_1942_not__le__imp__less,axiom,
% 5.12/5.32 ! [Y: nat,X: nat] :
% 5.12/5.32 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.12/5.32 => ( ord_less_nat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % not_le_imp_less
% 5.12/5.32 thf(fact_1943_not__le__imp__less,axiom,
% 5.12/5.32 ! [Y: int,X: int] :
% 5.12/5.32 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.12/5.32 => ( ord_less_int @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % not_le_imp_less
% 5.12/5.32 thf(fact_1944_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_real
% 5.12/5.32 = ( ^ [A3: real,B2: real] :
% 5.12/5.32 ( ( ord_less_real @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1945_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_set_nat
% 5.12/5.32 = ( ^ [A3: set_nat,B2: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1946_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_rat
% 5.12/5.32 = ( ^ [A3: rat,B2: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1947_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_num
% 5.12/5.32 = ( ^ [A3: num,B2: num] :
% 5.12/5.32 ( ( ord_less_num @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1948_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_nat
% 5.12/5.32 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1949_order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_int
% 5.12/5.32 = ( ^ [A3: int,B2: int] :
% 5.12/5.32 ( ( ord_less_int @ A3 @ B2 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.order_iff_strict
% 5.12/5.32 thf(fact_1950_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [A3: real,B2: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1951_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [A3: set_nat,B2: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1952_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [A3: rat,B2: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1953_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [A3: num,B2: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1954_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1955_order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [A3: int,B2: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_order
% 5.12/5.32 thf(fact_1956_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: real,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_real @ B @ C )
% 5.12/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1957_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ A @ B )
% 5.12/5.32 => ( ( ord_less_set_nat @ B @ C )
% 5.12/5.32 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1958_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: rat,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_rat @ B @ C )
% 5.12/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1959_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: num,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.32 => ( ( ord_less_num @ B @ C )
% 5.12/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1960_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: nat,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 => ( ( ord_less_nat @ B @ C )
% 5.12/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1961_order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [A: int,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.32 => ( ( ord_less_int @ B @ C )
% 5.12/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans1
% 5.12/5.32 thf(fact_1962_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: real,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_real @ B @ C )
% 5.12/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1963_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.12/5.32 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1964_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: rat,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1965_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: num,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_num @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.12/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1966_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: nat,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.12/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1967_order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [A: int,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_int @ A @ B )
% 5.12/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.12/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_trans2
% 5.12/5.32 thf(fact_1968_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [A3: real,B2: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1969_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [A3: set_nat,B2: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_set_nat @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1970_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [A3: rat,B2: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1971_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [A3: num,B2: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1972_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1973_order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [A3: int,B2: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.12/5.32 & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_iff_not
% 5.12/5.32 thf(fact_1974_dense__ge__bounded,axiom,
% 5.12/5.32 ! [Z2: real,X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ Z2 @ X )
% 5.12/5.32 => ( ! [W2: real] :
% 5.12/5.32 ( ( ord_less_real @ Z2 @ W2 )
% 5.12/5.32 => ( ( ord_less_real @ W2 @ X )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_ge_bounded
% 5.12/5.32 thf(fact_1975_dense__ge__bounded,axiom,
% 5.12/5.32 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ Z2 @ X )
% 5.12/5.32 => ( ! [W2: rat] :
% 5.12/5.32 ( ( ord_less_rat @ Z2 @ W2 )
% 5.12/5.32 => ( ( ord_less_rat @ W2 @ X )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_ge_bounded
% 5.12/5.32 thf(fact_1976_dense__le__bounded,axiom,
% 5.12/5.32 ! [X: real,Y: real,Z2: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ! [W2: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ W2 )
% 5.12/5.32 => ( ( ord_less_real @ W2 @ Y )
% 5.12/5.32 => ( ord_less_eq_real @ W2 @ Z2 ) ) )
% 5.12/5.32 => ( ord_less_eq_real @ Y @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_le_bounded
% 5.12/5.32 thf(fact_1977_dense__le__bounded,axiom,
% 5.12/5.32 ! [X: rat,Y: rat,Z2: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ! [W2: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ W2 )
% 5.12/5.32 => ( ( ord_less_rat @ W2 @ Y )
% 5.12/5.32 => ( ord_less_eq_rat @ W2 @ Z2 ) ) )
% 5.12/5.32 => ( ord_less_eq_rat @ Y @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dense_le_bounded
% 5.12/5.32 thf(fact_1978_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_real
% 5.12/5.32 = ( ^ [B2: real,A3: real] :
% 5.12/5.32 ( ( ord_less_real @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1979_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_set_nat
% 5.12/5.32 = ( ^ [B2: set_nat,A3: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1980_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_rat
% 5.12/5.32 = ( ^ [B2: rat,A3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1981_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_num
% 5.12/5.32 = ( ^ [B2: num,A3: num] :
% 5.12/5.32 ( ( ord_less_num @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1982_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_nat
% 5.12/5.32 = ( ^ [B2: nat,A3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1983_dual__order_Oorder__iff__strict,axiom,
% 5.12/5.32 ( ord_less_eq_int
% 5.12/5.32 = ( ^ [B2: int,A3: int] :
% 5.12/5.32 ( ( ord_less_int @ B2 @ A3 )
% 5.12/5.32 | ( A3 = B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.order_iff_strict
% 5.12/5.32 thf(fact_1984_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [B2: real,A3: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1985_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [B2: set_nat,A3: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1986_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [B2: rat,A3: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1987_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [B2: num,A3: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1988_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [B2: nat,A3: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1989_dual__order_Ostrict__iff__order,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [B2: int,A3: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.12/5.32 & ( A3 != B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_order
% 5.12/5.32 thf(fact_1990_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: real,A: real,C: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.32 => ( ( ord_less_real @ C @ B )
% 5.12/5.32 => ( ord_less_real @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1991_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ B @ A )
% 5.12/5.32 => ( ( ord_less_set_nat @ C @ B )
% 5.12/5.32 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1992_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: rat,A: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.32 => ( ( ord_less_rat @ C @ B )
% 5.12/5.32 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1993_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: num,A: num,C: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ B @ A )
% 5.12/5.32 => ( ( ord_less_num @ C @ B )
% 5.12/5.32 => ( ord_less_num @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1994_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: nat,A: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.12/5.32 => ( ( ord_less_nat @ C @ B )
% 5.12/5.32 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1995_dual__order_Ostrict__trans1,axiom,
% 5.12/5.32 ! [B: int,A: int,C: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.12/5.32 => ( ( ord_less_int @ C @ B )
% 5.12/5.32 => ( ord_less_int @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans1
% 5.12/5.32 thf(fact_1996_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: real,A: real,C: real] :
% 5.12/5.32 ( ( ord_less_real @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_real @ C @ B )
% 5.12/5.32 => ( ord_less_real @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_1997_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.12/5.32 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_1998_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: rat,A: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_rat @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_rat @ C @ B )
% 5.12/5.32 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_1999_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: num,A: num,C: num] :
% 5.12/5.32 ( ( ord_less_num @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_num @ C @ B )
% 5.12/5.32 => ( ord_less_num @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_2000_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: nat,A: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_nat @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_nat @ C @ B )
% 5.12/5.32 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_2001_dual__order_Ostrict__trans2,axiom,
% 5.12/5.32 ! [B: int,A: int,C: int] :
% 5.12/5.32 ( ( ord_less_int @ B @ A )
% 5.12/5.32 => ( ( ord_less_eq_int @ C @ B )
% 5.12/5.32 => ( ord_less_int @ C @ A ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_trans2
% 5.12/5.32 thf(fact_2002_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [B2: real,A3: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2003_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [B2: set_nat,A3: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_set_nat @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2004_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [B2: rat,A3: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2005_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [B2: num,A3: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2006_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [B2: nat,A3: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2007_dual__order_Ostrict__iff__not,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [B2: int,A3: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.12/5.32 & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_iff_not
% 5.12/5.32 thf(fact_2008_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2009_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ A @ B )
% 5.12/5.32 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2010_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ B )
% 5.12/5.32 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2011_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: num,B: num] :
% 5.12/5.32 ( ( ord_less_num @ A @ B )
% 5.12/5.32 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2012_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A @ B )
% 5.12/5.32 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2013_order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ A @ B )
% 5.12/5.32 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % order.strict_implies_order
% 5.12/5.32 thf(fact_2014_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ord_less_real @ B @ A )
% 5.12/5.32 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2015_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: set_nat,A: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ B @ A )
% 5.12/5.32 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2016_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ord_less_rat @ B @ A )
% 5.12/5.32 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2017_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: num,A: num] :
% 5.12/5.32 ( ( ord_less_num @ B @ A )
% 5.12/5.32 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2018_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ord_less_nat @ B @ A )
% 5.12/5.32 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2019_dual__order_Ostrict__implies__order,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ord_less_int @ B @ A )
% 5.12/5.32 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % dual_order.strict_implies_order
% 5.12/5.32 thf(fact_2020_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_real
% 5.12/5.32 = ( ^ [X2: real,Y6: real] :
% 5.12/5.32 ( ( ord_less_real @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2021_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_set_nat
% 5.12/5.32 = ( ^ [X2: set_nat,Y6: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2022_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_rat
% 5.12/5.32 = ( ^ [X2: rat,Y6: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2023_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_num
% 5.12/5.32 = ( ^ [X2: num,Y6: num] :
% 5.12/5.32 ( ( ord_less_num @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2024_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_nat
% 5.12/5.32 = ( ^ [X2: nat,Y6: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2025_order__le__less,axiom,
% 5.12/5.32 ( ord_less_eq_int
% 5.12/5.32 = ( ^ [X2: int,Y6: int] :
% 5.12/5.32 ( ( ord_less_int @ X2 @ Y6 )
% 5.12/5.32 | ( X2 = Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less
% 5.12/5.32 thf(fact_2026_order__less__le,axiom,
% 5.12/5.32 ( ord_less_real
% 5.12/5.32 = ( ^ [X2: real,Y6: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2027_order__less__le,axiom,
% 5.12/5.32 ( ord_less_set_nat
% 5.12/5.32 = ( ^ [X2: set_nat,Y6: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2028_order__less__le,axiom,
% 5.12/5.32 ( ord_less_rat
% 5.12/5.32 = ( ^ [X2: rat,Y6: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2029_order__less__le,axiom,
% 5.12/5.32 ( ord_less_num
% 5.12/5.32 = ( ^ [X2: num,Y6: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2030_order__less__le,axiom,
% 5.12/5.32 ( ord_less_nat
% 5.12/5.32 = ( ^ [X2: nat,Y6: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2031_order__less__le,axiom,
% 5.12/5.32 ( ord_less_int
% 5.12/5.32 = ( ^ [X2: int,Y6: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ X2 @ Y6 )
% 5.12/5.32 & ( X2 != Y6 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le
% 5.12/5.32 thf(fact_2032_linorder__not__le,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 5.12/5.32 = ( ord_less_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_le
% 5.12/5.32 thf(fact_2033_linorder__not__le,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 5.12/5.32 = ( ord_less_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_le
% 5.12/5.32 thf(fact_2034_linorder__not__le,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.12/5.32 = ( ord_less_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_le
% 5.12/5.32 thf(fact_2035_linorder__not__le,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.12/5.32 = ( ord_less_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_le
% 5.12/5.32 thf(fact_2036_linorder__not__le,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.12/5.32 = ( ord_less_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_le
% 5.12/5.32 thf(fact_2037_linorder__not__less,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.12/5.32 = ( ord_less_eq_real @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_less
% 5.12/5.32 thf(fact_2038_linorder__not__less,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.12/5.32 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_less
% 5.12/5.32 thf(fact_2039_linorder__not__less,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.12/5.32 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_less
% 5.12/5.32 thf(fact_2040_linorder__not__less,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.12/5.32 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_less
% 5.12/5.32 thf(fact_2041_linorder__not__less,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.12/5.32 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % linorder_not_less
% 5.12/5.32 thf(fact_2042_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: real,Y: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2043_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: set_nat,Y: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2044_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: rat,Y: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2045_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: num,Y: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2046_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2047_order__less__imp__le,axiom,
% 5.12/5.32 ! [X: int,Y: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_imp_le
% 5.12/5.32 thf(fact_2048_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2049_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2050_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2051_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: num,B: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_num @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2052_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2053_order__le__neq__trans,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.32 => ( ( A != B )
% 5.12/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_neq_trans
% 5.12/5.32 thf(fact_2054_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_real @ A @ B )
% 5.12/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2055_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: set_nat,B: set_nat] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.12/5.32 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2056_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2057_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: num,B: num] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_num @ A @ B )
% 5.12/5.32 => ( ord_less_num @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2058_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2059_order__neq__le__trans,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( A != B )
% 5.12/5.32 => ( ( ord_less_eq_int @ A @ B )
% 5.12/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_neq_le_trans
% 5.12/5.32 thf(fact_2060_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: real,Y: real,Z2: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.32 => ( ( ord_less_real @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2061_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: set_nat,Y: set_nat,Z2: set_nat] :
% 5.12/5.32 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_set_nat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_set_nat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2062_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: rat,Y: rat,Z2: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_rat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2063_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: num,Y: num,Z2: num] :
% 5.12/5.32 ( ( ord_less_eq_num @ X @ Y )
% 5.12/5.32 => ( ( ord_less_num @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2064_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: nat,Y: nat,Z2: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_nat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2065_order__le__less__trans,axiom,
% 5.12/5.32 ! [X: int,Y: int,Z2: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ X @ Y )
% 5.12/5.32 => ( ( ord_less_int @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_trans
% 5.12/5.32 thf(fact_2066_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: real,Y: real,Z2: real] :
% 5.12/5.32 ( ( ord_less_real @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_real @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_real @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2067_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: set_nat,Y: set_nat,Z2: set_nat] :
% 5.12/5.32 ( ( ord_less_set_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_set_nat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_set_nat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2068_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: rat,Y: rat,Z2: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_rat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_rat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2069_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: num,Y: num,Z2: num] :
% 5.12/5.32 ( ( ord_less_num @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_num @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_num @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2070_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: nat,Y: nat,Z2: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_nat @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_nat @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2071_order__less__le__trans,axiom,
% 5.12/5.32 ! [X: int,Y: int,Z2: int] :
% 5.12/5.32 ( ( ord_less_int @ X @ Y )
% 5.12/5.32 => ( ( ord_less_eq_int @ Y @ Z2 )
% 5.12/5.32 => ( ord_less_int @ X @ Z2 ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_less_le_trans
% 5.12/5.32 thf(fact_2072_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: real > real,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_real @ B @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2073_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_rat @ B @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2074_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: num > real,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_num @ B @ C )
% 5.12/5.32 => ( ! [X3: num,Y3: num] :
% 5.12/5.32 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2075_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_nat @ B @ C )
% 5.12/5.32 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2076_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: real,F: int > real,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_int @ B @ C )
% 5.12/5.32 => ( ! [X3: int,Y3: int] :
% 5.12/5.32 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2077_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_real @ B @ C )
% 5.12/5.32 => ( ! [X3: real,Y3: real] :
% 5.12/5.32 ( ( ord_less_real @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2078_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_rat @ B @ C )
% 5.12/5.32 => ( ! [X3: rat,Y3: rat] :
% 5.12/5.32 ( ( ord_less_rat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2079_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_num @ B @ C )
% 5.12/5.32 => ( ! [X3: num,Y3: num] :
% 5.12/5.32 ( ( ord_less_num @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2080_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_nat @ B @ C )
% 5.12/5.32 => ( ! [X3: nat,Y3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2081_order__le__less__subst1,axiom,
% 5.12/5.32 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.12/5.32 => ( ( ord_less_int @ B @ C )
% 5.12/5.32 => ( ! [X3: int,Y3: int] :
% 5.12/5.32 ( ( ord_less_int @ X3 @ Y3 )
% 5.12/5.32 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.12/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % order_le_less_subst1
% 5.12/5.32 thf(fact_2082_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.12/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % exp_ge_one_plus_x_over_n_power_n
% 5.12/5.32 thf(fact_2083_nat0__intermed__int__val,axiom,
% 5.12/5.32 ! [N: nat,F: nat > int,K: int] :
% 5.12/5.32 ( ! [I3: nat] :
% 5.12/5.32 ( ( ord_less_nat @ I3 @ N )
% 5.12/5.32 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.12/5.32 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.12/5.32 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.12/5.32 => ? [I3: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ I3 @ N )
% 5.12/5.32 & ( ( F @ I3 )
% 5.12/5.32 = K ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % nat0_intermed_int_val
% 5.12/5.32 thf(fact_2084_root__powr__inverse,axiom,
% 5.12/5.32 ! [N: nat,X: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.32 => ( ( root @ N @ X )
% 5.12/5.32 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % root_powr_inverse
% 5.12/5.32 thf(fact_2085_log__root,axiom,
% 5.12/5.32 ! [N: nat,A: real,B: real] :
% 5.12/5.32 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.32 => ( ( log2 @ B @ ( root @ N @ A ) )
% 5.12/5.32 = ( divide_divide_real @ ( log2 @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % log_root
% 5.12/5.32 thf(fact_2086_complete__interval,axiom,
% 5.12/5.32 ! [A: real,B: real,P: real > $o] :
% 5.12/5.32 ( ( ord_less_real @ A @ B )
% 5.12/5.32 => ( ( P @ A )
% 5.12/5.32 => ( ~ ( P @ B )
% 5.12/5.32 => ? [C2: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ C2 )
% 5.12/5.32 & ( ord_less_eq_real @ C2 @ B )
% 5.12/5.32 & ! [X4: real] :
% 5.12/5.32 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.12/5.32 & ( ord_less_real @ X4 @ C2 ) )
% 5.12/5.32 => ( P @ X4 ) )
% 5.12/5.32 & ! [D3: real] :
% 5.12/5.32 ( ! [X3: real] :
% 5.12/5.32 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.12/5.32 & ( ord_less_real @ X3 @ D3 ) )
% 5.12/5.32 => ( P @ X3 ) )
% 5.12/5.32 => ( ord_less_eq_real @ D3 @ C2 ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % complete_interval
% 5.12/5.32 thf(fact_2087_complete__interval,axiom,
% 5.12/5.32 ! [A: nat,B: nat,P: nat > $o] :
% 5.12/5.32 ( ( ord_less_nat @ A @ B )
% 5.12/5.32 => ( ( P @ A )
% 5.12/5.32 => ( ~ ( P @ B )
% 5.12/5.32 => ? [C2: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A @ C2 )
% 5.12/5.32 & ( ord_less_eq_nat @ C2 @ B )
% 5.12/5.32 & ! [X4: nat] :
% 5.12/5.32 ( ( ( ord_less_eq_nat @ A @ X4 )
% 5.12/5.32 & ( ord_less_nat @ X4 @ C2 ) )
% 5.12/5.32 => ( P @ X4 ) )
% 5.12/5.32 & ! [D3: nat] :
% 5.12/5.32 ( ! [X3: nat] :
% 5.12/5.32 ( ( ( ord_less_eq_nat @ A @ X3 )
% 5.12/5.32 & ( ord_less_nat @ X3 @ D3 ) )
% 5.12/5.32 => ( P @ X3 ) )
% 5.12/5.32 => ( ord_less_eq_nat @ D3 @ C2 ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % complete_interval
% 5.12/5.32 thf(fact_2088_complete__interval,axiom,
% 5.12/5.32 ! [A: int,B: int,P: int > $o] :
% 5.12/5.32 ( ( ord_less_int @ A @ B )
% 5.12/5.32 => ( ( P @ A )
% 5.12/5.32 => ( ~ ( P @ B )
% 5.12/5.32 => ? [C2: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A @ C2 )
% 5.12/5.32 & ( ord_less_eq_int @ C2 @ B )
% 5.12/5.32 & ! [X4: int] :
% 5.12/5.32 ( ( ( ord_less_eq_int @ A @ X4 )
% 5.12/5.32 & ( ord_less_int @ X4 @ C2 ) )
% 5.12/5.32 => ( P @ X4 ) )
% 5.12/5.32 & ! [D3: int] :
% 5.12/5.32 ( ! [X3: int] :
% 5.12/5.32 ( ( ( ord_less_eq_int @ A @ X3 )
% 5.12/5.32 & ( ord_less_int @ X3 @ D3 ) )
% 5.12/5.32 => ( P @ X3 ) )
% 5.12/5.32 => ( ord_less_eq_int @ D3 @ C2 ) ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % complete_interval
% 5.12/5.32 thf(fact_2089_log__of__power__le,axiom,
% 5.12/5.32 ! [M2: nat,B: real,N: nat] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.12/5.32 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.32 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.32 => ( ord_less_eq_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % log_of_power_le
% 5.12/5.32 thf(fact_2090_verit__le__mono__div__int,axiom,
% 5.12/5.32 ! [A2: int,B5: int,N: int] :
% 5.12/5.32 ( ( ord_less_int @ A2 @ B5 )
% 5.12/5.32 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.12/5.32 => ( ord_less_eq_int
% 5.12/5.32 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.12/5.32 @ ( if_int
% 5.12/5.32 @ ( ( modulo_modulo_int @ B5 @ N )
% 5.12/5.32 = zero_zero_int )
% 5.12/5.32 @ one_one_int
% 5.12/5.32 @ zero_zero_int ) )
% 5.12/5.32 @ ( divide_divide_int @ B5 @ N ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % verit_le_mono_div_int
% 5.12/5.32 thf(fact_2091_div__pos__geq,axiom,
% 5.12/5.32 ! [L: int,K: int] :
% 5.12/5.32 ( ( ord_less_int @ zero_zero_int @ L )
% 5.12/5.32 => ( ( ord_less_eq_int @ L @ K )
% 5.12/5.32 => ( ( divide_divide_int @ K @ L )
% 5.12/5.32 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % div_pos_geq
% 5.12/5.32 thf(fact_2092_div__pos__neg__trivial,axiom,
% 5.12/5.32 ! [K: int,L: int] :
% 5.12/5.32 ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.32 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.12/5.32 => ( ( divide_divide_int @ K @ L )
% 5.12/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % div_pos_neg_trivial
% 5.12/5.32 thf(fact_2093_verit__le__mono__div,axiom,
% 5.12/5.32 ! [A2: nat,B5: nat,N: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A2 @ B5 )
% 5.12/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.32 => ( ord_less_eq_nat
% 5.12/5.32 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.12/5.32 @ ( if_nat
% 5.12/5.32 @ ( ( modulo_modulo_nat @ B5 @ N )
% 5.12/5.32 = zero_zero_nat )
% 5.12/5.32 @ one_one_nat
% 5.12/5.32 @ zero_zero_nat ) )
% 5.12/5.32 @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % verit_le_mono_div
% 5.12/5.32 thf(fact_2094_even__odd__cases,axiom,
% 5.12/5.32 ! [X: nat] :
% 5.12/5.32 ( ! [N2: nat] :
% 5.12/5.32 ( X
% 5.12/5.32 != ( plus_plus_nat @ N2 @ N2 ) )
% 5.12/5.32 => ~ ! [N2: nat] :
% 5.12/5.32 ( X
% 5.12/5.32 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % even_odd_cases
% 5.12/5.32 thf(fact_2095_add__left__cancel,axiom,
% 5.12/5.32 ! [A: real,B: real,C: real] :
% 5.12/5.32 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.32 = ( plus_plus_real @ A @ C ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_left_cancel
% 5.12/5.32 thf(fact_2096_add__left__cancel,axiom,
% 5.12/5.32 ! [A: rat,B: rat,C: rat] :
% 5.12/5.32 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.32 = ( plus_plus_rat @ A @ C ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_left_cancel
% 5.12/5.32 thf(fact_2097_add__left__cancel,axiom,
% 5.12/5.32 ! [A: nat,B: nat,C: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ A @ B )
% 5.12/5.32 = ( plus_plus_nat @ A @ C ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_left_cancel
% 5.12/5.32 thf(fact_2098_add__left__cancel,axiom,
% 5.12/5.32 ! [A: int,B: int,C: int] :
% 5.12/5.32 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.32 = ( plus_plus_int @ A @ C ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_left_cancel
% 5.12/5.32 thf(fact_2099_add__right__cancel,axiom,
% 5.12/5.32 ! [B: real,A: real,C: real] :
% 5.12/5.32 ( ( ( plus_plus_real @ B @ A )
% 5.12/5.32 = ( plus_plus_real @ C @ A ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_right_cancel
% 5.12/5.32 thf(fact_2100_add__right__cancel,axiom,
% 5.12/5.32 ! [B: rat,A: rat,C: rat] :
% 5.12/5.32 ( ( ( plus_plus_rat @ B @ A )
% 5.12/5.32 = ( plus_plus_rat @ C @ A ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_right_cancel
% 5.12/5.32 thf(fact_2101_add__right__cancel,axiom,
% 5.12/5.32 ! [B: nat,A: nat,C: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ B @ A )
% 5.12/5.32 = ( plus_plus_nat @ C @ A ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_right_cancel
% 5.12/5.32 thf(fact_2102_add__right__cancel,axiom,
% 5.12/5.32 ! [B: int,A: int,C: int] :
% 5.12/5.32 ( ( ( plus_plus_int @ B @ A )
% 5.12/5.32 = ( plus_plus_int @ C @ A ) )
% 5.12/5.32 = ( B = C ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_right_cancel
% 5.12/5.32 thf(fact_2103_abs__exp__cancel,axiom,
% 5.12/5.32 ! [X: real] :
% 5.12/5.32 ( ( abs_abs_real @ ( exp_real @ X ) )
% 5.12/5.32 = ( exp_real @ X ) ) ).
% 5.12/5.32
% 5.12/5.32 % abs_exp_cancel
% 5.12/5.32 thf(fact_2104_add__le__cancel__left,axiom,
% 5.12/5.32 ! [C: real,A: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.12/5.32 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_left
% 5.12/5.32 thf(fact_2105_add__le__cancel__left,axiom,
% 5.12/5.32 ! [C: rat,A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.12/5.32 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_left
% 5.12/5.32 thf(fact_2106_add__le__cancel__left,axiom,
% 5.12/5.32 ! [C: nat,A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.12/5.32 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_left
% 5.12/5.32 thf(fact_2107_add__le__cancel__left,axiom,
% 5.12/5.32 ! [C: int,A: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.12/5.32 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_left
% 5.12/5.32 thf(fact_2108_add__le__cancel__right,axiom,
% 5.12/5.32 ! [A: real,C: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.32 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_right
% 5.12/5.32 thf(fact_2109_add__le__cancel__right,axiom,
% 5.12/5.32 ! [A: rat,C: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.32 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_right
% 5.12/5.32 thf(fact_2110_add__le__cancel__right,axiom,
% 5.12/5.32 ! [A: nat,C: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.32 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_right
% 5.12/5.32 thf(fact_2111_add__le__cancel__right,axiom,
% 5.12/5.32 ! [A: int,C: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.32 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_cancel_right
% 5.12/5.32 thf(fact_2112_double__eq__0__iff,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( ( plus_plus_real @ A @ A )
% 5.12/5.32 = zero_zero_real )
% 5.12/5.32 = ( A = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_eq_0_iff
% 5.12/5.32 thf(fact_2113_double__eq__0__iff,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( ( plus_plus_rat @ A @ A )
% 5.12/5.32 = zero_zero_rat )
% 5.12/5.32 = ( A = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_eq_0_iff
% 5.12/5.32 thf(fact_2114_double__eq__0__iff,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( ( plus_plus_int @ A @ A )
% 5.12/5.32 = zero_zero_int )
% 5.12/5.32 = ( A = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_eq_0_iff
% 5.12/5.32 thf(fact_2115_add__0,axiom,
% 5.12/5.32 ! [A: literal] :
% 5.12/5.32 ( ( plus_plus_literal @ zero_zero_literal @ A )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_0
% 5.12/5.32 thf(fact_2116_add__0,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_0
% 5.12/5.32 thf(fact_2117_add__0,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_0
% 5.12/5.32 thf(fact_2118_add__0,axiom,
% 5.12/5.32 ! [A: nat] :
% 5.12/5.32 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_0
% 5.12/5.32 thf(fact_2119_add__0,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_0
% 5.12/5.32 thf(fact_2120_zero__eq__add__iff__both__eq__0,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( zero_zero_nat
% 5.12/5.32 = ( plus_plus_nat @ X @ Y ) )
% 5.12/5.32 = ( ( X = zero_zero_nat )
% 5.12/5.32 & ( Y = zero_zero_nat ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_eq_add_iff_both_eq_0
% 5.12/5.32 thf(fact_2121_add__eq__0__iff__both__eq__0,axiom,
% 5.12/5.32 ! [X: nat,Y: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ X @ Y )
% 5.12/5.32 = zero_zero_nat )
% 5.12/5.32 = ( ( X = zero_zero_nat )
% 5.12/5.32 & ( Y = zero_zero_nat ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_eq_0_iff_both_eq_0
% 5.12/5.32 thf(fact_2122_add__cancel__right__right,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_real @ A @ B ) )
% 5.12/5.32 = ( B = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_right
% 5.12/5.32 thf(fact_2123_add__cancel__right__right,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_rat @ A @ B ) )
% 5.12/5.32 = ( B = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_right
% 5.12/5.32 thf(fact_2124_add__cancel__right__right,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_nat @ A @ B ) )
% 5.12/5.32 = ( B = zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_right
% 5.12/5.32 thf(fact_2125_add__cancel__right__right,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_int @ A @ B ) )
% 5.12/5.32 = ( B = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_right
% 5.12/5.32 thf(fact_2126_add__cancel__right__left,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_real @ B @ A ) )
% 5.12/5.32 = ( B = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_left
% 5.12/5.32 thf(fact_2127_add__cancel__right__left,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_rat @ B @ A ) )
% 5.12/5.32 = ( B = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_left
% 5.12/5.32 thf(fact_2128_add__cancel__right__left,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_nat @ B @ A ) )
% 5.12/5.32 = ( B = zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_left
% 5.12/5.32 thf(fact_2129_add__cancel__right__left,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( A
% 5.12/5.32 = ( plus_plus_int @ B @ A ) )
% 5.12/5.32 = ( B = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_right_left
% 5.12/5.32 thf(fact_2130_add__cancel__left__right,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_right
% 5.12/5.32 thf(fact_2131_add__cancel__left__right,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_right
% 5.12/5.32 thf(fact_2132_add__cancel__left__right,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ A @ B )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_right
% 5.12/5.32 thf(fact_2133_add__cancel__left__right,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_right
% 5.12/5.32 thf(fact_2134_add__cancel__left__left,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ( plus_plus_real @ B @ A )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_left
% 5.12/5.32 thf(fact_2135_add__cancel__left__left,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ( plus_plus_rat @ B @ A )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_left
% 5.12/5.32 thf(fact_2136_add__cancel__left__left,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ B @ A )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_left
% 5.12/5.32 thf(fact_2137_add__cancel__left__left,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ( plus_plus_int @ B @ A )
% 5.12/5.32 = A )
% 5.12/5.32 = ( B = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_cancel_left_left
% 5.12/5.32 thf(fact_2138_double__zero__sym,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( zero_zero_real
% 5.12/5.32 = ( plus_plus_real @ A @ A ) )
% 5.12/5.32 = ( A = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_zero_sym
% 5.12/5.32 thf(fact_2139_double__zero__sym,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( zero_zero_rat
% 5.12/5.32 = ( plus_plus_rat @ A @ A ) )
% 5.12/5.32 = ( A = zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_zero_sym
% 5.12/5.32 thf(fact_2140_double__zero__sym,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( zero_zero_int
% 5.12/5.32 = ( plus_plus_int @ A @ A ) )
% 5.12/5.32 = ( A = zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_zero_sym
% 5.12/5.32 thf(fact_2141_add_Oright__neutral,axiom,
% 5.12/5.32 ! [A: literal] :
% 5.12/5.32 ( ( plus_plus_literal @ A @ zero_zero_literal )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_neutral
% 5.12/5.32 thf(fact_2142_add_Oright__neutral,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_neutral
% 5.12/5.32 thf(fact_2143_add_Oright__neutral,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_neutral
% 5.12/5.32 thf(fact_2144_add_Oright__neutral,axiom,
% 5.12/5.32 ! [A: nat] :
% 5.12/5.32 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_neutral
% 5.12/5.32 thf(fact_2145_add_Oright__neutral,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_neutral
% 5.12/5.32 thf(fact_2146_add__less__cancel__right,axiom,
% 5.12/5.32 ! [A: real,C: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.32 = ( ord_less_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_right
% 5.12/5.32 thf(fact_2147_add__less__cancel__right,axiom,
% 5.12/5.32 ! [A: rat,C: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.32 = ( ord_less_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_right
% 5.12/5.32 thf(fact_2148_add__less__cancel__right,axiom,
% 5.12/5.32 ! [A: nat,C: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.32 = ( ord_less_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_right
% 5.12/5.32 thf(fact_2149_add__less__cancel__right,axiom,
% 5.12/5.32 ! [A: int,C: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.32 = ( ord_less_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_right
% 5.12/5.32 thf(fact_2150_add__less__cancel__left,axiom,
% 5.12/5.32 ! [C: real,A: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.12/5.32 = ( ord_less_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_left
% 5.12/5.32 thf(fact_2151_add__less__cancel__left,axiom,
% 5.12/5.32 ! [C: rat,A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.12/5.32 = ( ord_less_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_left
% 5.12/5.32 thf(fact_2152_add__less__cancel__left,axiom,
% 5.12/5.32 ! [C: nat,A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.12/5.32 = ( ord_less_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_left
% 5.12/5.32 thf(fact_2153_add__less__cancel__left,axiom,
% 5.12/5.32 ! [C: int,A: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.12/5.32 = ( ord_less_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_cancel_left
% 5.12/5.32 thf(fact_2154_add__diff__cancel,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel
% 5.12/5.32 thf(fact_2155_add__diff__cancel,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel
% 5.12/5.32 thf(fact_2156_add__diff__cancel,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel
% 5.12/5.32 thf(fact_2157_diff__add__cancel,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % diff_add_cancel
% 5.12/5.32 thf(fact_2158_diff__add__cancel,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % diff_add_cancel
% 5.12/5.32 thf(fact_2159_diff__add__cancel,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % diff_add_cancel
% 5.12/5.32 thf(fact_2160_add__diff__cancel__left,axiom,
% 5.12/5.32 ! [C: real,A: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.12/5.32 = ( minus_minus_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left
% 5.12/5.32 thf(fact_2161_add__diff__cancel__left,axiom,
% 5.12/5.32 ! [C: rat,A: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.12/5.32 = ( minus_minus_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left
% 5.12/5.32 thf(fact_2162_add__diff__cancel__left,axiom,
% 5.12/5.32 ! [C: nat,A: nat,B: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.12/5.32 = ( minus_minus_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left
% 5.12/5.32 thf(fact_2163_add__diff__cancel__left,axiom,
% 5.12/5.32 ! [C: int,A: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.12/5.32 = ( minus_minus_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left
% 5.12/5.32 thf(fact_2164_add__diff__cancel__left_H,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left'
% 5.12/5.32 thf(fact_2165_add__diff__cancel__left_H,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left'
% 5.12/5.32 thf(fact_2166_add__diff__cancel__left_H,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left'
% 5.12/5.32 thf(fact_2167_add__diff__cancel__left_H,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_left'
% 5.12/5.32 thf(fact_2168_add__diff__cancel__right,axiom,
% 5.12/5.32 ! [A: real,C: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.32 = ( minus_minus_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right
% 5.12/5.32 thf(fact_2169_add__diff__cancel__right,axiom,
% 5.12/5.32 ! [A: rat,C: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.32 = ( minus_minus_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right
% 5.12/5.32 thf(fact_2170_add__diff__cancel__right,axiom,
% 5.12/5.32 ! [A: nat,C: nat,B: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.32 = ( minus_minus_nat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right
% 5.12/5.32 thf(fact_2171_add__diff__cancel__right,axiom,
% 5.12/5.32 ! [A: int,C: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.32 = ( minus_minus_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right
% 5.12/5.32 thf(fact_2172_add__diff__cancel__right_H,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right'
% 5.12/5.32 thf(fact_2173_add__diff__cancel__right_H,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right'
% 5.12/5.32 thf(fact_2174_add__diff__cancel__right_H,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right'
% 5.12/5.32 thf(fact_2175_add__diff__cancel__right_H,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.12/5.32 = A ) ).
% 5.12/5.32
% 5.12/5.32 % add_diff_cancel_right'
% 5.12/5.32 thf(fact_2176_add__minus__cancel,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_minus_cancel
% 5.12/5.32 thf(fact_2177_add__minus__cancel,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_minus_cancel
% 5.12/5.32 thf(fact_2178_add__minus__cancel,axiom,
% 5.12/5.32 ! [A: complex,B: complex] :
% 5.12/5.32 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_minus_cancel
% 5.12/5.32 thf(fact_2179_add__minus__cancel,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_minus_cancel
% 5.12/5.32 thf(fact_2180_add__minus__cancel,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % add_minus_cancel
% 5.12/5.32 thf(fact_2181_minus__add__cancel,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_cancel
% 5.12/5.32 thf(fact_2182_minus__add__cancel,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_cancel
% 5.12/5.32 thf(fact_2183_minus__add__cancel,axiom,
% 5.12/5.32 ! [A: complex,B: complex] :
% 5.12/5.32 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_cancel
% 5.12/5.32 thf(fact_2184_minus__add__cancel,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_cancel
% 5.12/5.32 thf(fact_2185_minus__add__cancel,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.32 = B ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_cancel
% 5.12/5.32 thf(fact_2186_minus__add__distrib,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_distrib
% 5.12/5.32 thf(fact_2187_minus__add__distrib,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.12/5.32 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_distrib
% 5.12/5.32 thf(fact_2188_minus__add__distrib,axiom,
% 5.12/5.32 ! [A: complex,B: complex] :
% 5.12/5.32 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.12/5.32 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_distrib
% 5.12/5.32 thf(fact_2189_minus__add__distrib,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_distrib
% 5.12/5.32 thf(fact_2190_minus__add__distrib,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % minus_add_distrib
% 5.12/5.32 thf(fact_2191_abs__add__abs,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.12/5.32 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % abs_add_abs
% 5.12/5.32 thf(fact_2192_abs__add__abs,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.12/5.32 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % abs_add_abs
% 5.12/5.32 thf(fact_2193_abs__add__abs,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.12/5.32 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % abs_add_abs
% 5.12/5.32 thf(fact_2194_abs__add__abs,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.12/5.32 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % abs_add_abs
% 5.12/5.32 thf(fact_2195_add__Suc__right,axiom,
% 5.12/5.32 ! [M2: nat,N: nat] :
% 5.12/5.32 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 5.12/5.32 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_Suc_right
% 5.12/5.32 thf(fact_2196_Nat_Oadd__0__right,axiom,
% 5.12/5.32 ! [M2: nat] :
% 5.12/5.32 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 5.12/5.32 = M2 ) ).
% 5.12/5.32
% 5.12/5.32 % Nat.add_0_right
% 5.12/5.32 thf(fact_2197_add__is__0,axiom,
% 5.12/5.32 ! [M2: nat,N: nat] :
% 5.12/5.32 ( ( ( plus_plus_nat @ M2 @ N )
% 5.12/5.32 = zero_zero_nat )
% 5.12/5.32 = ( ( M2 = zero_zero_nat )
% 5.12/5.32 & ( N = zero_zero_nat ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_is_0
% 5.12/5.32 thf(fact_2198_nat__add__left__cancel__less,axiom,
% 5.12/5.32 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 5.12/5.32 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.32
% 5.12/5.32 % nat_add_left_cancel_less
% 5.12/5.32 thf(fact_2199_nat__add__left__cancel__le,axiom,
% 5.12/5.32 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 5.12/5.32 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.32
% 5.12/5.32 % nat_add_left_cancel_le
% 5.12/5.32 thf(fact_2200_diff__diff__left,axiom,
% 5.12/5.32 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J2 ) @ K )
% 5.12/5.32 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_diff_left
% 5.12/5.32 thf(fact_2201_powr__eq__0__iff,axiom,
% 5.12/5.32 ! [W: real,Z2: real] :
% 5.12/5.32 ( ( ( powr_real @ W @ Z2 )
% 5.12/5.32 = zero_zero_real )
% 5.12/5.32 = ( W = zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % powr_eq_0_iff
% 5.12/5.32 thf(fact_2202_powr__0,axiom,
% 5.12/5.32 ! [Z2: real] :
% 5.12/5.32 ( ( powr_real @ zero_zero_real @ Z2 )
% 5.12/5.32 = zero_zero_real ) ).
% 5.12/5.32
% 5.12/5.32 % powr_0
% 5.12/5.32 thf(fact_2203_powr__one__eq__one,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( powr_real @ one_one_real @ A )
% 5.12/5.32 = one_one_real ) ).
% 5.12/5.32
% 5.12/5.32 % powr_one_eq_one
% 5.12/5.32 thf(fact_2204_add__le__same__cancel1,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel1
% 5.12/5.32 thf(fact_2205_add__le__same__cancel1,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel1
% 5.12/5.32 thf(fact_2206_add__le__same__cancel1,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel1
% 5.12/5.32 thf(fact_2207_add__le__same__cancel1,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel1
% 5.12/5.32 thf(fact_2208_add__le__same__cancel2,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel2
% 5.12/5.32 thf(fact_2209_add__le__same__cancel2,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel2
% 5.12/5.32 thf(fact_2210_add__le__same__cancel2,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel2
% 5.12/5.32 thf(fact_2211_add__le__same__cancel2,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_le_same_cancel2
% 5.12/5.32 thf(fact_2212_le__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.12/5.32 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel1
% 5.12/5.32 thf(fact_2213_le__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel1
% 5.12/5.32 thf(fact_2214_le__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.32 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel1
% 5.12/5.32 thf(fact_2215_le__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.12/5.32 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel1
% 5.12/5.32 thf(fact_2216_le__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.12/5.32 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel2
% 5.12/5.32 thf(fact_2217_le__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.12/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel2
% 5.12/5.32 thf(fact_2218_le__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.12/5.32 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel2
% 5.12/5.32 thf(fact_2219_le__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.12/5.32 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_same_cancel2
% 5.12/5.32 thf(fact_2220_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.12/5.32 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_le_zero_iff_single_add_le_zero
% 5.12/5.32 thf(fact_2221_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.12/5.32 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_le_zero_iff_single_add_le_zero
% 5.12/5.32 thf(fact_2222_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.12/5.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_le_zero_iff_single_add_le_zero
% 5.12/5.32 thf(fact_2223_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.12/5.32 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_le_double_add_iff_zero_le_single_add
% 5.12/5.32 thf(fact_2224_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.12/5.32 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_le_double_add_iff_zero_le_single_add
% 5.12/5.32 thf(fact_2225_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.12/5.32 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_le_double_add_iff_zero_le_single_add
% 5.12/5.32 thf(fact_2226_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.12/5.32 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_less_double_add_iff_zero_less_single_add
% 5.12/5.32 thf(fact_2227_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.12/5.32 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_less_double_add_iff_zero_less_single_add
% 5.12/5.32 thf(fact_2228_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.12/5.32 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % zero_less_double_add_iff_zero_less_single_add
% 5.12/5.32 thf(fact_2229_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.12/5.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_less_zero_iff_single_add_less_zero
% 5.12/5.32 thf(fact_2230_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.12/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_less_zero_iff_single_add_less_zero
% 5.12/5.32 thf(fact_2231_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.12/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % double_add_less_zero_iff_single_add_less_zero
% 5.12/5.32 thf(fact_2232_less__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.12/5.32 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel2
% 5.12/5.32 thf(fact_2233_less__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.12/5.32 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel2
% 5.12/5.32 thf(fact_2234_less__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.12/5.32 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel2
% 5.12/5.32 thf(fact_2235_less__add__same__cancel2,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.12/5.32 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel2
% 5.12/5.32 thf(fact_2236_less__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.12/5.32 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel1
% 5.12/5.32 thf(fact_2237_less__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.32 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel1
% 5.12/5.32 thf(fact_2238_less__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.32 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel1
% 5.12/5.32 thf(fact_2239_less__add__same__cancel1,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.12/5.32 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % less_add_same_cancel1
% 5.12/5.32 thf(fact_2240_add__less__same__cancel2,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel2
% 5.12/5.32 thf(fact_2241_add__less__same__cancel2,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel2
% 5.12/5.32 thf(fact_2242_add__less__same__cancel2,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel2
% 5.12/5.32 thf(fact_2243_add__less__same__cancel2,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.12/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel2
% 5.12/5.32 thf(fact_2244_add__less__same__cancel1,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel1
% 5.12/5.32 thf(fact_2245_add__less__same__cancel1,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel1
% 5.12/5.32 thf(fact_2246_add__less__same__cancel1,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel1
% 5.12/5.32 thf(fact_2247_add__less__same__cancel1,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.12/5.32 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.12/5.32
% 5.12/5.32 % add_less_same_cancel1
% 5.12/5.32 thf(fact_2248_le__add__diff__inverse2,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.32 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse2
% 5.12/5.32 thf(fact_2249_le__add__diff__inverse2,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.32 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse2
% 5.12/5.32 thf(fact_2250_le__add__diff__inverse2,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.12/5.32 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse2
% 5.12/5.32 thf(fact_2251_le__add__diff__inverse2,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.12/5.32 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse2
% 5.12/5.32 thf(fact_2252_le__add__diff__inverse,axiom,
% 5.12/5.32 ! [B: real,A: real] :
% 5.12/5.32 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.32 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse
% 5.12/5.32 thf(fact_2253_le__add__diff__inverse,axiom,
% 5.12/5.32 ! [B: rat,A: rat] :
% 5.12/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.32 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse
% 5.12/5.32 thf(fact_2254_le__add__diff__inverse,axiom,
% 5.12/5.32 ! [B: nat,A: nat] :
% 5.12/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.12/5.32 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse
% 5.12/5.32 thf(fact_2255_le__add__diff__inverse,axiom,
% 5.12/5.32 ! [B: int,A: int] :
% 5.12/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.12/5.32 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.12/5.32 = A ) ) ).
% 5.12/5.32
% 5.12/5.32 % le_add_diff_inverse
% 5.12/5.32 thf(fact_2256_diff__add__zero,axiom,
% 5.12/5.32 ! [A: nat,B: nat] :
% 5.12/5.32 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.32 = zero_zero_nat ) ).
% 5.12/5.32
% 5.12/5.32 % diff_add_zero
% 5.12/5.32 thf(fact_2257_add_Oright__inverse,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.12/5.32 = zero_zero_int ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_inverse
% 5.12/5.32 thf(fact_2258_add_Oright__inverse,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.12/5.32 = zero_zero_real ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_inverse
% 5.12/5.32 thf(fact_2259_add_Oright__inverse,axiom,
% 5.12/5.32 ! [A: complex] :
% 5.12/5.32 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.12/5.32 = zero_zero_complex ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_inverse
% 5.12/5.32 thf(fact_2260_add_Oright__inverse,axiom,
% 5.12/5.32 ! [A: code_integer] :
% 5.12/5.32 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.32 = zero_z3403309356797280102nteger ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_inverse
% 5.12/5.32 thf(fact_2261_add_Oright__inverse,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.12/5.32 = zero_zero_rat ) ).
% 5.12/5.32
% 5.12/5.32 % add.right_inverse
% 5.12/5.32 thf(fact_2262_ab__left__minus,axiom,
% 5.12/5.32 ! [A: int] :
% 5.12/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.12/5.32 = zero_zero_int ) ).
% 5.12/5.32
% 5.12/5.32 % ab_left_minus
% 5.12/5.32 thf(fact_2263_ab__left__minus,axiom,
% 5.12/5.32 ! [A: real] :
% 5.12/5.32 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.12/5.32 = zero_zero_real ) ).
% 5.12/5.32
% 5.12/5.32 % ab_left_minus
% 5.12/5.32 thf(fact_2264_ab__left__minus,axiom,
% 5.12/5.32 ! [A: complex] :
% 5.12/5.32 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.12/5.32 = zero_zero_complex ) ).
% 5.12/5.32
% 5.12/5.32 % ab_left_minus
% 5.12/5.32 thf(fact_2265_ab__left__minus,axiom,
% 5.12/5.32 ! [A: code_integer] :
% 5.12/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.12/5.32 = zero_z3403309356797280102nteger ) ).
% 5.12/5.32
% 5.12/5.32 % ab_left_minus
% 5.12/5.32 thf(fact_2266_ab__left__minus,axiom,
% 5.12/5.32 ! [A: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.12/5.32 = zero_zero_rat ) ).
% 5.12/5.32
% 5.12/5.32 % ab_left_minus
% 5.12/5.32 thf(fact_2267_diff__minus__eq__add,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.12/5.32 = ( plus_plus_int @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_minus_eq_add
% 5.12/5.32 thf(fact_2268_diff__minus__eq__add,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.12/5.32 = ( plus_plus_real @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_minus_eq_add
% 5.12/5.32 thf(fact_2269_diff__minus__eq__add,axiom,
% 5.12/5.32 ! [A: complex,B: complex] :
% 5.12/5.32 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.12/5.32 = ( plus_plus_complex @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_minus_eq_add
% 5.12/5.32 thf(fact_2270_diff__minus__eq__add,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.12/5.32 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_minus_eq_add
% 5.12/5.32 thf(fact_2271_diff__minus__eq__add,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.12/5.32 = ( plus_plus_rat @ A @ B ) ) ).
% 5.12/5.32
% 5.12/5.32 % diff_minus_eq_add
% 5.12/5.32 thf(fact_2272_uminus__add__conv__diff,axiom,
% 5.12/5.32 ! [A: int,B: int] :
% 5.12/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.32 = ( minus_minus_int @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % uminus_add_conv_diff
% 5.12/5.32 thf(fact_2273_uminus__add__conv__diff,axiom,
% 5.12/5.32 ! [A: real,B: real] :
% 5.12/5.32 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.12/5.32 = ( minus_minus_real @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % uminus_add_conv_diff
% 5.12/5.32 thf(fact_2274_uminus__add__conv__diff,axiom,
% 5.12/5.32 ! [A: complex,B: complex] :
% 5.12/5.32 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.12/5.32 = ( minus_minus_complex @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % uminus_add_conv_diff
% 5.12/5.32 thf(fact_2275_uminus__add__conv__diff,axiom,
% 5.12/5.32 ! [A: code_integer,B: code_integer] :
% 5.12/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.12/5.32 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.12/5.32
% 5.12/5.32 % uminus_add_conv_diff
% 5.12/5.32 thf(fact_2276_uminus__add__conv__diff,axiom,
% 5.12/5.32 ! [A: rat,B: rat] :
% 5.12/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.12/5.33 = ( minus_minus_rat @ B @ A ) ) ).
% 5.12/5.33
% 5.12/5.33 % uminus_add_conv_diff
% 5.12/5.33 thf(fact_2277_of__nat__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_add
% 5.12/5.33 thf(fact_2278_of__nat__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_add
% 5.12/5.33 thf(fact_2279_of__nat__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_add
% 5.12/5.33 thf(fact_2280_of__nat__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_add
% 5.12/5.33 thf(fact_2281_of__nat__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_add
% 5.12/5.33 thf(fact_2282_add__gr__0,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.33 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_gr_0
% 5.12/5.33 thf(fact_2283_powr__zero__eq__one,axiom,
% 5.12/5.33 ! [X: real] :
% 5.12/5.33 ( ( ( X = zero_zero_real )
% 5.12/5.33 => ( ( powr_real @ X @ zero_zero_real )
% 5.12/5.33 = zero_zero_real ) )
% 5.12/5.33 & ( ( X != zero_zero_real )
% 5.12/5.33 => ( ( powr_real @ X @ zero_zero_real )
% 5.12/5.33 = one_one_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_zero_eq_one
% 5.12/5.33 thf(fact_2284_Nat_Oadd__diff__assoc,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J2 @ K ) )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J2 ) @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.add_diff_assoc
% 5.12/5.33 thf(fact_2285_Nat_Oadd__diff__assoc2,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K ) @ I )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I ) @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.add_diff_assoc2
% 5.12/5.33 thf(fact_2286_Nat_Odiff__diff__right,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J2 @ K ) )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.diff_diff_right
% 5.12/5.33 thf(fact_2287_artanh__minus__real,axiom,
% 5.12/5.33 ! [X: real] :
% 5.12/5.33 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.33 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.33 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % artanh_minus_real
% 5.12/5.33 thf(fact_2288_powr__gt__zero,axiom,
% 5.12/5.33 ! [X: real,A: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 5.12/5.33 = ( X != zero_zero_real ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_gt_zero
% 5.12/5.33 thf(fact_2289_real__add__minus__iff,axiom,
% 5.12/5.33 ! [X: real,A: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.12/5.33 = zero_zero_real )
% 5.12/5.33 = ( X = A ) ) ).
% 5.12/5.33
% 5.12/5.33 % real_add_minus_iff
% 5.12/5.33 thf(fact_2290_powr__nonneg__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.12/5.33 = ( A = zero_zero_real ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_nonneg_iff
% 5.12/5.33 thf(fact_2291_powr__less__cancel__iff,axiom,
% 5.12/5.33 ! [X: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.12/5.33 = ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_less_cancel_iff
% 5.12/5.33 thf(fact_2292_log__one,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( log2 @ A @ one_one_real )
% 5.12/5.33 = zero_zero_real ) ).
% 5.12/5.33
% 5.12/5.33 % log_one
% 5.12/5.33 thf(fact_2293_add__neg__numeral__special_I7_J,axiom,
% 5.12/5.33 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.33 = zero_zero_int ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(7)
% 5.12/5.33 thf(fact_2294_add__neg__numeral__special_I7_J,axiom,
% 5.12/5.33 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.33 = zero_zero_real ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(7)
% 5.12/5.33 thf(fact_2295_add__neg__numeral__special_I7_J,axiom,
% 5.12/5.33 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.33 = zero_zero_complex ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(7)
% 5.12/5.33 thf(fact_2296_add__neg__numeral__special_I7_J,axiom,
% 5.12/5.33 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.33 = zero_z3403309356797280102nteger ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(7)
% 5.12/5.33 thf(fact_2297_add__neg__numeral__special_I7_J,axiom,
% 5.12/5.33 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.33 = zero_zero_rat ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(7)
% 5.12/5.33 thf(fact_2298_add__neg__numeral__special_I8_J,axiom,
% 5.12/5.33 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.12/5.33 = zero_zero_int ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(8)
% 5.12/5.33 thf(fact_2299_add__neg__numeral__special_I8_J,axiom,
% 5.12/5.33 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.12/5.33 = zero_zero_real ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(8)
% 5.12/5.33 thf(fact_2300_add__neg__numeral__special_I8_J,axiom,
% 5.12/5.33 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.12/5.33 = zero_zero_complex ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(8)
% 5.12/5.33 thf(fact_2301_add__neg__numeral__special_I8_J,axiom,
% 5.12/5.33 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.12/5.33 = zero_z3403309356797280102nteger ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(8)
% 5.12/5.33 thf(fact_2302_add__neg__numeral__special_I8_J,axiom,
% 5.12/5.33 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.12/5.33 = zero_zero_rat ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_numeral_special(8)
% 5.12/5.33 thf(fact_2303_of__nat__Suc,axiom,
% 5.12/5.33 ! [M2: nat] :
% 5.12/5.33 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 5.12/5.33 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_Suc
% 5.12/5.33 thf(fact_2304_of__nat__Suc,axiom,
% 5.12/5.33 ! [M2: nat] :
% 5.12/5.33 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 5.12/5.33 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_Suc
% 5.12/5.33 thf(fact_2305_of__nat__Suc,axiom,
% 5.12/5.33 ! [M2: nat] :
% 5.12/5.33 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 5.12/5.33 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_Suc
% 5.12/5.33 thf(fact_2306_of__nat__Suc,axiom,
% 5.12/5.33 ! [M2: nat] :
% 5.12/5.33 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 5.12/5.33 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_Suc
% 5.12/5.33 thf(fact_2307_of__nat__Suc,axiom,
% 5.12/5.33 ! [M2: nat] :
% 5.12/5.33 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 5.12/5.33 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % of_nat_Suc
% 5.12/5.33 thf(fact_2308_diff__Suc__diff__eq2,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K ) ) @ I )
% 5.12/5.33 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_Suc_diff_eq2
% 5.12/5.33 thf(fact_2309_diff__Suc__diff__eq1,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J2 @ K ) ) )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_Suc_diff_eq1
% 5.12/5.33 thf(fact_2310_powr__eq__one__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ( powr_real @ A @ X )
% 5.12/5.33 = one_one_real )
% 5.12/5.33 = ( X = zero_zero_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_eq_one_iff
% 5.12/5.33 thf(fact_2311_powr__one__gt__zero__iff,axiom,
% 5.12/5.33 ! [X: real] :
% 5.12/5.33 ( ( ( powr_real @ X @ one_one_real )
% 5.12/5.33 = X )
% 5.12/5.33 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_one_gt_zero_iff
% 5.12/5.33 thf(fact_2312_powr__one,axiom,
% 5.12/5.33 ! [X: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( powr_real @ X @ one_one_real )
% 5.12/5.33 = X ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_one
% 5.12/5.33 thf(fact_2313_powr__le__cancel__iff,axiom,
% 5.12/5.33 ! [X: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.12/5.33 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_le_cancel_iff
% 5.12/5.33 thf(fact_2314_log__eq__one,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( A != one_one_real )
% 5.12/5.33 => ( ( log2 @ A @ A )
% 5.12/5.33 = one_one_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_eq_one
% 5.12/5.33 thf(fact_2315_log__less__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.33 => ( ( ord_less_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) )
% 5.12/5.33 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_less_cancel_iff
% 5.12/5.33 thf(fact_2316_log__less__one__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ ( log2 @ A @ X ) @ one_one_real )
% 5.12/5.33 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_less_one_cancel_iff
% 5.12/5.33 thf(fact_2317_one__less__log__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ one_one_real @ ( log2 @ A @ X ) )
% 5.12/5.33 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % one_less_log_cancel_iff
% 5.12/5.33 thf(fact_2318_log__less__zero__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ ( log2 @ A @ X ) @ zero_zero_real )
% 5.12/5.33 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_less_zero_cancel_iff
% 5.12/5.33 thf(fact_2319_zero__less__log__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ ( log2 @ A @ X ) )
% 5.12/5.33 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % zero_less_log_cancel_iff
% 5.12/5.33 thf(fact_2320_zle__add1__eq__le,axiom,
% 5.12/5.33 ! [W: int,Z2: int] :
% 5.12/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 5.12/5.33 = ( ord_less_eq_int @ W @ Z2 ) ) ).
% 5.12/5.33
% 5.12/5.33 % zle_add1_eq_le
% 5.12/5.33 thf(fact_2321_zero__le__log__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ ( log2 @ A @ X ) )
% 5.12/5.33 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % zero_le_log_cancel_iff
% 5.12/5.33 thf(fact_2322_log__le__zero__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( log2 @ A @ X ) @ zero_zero_real )
% 5.12/5.33 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_le_zero_cancel_iff
% 5.12/5.33 thf(fact_2323_one__le__log__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ one_one_real @ ( log2 @ A @ X ) )
% 5.12/5.33 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % one_le_log_cancel_iff
% 5.12/5.33 thf(fact_2324_log__le__one__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( log2 @ A @ X ) @ one_one_real )
% 5.12/5.33 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_le_one_cancel_iff
% 5.12/5.33 thf(fact_2325_log__le__cancel__iff,axiom,
% 5.12/5.33 ! [A: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) )
% 5.12/5.33 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_le_cancel_iff
% 5.12/5.33 thf(fact_2326_log__powr__cancel,axiom,
% 5.12/5.33 ! [A: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( A != one_one_real )
% 5.12/5.33 => ( ( log2 @ A @ ( powr_real @ A @ Y ) )
% 5.12/5.33 = Y ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_powr_cancel
% 5.12/5.33 thf(fact_2327_powr__log__cancel,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( A != one_one_real )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( powr_real @ A @ ( log2 @ A @ X ) )
% 5.12/5.33 = X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_log_cancel
% 5.12/5.33 thf(fact_2328_log__pow__cancel,axiom,
% 5.12/5.33 ! [A: real,B: nat] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( A != one_one_real )
% 5.12/5.33 => ( ( log2 @ A @ ( power_power_real @ A @ B ) )
% 5.12/5.33 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_pow_cancel
% 5.12/5.33 thf(fact_2329_is__num__normalize_I1_J,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(1)
% 5.12/5.33 thf(fact_2330_is__num__normalize_I1_J,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(1)
% 5.12/5.33 thf(fact_2331_is__num__normalize_I1_J,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(1)
% 5.12/5.33 thf(fact_2332_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_semigroup_add_class.add_ac(1)
% 5.12/5.33 thf(fact_2333_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_semigroup_add_class.add_ac(1)
% 5.12/5.33 thf(fact_2334_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_semigroup_add_class.add_ac(1)
% 5.12/5.33 thf(fact_2335_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_semigroup_add_class.add_ac(1)
% 5.12/5.33 thf(fact_2336_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ( plus_plus_real @ I @ K )
% 5.12/5.33 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(4)
% 5.12/5.33 thf(fact_2337_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ( plus_plus_rat @ I @ K )
% 5.12/5.33 = ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(4)
% 5.12/5.33 thf(fact_2338_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ( plus_plus_nat @ I @ K )
% 5.12/5.33 = ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(4)
% 5.12/5.33 thf(fact_2339_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ( plus_plus_int @ I @ K )
% 5.12/5.33 = ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(4)
% 5.12/5.33 thf(fact_2340_group__cancel_Oadd1,axiom,
% 5.12/5.33 ! [A2: real,K: real,A: real,B: real] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_real @ K @ A ) )
% 5.12/5.33 => ( ( plus_plus_real @ A2 @ B )
% 5.12/5.33 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add1
% 5.12/5.33 thf(fact_2341_group__cancel_Oadd1,axiom,
% 5.12/5.33 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_rat @ K @ A ) )
% 5.12/5.33 => ( ( plus_plus_rat @ A2 @ B )
% 5.12/5.33 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add1
% 5.12/5.33 thf(fact_2342_group__cancel_Oadd1,axiom,
% 5.12/5.33 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_nat @ K @ A ) )
% 5.12/5.33 => ( ( plus_plus_nat @ A2 @ B )
% 5.12/5.33 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add1
% 5.12/5.33 thf(fact_2343_group__cancel_Oadd1,axiom,
% 5.12/5.33 ! [A2: int,K: int,A: int,B: int] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_int @ K @ A ) )
% 5.12/5.33 => ( ( plus_plus_int @ A2 @ B )
% 5.12/5.33 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add1
% 5.12/5.33 thf(fact_2344_group__cancel_Oadd2,axiom,
% 5.12/5.33 ! [B5: real,K: real,B: real,A: real] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_real @ K @ B ) )
% 5.12/5.33 => ( ( plus_plus_real @ A @ B5 )
% 5.12/5.33 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add2
% 5.12/5.33 thf(fact_2345_group__cancel_Oadd2,axiom,
% 5.12/5.33 ! [B5: rat,K: rat,B: rat,A: rat] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_rat @ K @ B ) )
% 5.12/5.33 => ( ( plus_plus_rat @ A @ B5 )
% 5.12/5.33 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add2
% 5.12/5.33 thf(fact_2346_group__cancel_Oadd2,axiom,
% 5.12/5.33 ! [B5: nat,K: nat,B: nat,A: nat] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_nat @ K @ B ) )
% 5.12/5.33 => ( ( plus_plus_nat @ A @ B5 )
% 5.12/5.33 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add2
% 5.12/5.33 thf(fact_2347_group__cancel_Oadd2,axiom,
% 5.12/5.33 ! [B5: int,K: int,B: int,A: int] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_int @ K @ B ) )
% 5.12/5.33 => ( ( plus_plus_int @ A @ B5 )
% 5.12/5.33 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.add2
% 5.12/5.33 thf(fact_2348_add_Oassoc,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.assoc
% 5.12/5.33 thf(fact_2349_add_Oassoc,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.assoc
% 5.12/5.33 thf(fact_2350_add_Oassoc,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.assoc
% 5.12/5.33 thf(fact_2351_add_Oassoc,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.assoc
% 5.12/5.33 thf(fact_2352_add_Oleft__cancel,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = ( plus_plus_real @ A @ C ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_cancel
% 5.12/5.33 thf(fact_2353_add_Oleft__cancel,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = ( plus_plus_rat @ A @ C ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_cancel
% 5.12/5.33 thf(fact_2354_add_Oleft__cancel,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = ( plus_plus_int @ A @ C ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_cancel
% 5.12/5.33 thf(fact_2355_add_Oright__cancel,axiom,
% 5.12/5.33 ! [B: real,A: real,C: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ B @ A )
% 5.12/5.33 = ( plus_plus_real @ C @ A ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.right_cancel
% 5.12/5.33 thf(fact_2356_add_Oright__cancel,axiom,
% 5.12/5.33 ! [B: rat,A: rat,C: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ B @ A )
% 5.12/5.33 = ( plus_plus_rat @ C @ A ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.right_cancel
% 5.12/5.33 thf(fact_2357_add_Oright__cancel,axiom,
% 5.12/5.33 ! [B: int,A: int,C: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ B @ A )
% 5.12/5.33 = ( plus_plus_int @ C @ A ) )
% 5.12/5.33 = ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.right_cancel
% 5.12/5.33 thf(fact_2358_add_Ocommute,axiom,
% 5.12/5.33 ( plus_plus_real
% 5.12/5.33 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.commute
% 5.12/5.33 thf(fact_2359_add_Ocommute,axiom,
% 5.12/5.33 ( plus_plus_rat
% 5.12/5.33 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.commute
% 5.12/5.33 thf(fact_2360_add_Ocommute,axiom,
% 5.12/5.33 ( plus_plus_nat
% 5.12/5.33 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.commute
% 5.12/5.33 thf(fact_2361_add_Ocommute,axiom,
% 5.12/5.33 ( plus_plus_int
% 5.12/5.33 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.commute
% 5.12/5.33 thf(fact_2362_add_Oleft__commute,axiom,
% 5.12/5.33 ! [B: real,A: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.12/5.33 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_commute
% 5.12/5.33 thf(fact_2363_add_Oleft__commute,axiom,
% 5.12/5.33 ! [B: rat,A: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.12/5.33 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_commute
% 5.12/5.33 thf(fact_2364_add_Oleft__commute,axiom,
% 5.12/5.33 ! [B: nat,A: nat,C: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.12/5.33 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_commute
% 5.12/5.33 thf(fact_2365_add_Oleft__commute,axiom,
% 5.12/5.33 ! [B: int,A: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.12/5.33 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.left_commute
% 5.12/5.33 thf(fact_2366_add__left__imp__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = ( plus_plus_real @ A @ C ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_imp_eq
% 5.12/5.33 thf(fact_2367_add__left__imp__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = ( plus_plus_rat @ A @ C ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_imp_eq
% 5.12/5.33 thf(fact_2368_add__left__imp__eq,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ( plus_plus_nat @ A @ B )
% 5.12/5.33 = ( plus_plus_nat @ A @ C ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_imp_eq
% 5.12/5.33 thf(fact_2369_add__left__imp__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = ( plus_plus_int @ A @ C ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_imp_eq
% 5.12/5.33 thf(fact_2370_add__right__imp__eq,axiom,
% 5.12/5.33 ! [B: real,A: real,C: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ B @ A )
% 5.12/5.33 = ( plus_plus_real @ C @ A ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_imp_eq
% 5.12/5.33 thf(fact_2371_add__right__imp__eq,axiom,
% 5.12/5.33 ! [B: rat,A: rat,C: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ B @ A )
% 5.12/5.33 = ( plus_plus_rat @ C @ A ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_imp_eq
% 5.12/5.33 thf(fact_2372_add__right__imp__eq,axiom,
% 5.12/5.33 ! [B: nat,A: nat,C: nat] :
% 5.12/5.33 ( ( ( plus_plus_nat @ B @ A )
% 5.12/5.33 = ( plus_plus_nat @ C @ A ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_imp_eq
% 5.12/5.33 thf(fact_2373_add__right__imp__eq,axiom,
% 5.12/5.33 ! [B: int,A: int,C: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ B @ A )
% 5.12/5.33 = ( plus_plus_int @ C @ A ) )
% 5.12/5.33 => ( B = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_imp_eq
% 5.12/5.33 thf(fact_2374_powr__powr__swap,axiom,
% 5.12/5.33 ! [X: real,A: real,B: real] :
% 5.12/5.33 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.12/5.33 = ( powr_real @ ( powr_real @ X @ B ) @ A ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_powr_swap
% 5.12/5.33 thf(fact_2375_zadd__int__left,axiom,
% 5.12/5.33 ! [M2: nat,N: nat,Z2: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z2 ) )
% 5.12/5.33 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) ) @ Z2 ) ) ).
% 5.12/5.33
% 5.12/5.33 % zadd_int_left
% 5.12/5.33 thf(fact_2376_int__plus,axiom,
% 5.12/5.33 ! [N: nat,M2: nat] :
% 5.12/5.33 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.33 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % int_plus
% 5.12/5.33 thf(fact_2377_int__ops_I5_J,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.33 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % int_ops(5)
% 5.12/5.33 thf(fact_2378_log__base__powr,axiom,
% 5.12/5.33 ! [A: real,B: real,X: real] :
% 5.12/5.33 ( ( A != zero_zero_real )
% 5.12/5.33 => ( ( log2 @ ( powr_real @ A @ B ) @ X )
% 5.12/5.33 = ( divide_divide_real @ ( log2 @ A @ X ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_base_powr
% 5.12/5.33 thf(fact_2379_nat__int__add,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.12/5.33 = ( plus_plus_nat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % nat_int_add
% 5.12/5.33 thf(fact_2380_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_eq_real @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(3)
% 5.12/5.33 thf(fact_2381_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_eq_rat @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(3)
% 5.12/5.33 thf(fact_2382_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(3)
% 5.12/5.33 thf(fact_2383_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(3)
% 5.12/5.33 thf(fact_2384_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_eq_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(2)
% 5.12/5.33 thf(fact_2385_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(2)
% 5.12/5.33 thf(fact_2386_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(2)
% 5.12/5.33 thf(fact_2387_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_eq_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(2)
% 5.12/5.33 thf(fact_2388_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_eq_real @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(1)
% 5.12/5.33 thf(fact_2389_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_eq_rat @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(1)
% 5.12/5.33 thf(fact_2390_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(1)
% 5.12/5.33 thf(fact_2391_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_semiring(1)
% 5.12/5.33 thf(fact_2392_add__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_real @ C @ D )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono
% 5.12/5.33 thf(fact_2393_add__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_rat @ C @ D )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono
% 5.12/5.33 thf(fact_2394_add__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_nat @ C @ D )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono
% 5.12/5.33 thf(fact_2395_add__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_int @ C @ D )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono
% 5.12/5.33 thf(fact_2396_add__left__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_mono
% 5.12/5.33 thf(fact_2397_add__left__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_mono
% 5.12/5.33 thf(fact_2398_add__left__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_mono
% 5.12/5.33 thf(fact_2399_add__left__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_left_mono
% 5.12/5.33 thf(fact_2400_less__eqE,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ~ ! [C2: nat] :
% 5.12/5.33 ( B
% 5.12/5.33 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_eqE
% 5.12/5.33 thf(fact_2401_add__right__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_mono
% 5.12/5.33 thf(fact_2402_add__right__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_mono
% 5.12/5.33 thf(fact_2403_add__right__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_mono
% 5.12/5.33 thf(fact_2404_add__right__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_right_mono
% 5.12/5.33 thf(fact_2405_le__iff__add,axiom,
% 5.12/5.33 ( ord_less_eq_nat
% 5.12/5.33 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.33 ? [C3: nat] :
% 5.12/5.33 ( B2
% 5.12/5.33 = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_iff_add
% 5.12/5.33 thf(fact_2406_add__le__imp__le__left,axiom,
% 5.12/5.33 ! [C: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.12/5.33 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_left
% 5.12/5.33 thf(fact_2407_add__le__imp__le__left,axiom,
% 5.12/5.33 ! [C: rat,A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.12/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_left
% 5.12/5.33 thf(fact_2408_add__le__imp__le__left,axiom,
% 5.12/5.33 ! [C: nat,A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.12/5.33 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_left
% 5.12/5.33 thf(fact_2409_add__le__imp__le__left,axiom,
% 5.12/5.33 ! [C: int,A: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.12/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_left
% 5.12/5.33 thf(fact_2410_add__le__imp__le__right,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.33 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_right
% 5.12/5.33 thf(fact_2411_add__le__imp__le__right,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_right
% 5.12/5.33 thf(fact_2412_add__le__imp__le__right,axiom,
% 5.12/5.33 ! [A: nat,C: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.33 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_right
% 5.12/5.33 thf(fact_2413_add__le__imp__le__right,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_right
% 5.12/5.33 thf(fact_2414_add_Ogroup__left__neutral,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.group_left_neutral
% 5.12/5.33 thf(fact_2415_add_Ogroup__left__neutral,axiom,
% 5.12/5.33 ! [A: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.group_left_neutral
% 5.12/5.33 thf(fact_2416_add_Ogroup__left__neutral,axiom,
% 5.12/5.33 ! [A: int] :
% 5.12/5.33 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.group_left_neutral
% 5.12/5.33 thf(fact_2417_add_Ocomm__neutral,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.comm_neutral
% 5.12/5.33 thf(fact_2418_add_Ocomm__neutral,axiom,
% 5.12/5.33 ! [A: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.comm_neutral
% 5.12/5.33 thf(fact_2419_add_Ocomm__neutral,axiom,
% 5.12/5.33 ! [A: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.comm_neutral
% 5.12/5.33 thf(fact_2420_add_Ocomm__neutral,axiom,
% 5.12/5.33 ! [A: int] :
% 5.12/5.33 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % add.comm_neutral
% 5.12/5.33 thf(fact_2421_comm__monoid__add__class_Oadd__0,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % comm_monoid_add_class.add_0
% 5.12/5.33 thf(fact_2422_comm__monoid__add__class_Oadd__0,axiom,
% 5.12/5.33 ! [A: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % comm_monoid_add_class.add_0
% 5.12/5.33 thf(fact_2423_comm__monoid__add__class_Oadd__0,axiom,
% 5.12/5.33 ! [A: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % comm_monoid_add_class.add_0
% 5.12/5.33 thf(fact_2424_comm__monoid__add__class_Oadd__0,axiom,
% 5.12/5.33 ! [A: int] :
% 5.12/5.33 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % comm_monoid_add_class.add_0
% 5.12/5.33 thf(fact_2425_verit__sum__simplify,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % verit_sum_simplify
% 5.12/5.33 thf(fact_2426_verit__sum__simplify,axiom,
% 5.12/5.33 ! [A: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % verit_sum_simplify
% 5.12/5.33 thf(fact_2427_verit__sum__simplify,axiom,
% 5.12/5.33 ! [A: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % verit_sum_simplify
% 5.12/5.33 thf(fact_2428_verit__sum__simplify,axiom,
% 5.12/5.33 ! [A: int] :
% 5.12/5.33 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.12/5.33 = A ) ).
% 5.12/5.33
% 5.12/5.33 % verit_sum_simplify
% 5.12/5.33 thf(fact_2429_add__less__imp__less__right,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.33 => ( ord_less_real @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_right
% 5.12/5.33 thf(fact_2430_add__less__imp__less__right,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.33 => ( ord_less_rat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_right
% 5.12/5.33 thf(fact_2431_add__less__imp__less__right,axiom,
% 5.12/5.33 ! [A: nat,C: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.33 => ( ord_less_nat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_right
% 5.12/5.33 thf(fact_2432_add__less__imp__less__right,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.33 => ( ord_less_int @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_right
% 5.12/5.33 thf(fact_2433_add__less__imp__less__left,axiom,
% 5.12/5.33 ! [C: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.12/5.33 => ( ord_less_real @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_left
% 5.12/5.33 thf(fact_2434_add__less__imp__less__left,axiom,
% 5.12/5.33 ! [C: rat,A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.12/5.33 => ( ord_less_rat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_left
% 5.12/5.33 thf(fact_2435_add__less__imp__less__left,axiom,
% 5.12/5.33 ! [C: nat,A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.12/5.33 => ( ord_less_nat @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_left
% 5.12/5.33 thf(fact_2436_add__less__imp__less__left,axiom,
% 5.12/5.33 ! [C: int,A: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.12/5.33 => ( ord_less_int @ A @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_imp_less_left
% 5.12/5.33 thf(fact_2437_add__strict__right__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_right_mono
% 5.12/5.33 thf(fact_2438_add__strict__right__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_right_mono
% 5.12/5.33 thf(fact_2439_add__strict__right__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_right_mono
% 5.12/5.33 thf(fact_2440_add__strict__right__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_right_mono
% 5.12/5.33 thf(fact_2441_add__strict__left__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_left_mono
% 5.12/5.33 thf(fact_2442_add__strict__left__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_left_mono
% 5.12/5.33 thf(fact_2443_add__strict__left__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_left_mono
% 5.12/5.33 thf(fact_2444_add__strict__left__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_left_mono
% 5.12/5.33 thf(fact_2445_add__strict__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_real @ C @ D )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_mono
% 5.12/5.33 thf(fact_2446_add__strict__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ( ord_less_rat @ C @ D )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_mono
% 5.12/5.33 thf(fact_2447_add__strict__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_nat @ C @ D )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_mono
% 5.12/5.33 thf(fact_2448_add__strict__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ( ord_less_int @ C @ D )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_strict_mono
% 5.12/5.33 thf(fact_2449_add__mono__thms__linordered__field_I1_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_real @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(1)
% 5.12/5.33 thf(fact_2450_add__mono__thms__linordered__field_I1_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_rat @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(1)
% 5.12/5.33 thf(fact_2451_add__mono__thms__linordered__field_I1_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(1)
% 5.12/5.33 thf(fact_2452_add__mono__thms__linordered__field_I1_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_int @ I @ J2 )
% 5.12/5.33 & ( K = L ) )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(1)
% 5.12/5.33 thf(fact_2453_add__mono__thms__linordered__field_I2_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(2)
% 5.12/5.33 thf(fact_2454_add__mono__thms__linordered__field_I2_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(2)
% 5.12/5.33 thf(fact_2455_add__mono__thms__linordered__field_I2_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(2)
% 5.12/5.33 thf(fact_2456_add__mono__thms__linordered__field_I2_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( I = J2 )
% 5.12/5.33 & ( ord_less_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(2)
% 5.12/5.33 thf(fact_2457_add__mono__thms__linordered__field_I5_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_real @ I @ J2 )
% 5.12/5.33 & ( ord_less_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(5)
% 5.12/5.33 thf(fact_2458_add__mono__thms__linordered__field_I5_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_rat @ I @ J2 )
% 5.12/5.33 & ( ord_less_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(5)
% 5.12/5.33 thf(fact_2459_add__mono__thms__linordered__field_I5_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 & ( ord_less_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(5)
% 5.12/5.33 thf(fact_2460_add__mono__thms__linordered__field_I5_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_int @ I @ J2 )
% 5.12/5.33 & ( ord_less_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(5)
% 5.12/5.33 thf(fact_2461_add__diff__add,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real,D: real] :
% 5.12/5.33 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.12/5.33 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_add
% 5.12/5.33 thf(fact_2462_add__diff__add,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.12/5.33 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.12/5.33 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_add
% 5.12/5.33 thf(fact_2463_add__diff__add,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int,D: int] :
% 5.12/5.33 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.12/5.33 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_add
% 5.12/5.33 thf(fact_2464_group__cancel_Osub1,axiom,
% 5.12/5.33 ! [A2: real,K: real,A: real,B: real] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_real @ K @ A ) )
% 5.12/5.33 => ( ( minus_minus_real @ A2 @ B )
% 5.12/5.33 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub1
% 5.12/5.33 thf(fact_2465_group__cancel_Osub1,axiom,
% 5.12/5.33 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_rat @ K @ A ) )
% 5.12/5.33 => ( ( minus_minus_rat @ A2 @ B )
% 5.12/5.33 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub1
% 5.12/5.33 thf(fact_2466_group__cancel_Osub1,axiom,
% 5.12/5.33 ! [A2: int,K: int,A: int,B: int] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_int @ K @ A ) )
% 5.12/5.33 => ( ( minus_minus_int @ A2 @ B )
% 5.12/5.33 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub1
% 5.12/5.33 thf(fact_2467_diff__eq__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ( minus_minus_real @ A @ B )
% 5.12/5.33 = C )
% 5.12/5.33 = ( A
% 5.12/5.33 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_eq_eq
% 5.12/5.33 thf(fact_2468_diff__eq__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ( minus_minus_rat @ A @ B )
% 5.12/5.33 = C )
% 5.12/5.33 = ( A
% 5.12/5.33 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_eq_eq
% 5.12/5.33 thf(fact_2469_diff__eq__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ( minus_minus_int @ A @ B )
% 5.12/5.33 = C )
% 5.12/5.33 = ( A
% 5.12/5.33 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_eq_eq
% 5.12/5.33 thf(fact_2470_eq__diff__eq,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( minus_minus_real @ C @ B ) )
% 5.12/5.33 = ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_diff_eq
% 5.12/5.33 thf(fact_2471_eq__diff__eq,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( minus_minus_rat @ C @ B ) )
% 5.12/5.33 = ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_diff_eq
% 5.12/5.33 thf(fact_2472_eq__diff__eq,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( minus_minus_int @ C @ B ) )
% 5.12/5.33 = ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = C ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_diff_eq
% 5.12/5.33 thf(fact_2473_add__diff__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.12/5.33 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_eq
% 5.12/5.33 thf(fact_2474_add__diff__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.12/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_eq
% 5.12/5.33 thf(fact_2475_add__diff__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.12/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_eq
% 5.12/5.33 thf(fact_2476_diff__diff__eq2,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.12/5.33 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq2
% 5.12/5.33 thf(fact_2477_diff__diff__eq2,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.12/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq2
% 5.12/5.33 thf(fact_2478_diff__diff__eq2,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.12/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq2
% 5.12/5.33 thf(fact_2479_diff__add__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq
% 5.12/5.33 thf(fact_2480_diff__add__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq
% 5.12/5.33 thf(fact_2481_diff__add__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq
% 5.12/5.33 thf(fact_2482_diff__add__eq__diff__diff__swap,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.12/5.33 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq_diff_diff_swap
% 5.12/5.33 thf(fact_2483_diff__add__eq__diff__diff__swap,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.33 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq_diff_diff_swap
% 5.12/5.33 thf(fact_2484_diff__add__eq__diff__diff__swap,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.12/5.33 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_eq_diff_diff_swap
% 5.12/5.33 thf(fact_2485_add__implies__diff,axiom,
% 5.12/5.33 ! [C: real,B: real,A: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ C @ B )
% 5.12/5.33 = A )
% 5.12/5.33 => ( C
% 5.12/5.33 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_implies_diff
% 5.12/5.33 thf(fact_2486_add__implies__diff,axiom,
% 5.12/5.33 ! [C: rat,B: rat,A: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ C @ B )
% 5.12/5.33 = A )
% 5.12/5.33 => ( C
% 5.12/5.33 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_implies_diff
% 5.12/5.33 thf(fact_2487_add__implies__diff,axiom,
% 5.12/5.33 ! [C: nat,B: nat,A: nat] :
% 5.12/5.33 ( ( ( plus_plus_nat @ C @ B )
% 5.12/5.33 = A )
% 5.12/5.33 => ( C
% 5.12/5.33 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_implies_diff
% 5.12/5.33 thf(fact_2488_add__implies__diff,axiom,
% 5.12/5.33 ! [C: int,B: int,A: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ C @ B )
% 5.12/5.33 = A )
% 5.12/5.33 => ( C
% 5.12/5.33 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_implies_diff
% 5.12/5.33 thf(fact_2489_diff__diff__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq
% 5.12/5.33 thf(fact_2490_diff__diff__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq
% 5.12/5.33 thf(fact_2491_diff__diff__eq,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq
% 5.12/5.33 thf(fact_2492_diff__diff__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.33 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_diff_eq
% 5.12/5.33 thf(fact_2493_add__divide__distrib,axiom,
% 5.12/5.33 ! [A: complex,B: complex,C: complex] :
% 5.12/5.33 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_divide_distrib
% 5.12/5.33 thf(fact_2494_add__divide__distrib,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_divide_distrib
% 5.12/5.33 thf(fact_2495_add__divide__distrib,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_divide_distrib
% 5.12/5.33 thf(fact_2496_is__num__normalize_I8_J,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.33 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(8)
% 5.12/5.33 thf(fact_2497_is__num__normalize_I8_J,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.12/5.33 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(8)
% 5.12/5.33 thf(fact_2498_is__num__normalize_I8_J,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.12/5.33 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(8)
% 5.12/5.33 thf(fact_2499_is__num__normalize_I8_J,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(8)
% 5.12/5.33 thf(fact_2500_is__num__normalize_I8_J,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.33 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % is_num_normalize(8)
% 5.12/5.33 thf(fact_2501_group__cancel_Oneg1,axiom,
% 5.12/5.33 ! [A2: int,K: int,A: int] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_int @ K @ A ) )
% 5.12/5.33 => ( ( uminus_uminus_int @ A2 )
% 5.12/5.33 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.neg1
% 5.12/5.33 thf(fact_2502_group__cancel_Oneg1,axiom,
% 5.12/5.33 ! [A2: real,K: real,A: real] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_real @ K @ A ) )
% 5.12/5.33 => ( ( uminus_uminus_real @ A2 )
% 5.12/5.33 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.neg1
% 5.12/5.33 thf(fact_2503_group__cancel_Oneg1,axiom,
% 5.12/5.33 ! [A2: complex,K: complex,A: complex] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_complex @ K @ A ) )
% 5.12/5.33 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.12/5.33 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.neg1
% 5.12/5.33 thf(fact_2504_group__cancel_Oneg1,axiom,
% 5.12/5.33 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.12/5.33 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.neg1
% 5.12/5.33 thf(fact_2505_group__cancel_Oneg1,axiom,
% 5.12/5.33 ! [A2: rat,K: rat,A: rat] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_rat @ K @ A ) )
% 5.12/5.33 => ( ( uminus_uminus_rat @ A2 )
% 5.12/5.33 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.neg1
% 5.12/5.33 thf(fact_2506_add_Oinverse__distrib__swap,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.33 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_distrib_swap
% 5.12/5.33 thf(fact_2507_add_Oinverse__distrib__swap,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.12/5.33 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_distrib_swap
% 5.12/5.33 thf(fact_2508_add_Oinverse__distrib__swap,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.12/5.33 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_distrib_swap
% 5.12/5.33 thf(fact_2509_add_Oinverse__distrib__swap,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_distrib_swap
% 5.12/5.33 thf(fact_2510_add_Oinverse__distrib__swap,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.33 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_distrib_swap
% 5.12/5.33 thf(fact_2511_nat__arith_Osuc1,axiom,
% 5.12/5.33 ! [A2: nat,K: nat,A: nat] :
% 5.12/5.33 ( ( A2
% 5.12/5.33 = ( plus_plus_nat @ K @ A ) )
% 5.12/5.33 => ( ( suc @ A2 )
% 5.12/5.33 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % nat_arith.suc1
% 5.12/5.33 thf(fact_2512_add__Suc,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 5.12/5.33 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_Suc
% 5.12/5.33 thf(fact_2513_add__Suc__shift,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 5.12/5.33 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_Suc_shift
% 5.12/5.33 thf(fact_2514_Euclid__induct,axiom,
% 5.12/5.33 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.12/5.33 ( ! [A4: nat,B3: nat] :
% 5.12/5.33 ( ( P @ A4 @ B3 )
% 5.12/5.33 = ( P @ B3 @ A4 ) )
% 5.12/5.33 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 5.12/5.33 => ( ! [A4: nat,B3: nat] :
% 5.12/5.33 ( ( P @ A4 @ B3 )
% 5.12/5.33 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
% 5.12/5.33 => ( P @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Euclid_induct
% 5.12/5.33 thf(fact_2515_add__eq__self__zero,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ( plus_plus_nat @ M2 @ N )
% 5.12/5.33 = M2 )
% 5.12/5.33 => ( N = zero_zero_nat ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_self_zero
% 5.12/5.33 thf(fact_2516_plus__nat_Oadd__0,axiom,
% 5.12/5.33 ! [N: nat] :
% 5.12/5.33 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.12/5.33 = N ) ).
% 5.12/5.33
% 5.12/5.33 % plus_nat.add_0
% 5.12/5.33 thf(fact_2517_less__add__eq__less,axiom,
% 5.12/5.33 ! [K: nat,L: nat,M2: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_nat @ K @ L )
% 5.12/5.33 => ( ( ( plus_plus_nat @ M2 @ L )
% 5.12/5.33 = ( plus_plus_nat @ K @ N ) )
% 5.12/5.33 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_eq_less
% 5.12/5.33 thf(fact_2518_trans__less__add2,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,M2: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % trans_less_add2
% 5.12/5.33 thf(fact_2519_trans__less__add1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,M2: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_nat @ I @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % trans_less_add1
% 5.12/5.33 thf(fact_2520_add__less__mono1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_mono1
% 5.12/5.33 thf(fact_2521_not__add__less2,axiom,
% 5.12/5.33 ! [J2: nat,I: nat] :
% 5.12/5.33 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I ) @ I ) ).
% 5.12/5.33
% 5.12/5.33 % not_add_less2
% 5.12/5.33 thf(fact_2522_not__add__less1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat] :
% 5.12/5.33 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J2 ) @ I ) ).
% 5.12/5.33
% 5.12/5.33 % not_add_less1
% 5.12/5.33 thf(fact_2523_add__less__mono,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 => ( ( ord_less_nat @ K @ L )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_mono
% 5.12/5.33 thf(fact_2524_add__lessD1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.33 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J2 ) @ K )
% 5.12/5.33 => ( ord_less_nat @ I @ K ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_lessD1
% 5.12/5.33 thf(fact_2525_plus__int__code_I1_J,axiom,
% 5.12/5.33 ! [K: int] :
% 5.12/5.33 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.12/5.33 = K ) ).
% 5.12/5.33
% 5.12/5.33 % plus_int_code(1)
% 5.12/5.33 thf(fact_2526_plus__int__code_I2_J,axiom,
% 5.12/5.33 ! [L: int] :
% 5.12/5.33 ( ( plus_plus_int @ zero_zero_int @ L )
% 5.12/5.33 = L ) ).
% 5.12/5.33
% 5.12/5.33 % plus_int_code(2)
% 5.12/5.33 thf(fact_2527_add__leE,axiom,
% 5.12/5.33 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 5.12/5.33 => ~ ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.33 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_leE
% 5.12/5.33 thf(fact_2528_le__add1,axiom,
% 5.12/5.33 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M2 ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_add1
% 5.12/5.33 thf(fact_2529_le__add2,axiom,
% 5.12/5.33 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M2 @ N ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_add2
% 5.12/5.33 thf(fact_2530_add__leD1,axiom,
% 5.12/5.33 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_leD1
% 5.12/5.33 thf(fact_2531_add__leD2,axiom,
% 5.12/5.33 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_leD2
% 5.12/5.33 thf(fact_2532_le__Suc__ex,axiom,
% 5.12/5.33 ! [K: nat,L: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ L )
% 5.12/5.33 => ? [N2: nat] :
% 5.12/5.33 ( L
% 5.12/5.33 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_Suc_ex
% 5.12/5.33 thf(fact_2533_add__le__mono,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 => ( ( ord_less_eq_nat @ K @ L )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_mono
% 5.12/5.33 thf(fact_2534_add__le__mono1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_mono1
% 5.12/5.33 thf(fact_2535_trans__le__add1,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,M2: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % trans_le_add1
% 5.12/5.33 thf(fact_2536_trans__le__add2,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,M2: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % trans_le_add2
% 5.12/5.33 thf(fact_2537_nat__le__iff__add,axiom,
% 5.12/5.33 ( ord_less_eq_nat
% 5.12/5.33 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.33 ? [K3: nat] :
% 5.12/5.33 ( N4
% 5.12/5.33 = ( plus_plus_nat @ M5 @ K3 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % nat_le_iff_add
% 5.12/5.33 thf(fact_2538_Nat_Odiff__cancel,axiom,
% 5.12/5.33 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 5.12/5.33 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.diff_cancel
% 5.12/5.33 thf(fact_2539_diff__cancel2,axiom,
% 5.12/5.33 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.33 = ( minus_minus_nat @ M2 @ N ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_cancel2
% 5.12/5.33 thf(fact_2540_diff__add__inverse,axiom,
% 5.12/5.33 ! [N: nat,M2: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M2 ) @ N )
% 5.12/5.33 = M2 ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_inverse
% 5.12/5.33 thf(fact_2541_diff__add__inverse2,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ N )
% 5.12/5.33 = M2 ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_inverse2
% 5.12/5.33 thf(fact_2542_less__log__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ Y @ ( log2 @ B @ X ) )
% 5.12/5.33 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_log_iff
% 5.12/5.33 thf(fact_2543_log__less__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ ( log2 @ B @ X ) @ Y )
% 5.12/5.33 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_less_iff
% 5.12/5.33 thf(fact_2544_less__powr__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 5.12/5.33 = ( ord_less_real @ ( log2 @ B @ X ) @ Y ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_powr_iff
% 5.12/5.33 thf(fact_2545_powr__less__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 5.12/5.33 = ( ord_less_real @ Y @ ( log2 @ B @ X ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_less_iff
% 5.12/5.33 thf(fact_2546_nat__add__distrib,axiom,
% 5.12/5.33 ! [Z2: int,Z3: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 5.12/5.33 => ( ( nat2 @ ( plus_plus_int @ Z2 @ Z3 ) )
% 5.12/5.33 = ( plus_plus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z3 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % nat_add_distrib
% 5.12/5.33 thf(fact_2547_nat__abs__triangle__ineq,axiom,
% 5.12/5.33 ! [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 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % nat_abs_triangle_ineq
% 5.12/5.33 thf(fact_2548_powr__le__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 5.12/5.33 = ( ord_less_eq_real @ Y @ ( log2 @ B @ X ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_le_iff
% 5.12/5.33 thf(fact_2549_le__powr__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 5.12/5.33 = ( ord_less_eq_real @ ( log2 @ B @ X ) @ Y ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_powr_iff
% 5.12/5.33 thf(fact_2550_log__le__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( log2 @ B @ X ) @ Y )
% 5.12/5.33 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_le_iff
% 5.12/5.33 thf(fact_2551_le__log__iff,axiom,
% 5.12/5.33 ! [B: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ Y @ ( log2 @ B @ X ) )
% 5.12/5.33 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_log_iff
% 5.12/5.33 thf(fact_2552_powr__non__neg,axiom,
% 5.12/5.33 ! [A: real,X: real] :
% 5.12/5.33 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 5.12/5.33
% 5.12/5.33 % powr_non_neg
% 5.12/5.33 thf(fact_2553_powr__less__mono2__neg,axiom,
% 5.12/5.33 ! [A: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_real @ X @ Y )
% 5.12/5.33 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_less_mono2_neg
% 5.12/5.33 thf(fact_2554_powr__ge__pzero,axiom,
% 5.12/5.33 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_ge_pzero
% 5.12/5.33 thf(fact_2555_powr__mono2,axiom,
% 5.12/5.33 ! [A: real,X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.33 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_mono2
% 5.12/5.33 thf(fact_2556_powr__less__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,X: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.33 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_less_mono
% 5.12/5.33 thf(fact_2557_powr__less__cancel,axiom,
% 5.12/5.33 ! [X: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.12/5.33 => ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.33 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_less_cancel
% 5.12/5.33 thf(fact_2558_powr__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,X: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.33 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % powr_mono
% 5.12/5.33 thf(fact_2559_add__decreasing,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_eq_real @ C @ B )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing
% 5.12/5.33 thf(fact_2560_add__decreasing,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_eq_rat @ C @ B )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing
% 5.12/5.33 thf(fact_2561_add__decreasing,axiom,
% 5.12/5.33 ! [A: nat,C: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.12/5.33 => ( ( ord_less_eq_nat @ C @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing
% 5.12/5.33 thf(fact_2562_add__decreasing,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_eq_int @ C @ B )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing
% 5.12/5.33 thf(fact_2563_add__increasing,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( ord_less_eq_real @ B @ C )
% 5.12/5.33 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing
% 5.12/5.33 thf(fact_2564_add__increasing,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.33 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.33 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing
% 5.12/5.33 thf(fact_2565_add__increasing,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.33 => ( ( ord_less_eq_nat @ B @ C )
% 5.12/5.33 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing
% 5.12/5.33 thf(fact_2566_add__increasing,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.33 => ( ( ord_less_eq_int @ B @ C )
% 5.12/5.33 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing
% 5.12/5.33 thf(fact_2567_add__decreasing2,axiom,
% 5.12/5.33 ! [C: real,A: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing2
% 5.12/5.33 thf(fact_2568_add__decreasing2,axiom,
% 5.12/5.33 ! [C: rat,A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing2
% 5.12/5.33 thf(fact_2569_add__decreasing2,axiom,
% 5.12/5.33 ! [C: nat,A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.12/5.33 => ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing2
% 5.12/5.33 thf(fact_2570_add__decreasing2,axiom,
% 5.12/5.33 ! [C: int,A: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_eq_int @ A @ B )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_decreasing2
% 5.12/5.33 thf(fact_2571_add__increasing2,axiom,
% 5.12/5.33 ! [C: real,B: real,A: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.33 => ( ( ord_less_eq_real @ B @ A )
% 5.12/5.33 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing2
% 5.12/5.33 thf(fact_2572_add__increasing2,axiom,
% 5.12/5.33 ! [C: rat,B: rat,A: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.33 => ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.33 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing2
% 5.12/5.33 thf(fact_2573_add__increasing2,axiom,
% 5.12/5.33 ! [C: nat,B: nat,A: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.33 => ( ( ord_less_eq_nat @ B @ A )
% 5.12/5.33 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing2
% 5.12/5.33 thf(fact_2574_add__increasing2,axiom,
% 5.12/5.33 ! [C: int,B: int,A: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.33 => ( ( ord_less_eq_int @ B @ A )
% 5.12/5.33 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_increasing2
% 5.12/5.33 thf(fact_2575_add__nonneg__nonneg,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_nonneg
% 5.12/5.33 thf(fact_2576_add__nonneg__nonneg,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.33 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_nonneg
% 5.12/5.33 thf(fact_2577_add__nonneg__nonneg,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_nonneg
% 5.12/5.33 thf(fact_2578_add__nonneg__nonneg,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_nonneg
% 5.12/5.33 thf(fact_2579_add__nonpos__nonpos,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.12/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_nonpos
% 5.12/5.33 thf(fact_2580_add__nonpos__nonpos,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.12/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_nonpos
% 5.12/5.33 thf(fact_2581_add__nonpos__nonpos,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.12/5.33 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_nonpos
% 5.12/5.33 thf(fact_2582_add__nonpos__nonpos,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_nonpos
% 5.12/5.33 thf(fact_2583_add__nonneg__eq__0__iff,axiom,
% 5.12/5.33 ! [X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.33 => ( ( ( plus_plus_real @ X @ Y )
% 5.12/5.33 = zero_zero_real )
% 5.12/5.33 = ( ( X = zero_zero_real )
% 5.12/5.33 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_eq_0_iff
% 5.12/5.33 thf(fact_2584_add__nonneg__eq__0__iff,axiom,
% 5.12/5.33 ! [X: rat,Y: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.33 => ( ( ( plus_plus_rat @ X @ Y )
% 5.12/5.33 = zero_zero_rat )
% 5.12/5.33 = ( ( X = zero_zero_rat )
% 5.12/5.33 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_eq_0_iff
% 5.12/5.33 thf(fact_2585_add__nonneg__eq__0__iff,axiom,
% 5.12/5.33 ! [X: nat,Y: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.12/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.12/5.33 => ( ( ( plus_plus_nat @ X @ Y )
% 5.12/5.33 = zero_zero_nat )
% 5.12/5.33 = ( ( X = zero_zero_nat )
% 5.12/5.33 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_eq_0_iff
% 5.12/5.33 thf(fact_2586_add__nonneg__eq__0__iff,axiom,
% 5.12/5.33 ! [X: int,Y: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.33 => ( ( ( plus_plus_int @ X @ Y )
% 5.12/5.33 = zero_zero_int )
% 5.12/5.33 = ( ( X = zero_zero_int )
% 5.12/5.33 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonneg_eq_0_iff
% 5.12/5.33 thf(fact_2587_add__nonpos__eq__0__iff,axiom,
% 5.12/5.33 ! [X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.12/5.33 => ( ( ( plus_plus_real @ X @ Y )
% 5.12/5.33 = zero_zero_real )
% 5.12/5.33 = ( ( X = zero_zero_real )
% 5.12/5.33 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_eq_0_iff
% 5.12/5.33 thf(fact_2588_add__nonpos__eq__0__iff,axiom,
% 5.12/5.33 ! [X: rat,Y: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.12/5.33 => ( ( ( plus_plus_rat @ X @ Y )
% 5.12/5.33 = zero_zero_rat )
% 5.12/5.33 = ( ( X = zero_zero_rat )
% 5.12/5.33 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_eq_0_iff
% 5.12/5.33 thf(fact_2589_add__nonpos__eq__0__iff,axiom,
% 5.12/5.33 ! [X: nat,Y: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.12/5.33 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.12/5.33 => ( ( ( plus_plus_nat @ X @ Y )
% 5.12/5.33 = zero_zero_nat )
% 5.12/5.33 = ( ( X = zero_zero_nat )
% 5.12/5.33 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_eq_0_iff
% 5.12/5.33 thf(fact_2590_add__nonpos__eq__0__iff,axiom,
% 5.12/5.33 ! [X: int,Y: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.12/5.33 => ( ( ( plus_plus_int @ X @ Y )
% 5.12/5.33 = zero_zero_int )
% 5.12/5.33 = ( ( X = zero_zero_int )
% 5.12/5.33 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_nonpos_eq_0_iff
% 5.12/5.33 thf(fact_2591_add__mono__thms__linordered__field_I4_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_eq_real @ I @ J2 )
% 5.12/5.33 & ( ord_less_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(4)
% 5.12/5.33 thf(fact_2592_add__mono__thms__linordered__field_I4_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_eq_rat @ I @ J2 )
% 5.12/5.33 & ( ord_less_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(4)
% 5.12/5.33 thf(fact_2593_add__mono__thms__linordered__field_I4_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 & ( ord_less_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(4)
% 5.12/5.33 thf(fact_2594_add__mono__thms__linordered__field_I4_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.33 & ( ord_less_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(4)
% 5.12/5.33 thf(fact_2595_add__mono__thms__linordered__field_I3_J,axiom,
% 5.12/5.33 ! [I: real,J2: real,K: real,L: real] :
% 5.12/5.33 ( ( ( ord_less_real @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_real @ K @ L ) )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(3)
% 5.12/5.33 thf(fact_2596_add__mono__thms__linordered__field_I3_J,axiom,
% 5.12/5.33 ! [I: rat,J2: rat,K: rat,L: rat] :
% 5.12/5.33 ( ( ( ord_less_rat @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_rat @ K @ L ) )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(3)
% 5.12/5.33 thf(fact_2597_add__mono__thms__linordered__field_I3_J,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.33 ( ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_nat @ K @ L ) )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(3)
% 5.12/5.33 thf(fact_2598_add__mono__thms__linordered__field_I3_J,axiom,
% 5.12/5.33 ! [I: int,J2: int,K: int,L: int] :
% 5.12/5.33 ( ( ( ord_less_int @ I @ J2 )
% 5.12/5.33 & ( ord_less_eq_int @ K @ L ) )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono_thms_linordered_field(3)
% 5.12/5.33 thf(fact_2599_add__le__less__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_real @ C @ D )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_less_mono
% 5.12/5.33 thf(fact_2600_add__le__less__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.33 => ( ( ord_less_rat @ C @ D )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_less_mono
% 5.12/5.33 thf(fact_2601_add__le__less__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_nat @ C @ D )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_less_mono
% 5.12/5.33 thf(fact_2602_add__le__less__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.33 => ( ( ord_less_int @ C @ D )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_less_mono
% 5.12/5.33 thf(fact_2603_add__less__le__mono,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_real @ C @ D )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_le_mono
% 5.12/5.33 thf(fact_2604_add__less__le__mono,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_rat @ C @ D )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_le_mono
% 5.12/5.33 thf(fact_2605_add__less__le__mono,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_nat @ C @ D )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_le_mono
% 5.12/5.33 thf(fact_2606_add__less__le__mono,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_int @ C @ D )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_le_mono
% 5.12/5.33 thf(fact_2607_add__less__zeroD,axiom,
% 5.12/5.33 ! [X: real,Y: real] :
% 5.12/5.33 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.33 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_zeroD
% 5.12/5.33 thf(fact_2608_add__less__zeroD,axiom,
% 5.12/5.33 ! [X: rat,Y: rat] :
% 5.12/5.33 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.12/5.33 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_zeroD
% 5.12/5.33 thf(fact_2609_add__less__zeroD,axiom,
% 5.12/5.33 ! [X: int,Y: int] :
% 5.12/5.33 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.12/5.33 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_less_zeroD
% 5.12/5.33 thf(fact_2610_pos__add__strict,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ B @ C )
% 5.12/5.33 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % pos_add_strict
% 5.12/5.33 thf(fact_2611_pos__add__strict,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.33 => ( ( ord_less_rat @ B @ C )
% 5.12/5.33 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % pos_add_strict
% 5.12/5.33 thf(fact_2612_pos__add__strict,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.33 => ( ( ord_less_nat @ B @ C )
% 5.12/5.33 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % pos_add_strict
% 5.12/5.33 thf(fact_2613_pos__add__strict,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.33 => ( ( ord_less_int @ B @ C )
% 5.12/5.33 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % pos_add_strict
% 5.12/5.33 thf(fact_2614_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ~ ! [C2: nat] :
% 5.12/5.33 ( ( B
% 5.12/5.33 = ( plus_plus_nat @ A @ C2 ) )
% 5.12/5.33 => ( C2 = zero_zero_nat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % canonically_ordered_monoid_add_class.lessE
% 5.12/5.33 thf(fact_2615_add__pos__pos,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.33 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.33 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_pos_pos
% 5.12/5.33 thf(fact_2616_add__pos__pos,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.33 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.33 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_pos_pos
% 5.12/5.33 thf(fact_2617_add__pos__pos,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.33 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.33 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_pos_pos
% 5.12/5.33 thf(fact_2618_add__pos__pos,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.33 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.33 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_pos_pos
% 5.12/5.33 thf(fact_2619_add__neg__neg,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.33 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_neg
% 5.12/5.33 thf(fact_2620_add__neg__neg,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.33 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_neg
% 5.12/5.33 thf(fact_2621_add__neg__neg,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.12/5.33 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_neg
% 5.12/5.33 thf(fact_2622_add__neg__neg,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.33 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_neg_neg
% 5.12/5.33 thf(fact_2623_log__def,axiom,
% 5.12/5.33 ( log2
% 5.12/5.33 = ( ^ [A3: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % log_def
% 5.12/5.33 thf(fact_2624_add__le__add__imp__diff__le,axiom,
% 5.12/5.33 ! [I: real,K: real,N: real,J2: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K ) )
% 5.12/5.33 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K ) )
% 5.12/5.33 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_add_imp_diff_le
% 5.12/5.33 thf(fact_2625_add__le__add__imp__diff__le,axiom,
% 5.12/5.33 ! [I: rat,K: rat,N: rat,J2: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K ) )
% 5.12/5.33 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K ) )
% 5.12/5.33 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_add_imp_diff_le
% 5.12/5.33 thf(fact_2626_add__le__add__imp__diff__le,axiom,
% 5.12/5.33 ! [I: nat,K: nat,N: nat,J2: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K ) )
% 5.12/5.33 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K ) )
% 5.12/5.33 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_add_imp_diff_le
% 5.12/5.33 thf(fact_2627_add__le__add__imp__diff__le,axiom,
% 5.12/5.33 ! [I: int,K: int,N: int,J2: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K ) )
% 5.12/5.33 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.12/5.33 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K ) )
% 5.12/5.33 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J2 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_add_imp_diff_le
% 5.12/5.33 thf(fact_2628_add__le__imp__le__diff,axiom,
% 5.12/5.33 ! [I: real,K: real,N: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_diff
% 5.12/5.33 thf(fact_2629_add__le__imp__le__diff,axiom,
% 5.12/5.33 ! [I: rat,K: rat,N: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_diff
% 5.12/5.33 thf(fact_2630_add__le__imp__le__diff,axiom,
% 5.12/5.33 ! [I: nat,K: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_diff
% 5.12/5.33 thf(fact_2631_add__le__imp__le__diff,axiom,
% 5.12/5.33 ! [I: int,K: int,N: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.12/5.33 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_le_imp_le_diff
% 5.12/5.33 thf(fact_2632_diff__le__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_le_eq
% 5.12/5.33 thf(fact_2633_diff__le__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_le_eq
% 5.12/5.33 thf(fact_2634_diff__le__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_le_eq
% 5.12/5.33 thf(fact_2635_le__diff__eq,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.12/5.33 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_diff_eq
% 5.12/5.33 thf(fact_2636_le__diff__eq,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.12/5.33 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_diff_eq
% 5.12/5.33 thf(fact_2637_le__diff__eq,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.12/5.33 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_diff_eq
% 5.12/5.33 thf(fact_2638_diff__add,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add
% 5.12/5.33 thf(fact_2639_le__add__diff,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_add_diff
% 5.12/5.33 thf(fact_2640_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.12/5.33 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.12/5.33 thf(fact_2641_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.12/5.33 thf(fact_2642_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.12/5.33 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.12/5.33 thf(fact_2643_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.12/5.33 thf(fact_2644_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.12/5.33 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.12/5.33 thf(fact_2645_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.12/5.33 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.12/5.33 thf(fact_2646_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.12/5.33 thf(fact_2647_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.33 => ( ( ( minus_minus_nat @ B @ A )
% 5.12/5.33 = C )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.12/5.33 thf(fact_2648_add__mono1,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono1
% 5.12/5.33 thf(fact_2649_add__mono1,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono1
% 5.12/5.33 thf(fact_2650_add__mono1,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono1
% 5.12/5.33 thf(fact_2651_add__mono1,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_mono1
% 5.12/5.33 thf(fact_2652_less__add__one,axiom,
% 5.12/5.33 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_one
% 5.12/5.33 thf(fact_2653_less__add__one,axiom,
% 5.12/5.33 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_one
% 5.12/5.33 thf(fact_2654_less__add__one,axiom,
% 5.12/5.33 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_one
% 5.12/5.33 thf(fact_2655_less__add__one,axiom,
% 5.12/5.33 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_one
% 5.12/5.33 thf(fact_2656_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ~ ( ord_less_real @ A @ B )
% 5.12/5.33 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.12/5.33 = A ) ) ).
% 5.12/5.33
% 5.12/5.33 % linordered_semidom_class.add_diff_inverse
% 5.12/5.33 thf(fact_2657_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ~ ( ord_less_rat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.12/5.33 = A ) ) ).
% 5.12/5.33
% 5.12/5.33 % linordered_semidom_class.add_diff_inverse
% 5.12/5.33 thf(fact_2658_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.12/5.33 ! [A: nat,B: nat] :
% 5.12/5.33 ( ~ ( ord_less_nat @ A @ B )
% 5.12/5.33 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.12/5.33 = A ) ) ).
% 5.12/5.33
% 5.12/5.33 % linordered_semidom_class.add_diff_inverse
% 5.12/5.33 thf(fact_2659_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ~ ( ord_less_int @ A @ B )
% 5.12/5.33 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.12/5.33 = A ) ) ).
% 5.12/5.33
% 5.12/5.33 % linordered_semidom_class.add_diff_inverse
% 5.12/5.33 thf(fact_2660_diff__less__eq,axiom,
% 5.12/5.33 ! [A: real,B: real,C: real] :
% 5.12/5.33 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_less_eq
% 5.12/5.33 thf(fact_2661_diff__less__eq,axiom,
% 5.12/5.33 ! [A: rat,B: rat,C: rat] :
% 5.12/5.33 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_less_eq
% 5.12/5.33 thf(fact_2662_diff__less__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.33 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_less_eq
% 5.12/5.33 thf(fact_2663_less__diff__eq,axiom,
% 5.12/5.33 ! [A: real,C: real,B: real] :
% 5.12/5.33 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.12/5.33 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_diff_eq
% 5.12/5.33 thf(fact_2664_less__diff__eq,axiom,
% 5.12/5.33 ! [A: rat,C: rat,B: rat] :
% 5.12/5.33 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.12/5.33 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_diff_eq
% 5.12/5.33 thf(fact_2665_less__diff__eq,axiom,
% 5.12/5.33 ! [A: int,C: int,B: int] :
% 5.12/5.33 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.12/5.33 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_diff_eq
% 5.12/5.33 thf(fact_2666_add__eq__0__iff,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = zero_zero_int )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( uminus_uminus_int @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_0_iff
% 5.12/5.33 thf(fact_2667_add__eq__0__iff,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = zero_zero_real )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_0_iff
% 5.12/5.33 thf(fact_2668_add__eq__0__iff,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( ( plus_plus_complex @ A @ B )
% 5.12/5.33 = zero_zero_complex )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_0_iff
% 5.12/5.33 thf(fact_2669_add__eq__0__iff,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.12/5.33 = zero_z3403309356797280102nteger )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_0_iff
% 5.12/5.33 thf(fact_2670_add__eq__0__iff,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = zero_zero_rat )
% 5.12/5.33 = ( B
% 5.12/5.33 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_eq_0_iff
% 5.12/5.33 thf(fact_2671_ab__group__add__class_Oab__left__minus,axiom,
% 5.12/5.33 ! [A: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.12/5.33 = zero_zero_int ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_left_minus
% 5.12/5.33 thf(fact_2672_ab__group__add__class_Oab__left__minus,axiom,
% 5.12/5.33 ! [A: real] :
% 5.12/5.33 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.12/5.33 = zero_zero_real ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_left_minus
% 5.12/5.33 thf(fact_2673_ab__group__add__class_Oab__left__minus,axiom,
% 5.12/5.33 ! [A: complex] :
% 5.12/5.33 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.12/5.33 = zero_zero_complex ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_left_minus
% 5.12/5.33 thf(fact_2674_ab__group__add__class_Oab__left__minus,axiom,
% 5.12/5.33 ! [A: code_integer] :
% 5.12/5.33 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.12/5.33 = zero_z3403309356797280102nteger ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_left_minus
% 5.12/5.33 thf(fact_2675_ab__group__add__class_Oab__left__minus,axiom,
% 5.12/5.33 ! [A: rat] :
% 5.12/5.33 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.12/5.33 = zero_zero_rat ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_left_minus
% 5.12/5.33 thf(fact_2676_add_Oinverse__unique,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = zero_zero_int )
% 5.12/5.33 => ( ( uminus_uminus_int @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_unique
% 5.12/5.33 thf(fact_2677_add_Oinverse__unique,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = zero_zero_real )
% 5.12/5.33 => ( ( uminus_uminus_real @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_unique
% 5.12/5.33 thf(fact_2678_add_Oinverse__unique,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( ( plus_plus_complex @ A @ B )
% 5.12/5.33 = zero_zero_complex )
% 5.12/5.33 => ( ( uminus1482373934393186551omplex @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_unique
% 5.12/5.33 thf(fact_2679_add_Oinverse__unique,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.12/5.33 = zero_z3403309356797280102nteger )
% 5.12/5.33 => ( ( uminus1351360451143612070nteger @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_unique
% 5.12/5.33 thf(fact_2680_add_Oinverse__unique,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = zero_zero_rat )
% 5.12/5.33 => ( ( uminus_uminus_rat @ A )
% 5.12/5.33 = B ) ) ).
% 5.12/5.33
% 5.12/5.33 % add.inverse_unique
% 5.12/5.33 thf(fact_2681_eq__neg__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( uminus_uminus_int @ B ) )
% 5.12/5.33 = ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = zero_zero_int ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_neg_iff_add_eq_0
% 5.12/5.33 thf(fact_2682_eq__neg__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( uminus_uminus_real @ B ) )
% 5.12/5.33 = ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = zero_zero_real ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_neg_iff_add_eq_0
% 5.12/5.33 thf(fact_2683_eq__neg__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( uminus1482373934393186551omplex @ B ) )
% 5.12/5.33 = ( ( plus_plus_complex @ A @ B )
% 5.12/5.33 = zero_zero_complex ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_neg_iff_add_eq_0
% 5.12/5.33 thf(fact_2684_eq__neg__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( uminus1351360451143612070nteger @ B ) )
% 5.12/5.33 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.12/5.33 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_neg_iff_add_eq_0
% 5.12/5.33 thf(fact_2685_eq__neg__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( A
% 5.12/5.33 = ( uminus_uminus_rat @ B ) )
% 5.12/5.33 = ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = zero_zero_rat ) ) ).
% 5.12/5.33
% 5.12/5.33 % eq_neg_iff_add_eq_0
% 5.12/5.33 thf(fact_2686_neg__eq__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: int,B: int] :
% 5.12/5.33 ( ( ( uminus_uminus_int @ A )
% 5.12/5.33 = B )
% 5.12/5.33 = ( ( plus_plus_int @ A @ B )
% 5.12/5.33 = zero_zero_int ) ) ).
% 5.12/5.33
% 5.12/5.33 % neg_eq_iff_add_eq_0
% 5.12/5.33 thf(fact_2687_neg__eq__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: real,B: real] :
% 5.12/5.33 ( ( ( uminus_uminus_real @ A )
% 5.12/5.33 = B )
% 5.12/5.33 = ( ( plus_plus_real @ A @ B )
% 5.12/5.33 = zero_zero_real ) ) ).
% 5.12/5.33
% 5.12/5.33 % neg_eq_iff_add_eq_0
% 5.12/5.33 thf(fact_2688_neg__eq__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: complex,B: complex] :
% 5.12/5.33 ( ( ( uminus1482373934393186551omplex @ A )
% 5.12/5.33 = B )
% 5.12/5.33 = ( ( plus_plus_complex @ A @ B )
% 5.12/5.33 = zero_zero_complex ) ) ).
% 5.12/5.33
% 5.12/5.33 % neg_eq_iff_add_eq_0
% 5.12/5.33 thf(fact_2689_neg__eq__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] :
% 5.12/5.33 ( ( ( uminus1351360451143612070nteger @ A )
% 5.12/5.33 = B )
% 5.12/5.33 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.12/5.33 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.33
% 5.12/5.33 % neg_eq_iff_add_eq_0
% 5.12/5.33 thf(fact_2690_neg__eq__iff__add__eq__0,axiom,
% 5.12/5.33 ! [A: rat,B: rat] :
% 5.12/5.33 ( ( ( uminus_uminus_rat @ A )
% 5.12/5.33 = B )
% 5.12/5.33 = ( ( plus_plus_rat @ A @ B )
% 5.12/5.33 = zero_zero_rat ) ) ).
% 5.12/5.33
% 5.12/5.33 % neg_eq_iff_add_eq_0
% 5.12/5.33 thf(fact_2691_group__cancel_Osub2,axiom,
% 5.12/5.33 ! [B5: int,K: int,B: int,A: int] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_int @ K @ B ) )
% 5.12/5.33 => ( ( minus_minus_int @ A @ B5 )
% 5.12/5.33 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub2
% 5.12/5.33 thf(fact_2692_group__cancel_Osub2,axiom,
% 5.12/5.33 ! [B5: real,K: real,B: real,A: real] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_real @ K @ B ) )
% 5.12/5.33 => ( ( minus_minus_real @ A @ B5 )
% 5.12/5.33 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub2
% 5.12/5.33 thf(fact_2693_group__cancel_Osub2,axiom,
% 5.12/5.33 ! [B5: complex,K: complex,B: complex,A: complex] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_complex @ K @ B ) )
% 5.12/5.33 => ( ( minus_minus_complex @ A @ B5 )
% 5.12/5.33 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub2
% 5.12/5.33 thf(fact_2694_group__cancel_Osub2,axiom,
% 5.12/5.33 ! [B5: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.12/5.33 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub2
% 5.12/5.33 thf(fact_2695_group__cancel_Osub2,axiom,
% 5.12/5.33 ! [B5: rat,K: rat,B: rat,A: rat] :
% 5.12/5.33 ( ( B5
% 5.12/5.33 = ( plus_plus_rat @ K @ B ) )
% 5.12/5.33 => ( ( minus_minus_rat @ A @ B5 )
% 5.12/5.33 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % group_cancel.sub2
% 5.12/5.33 thf(fact_2696_diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_int
% 5.12/5.33 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_conv_add_uminus
% 5.12/5.33 thf(fact_2697_diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_real
% 5.12/5.33 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_conv_add_uminus
% 5.12/5.33 thf(fact_2698_diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_complex
% 5.12/5.33 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_conv_add_uminus
% 5.12/5.33 thf(fact_2699_diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_8373710615458151222nteger
% 5.12/5.33 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_conv_add_uminus
% 5.12/5.33 thf(fact_2700_diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_rat
% 5.12/5.33 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % diff_conv_add_uminus
% 5.12/5.33 thf(fact_2701_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_int
% 5.12/5.33 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.12/5.33 thf(fact_2702_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_real
% 5.12/5.33 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.12/5.33 thf(fact_2703_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_complex
% 5.12/5.33 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.12/5.33 thf(fact_2704_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_8373710615458151222nteger
% 5.12/5.33 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.12/5.33 thf(fact_2705_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.12/5.33 ( minus_minus_rat
% 5.12/5.33 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.12/5.33 thf(fact_2706_abs__triangle__ineq,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % abs_triangle_ineq
% 5.12/5.33 thf(fact_2707_abs__triangle__ineq,axiom,
% 5.12/5.33 ! [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 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % abs_triangle_ineq
% 5.12/5.33 thf(fact_2708_abs__triangle__ineq,axiom,
% 5.12/5.33 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % abs_triangle_ineq
% 5.12/5.33 thf(fact_2709_abs__triangle__ineq,axiom,
% 5.12/5.33 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % abs_triangle_ineq
% 5.12/5.33 thf(fact_2710_div__add1__eq,axiom,
% 5.12/5.33 ! [A: int,B: int,C: int] :
% 5.12/5.33 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.33 = ( 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 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % div_add1_eq
% 5.12/5.33 thf(fact_2711_div__add1__eq,axiom,
% 5.12/5.33 ! [A: nat,B: nat,C: nat] :
% 5.12/5.33 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.33 = ( 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 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % div_add1_eq
% 5.12/5.33 thf(fact_2712_div__add1__eq,axiom,
% 5.12/5.33 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.33 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.12/5.33 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % div_add1_eq
% 5.12/5.33 thf(fact_2713_div__add1__eq,axiom,
% 5.12/5.33 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.12/5.33 ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 5.12/5.33 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C ) @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % div_add1_eq
% 5.12/5.33 thf(fact_2714_add__is__1,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ( plus_plus_nat @ M2 @ N )
% 5.12/5.33 = ( suc @ zero_zero_nat ) )
% 5.12/5.33 = ( ( ( M2
% 5.12/5.33 = ( suc @ zero_zero_nat ) )
% 5.12/5.33 & ( N = zero_zero_nat ) )
% 5.12/5.33 | ( ( M2 = zero_zero_nat )
% 5.12/5.33 & ( N
% 5.12/5.33 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_is_1
% 5.12/5.33 thf(fact_2715_one__is__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ( suc @ zero_zero_nat )
% 5.12/5.33 = ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.33 = ( ( ( M2
% 5.12/5.33 = ( suc @ zero_zero_nat ) )
% 5.12/5.33 & ( N = zero_zero_nat ) )
% 5.12/5.33 | ( ( M2 = zero_zero_nat )
% 5.12/5.33 & ( N
% 5.12/5.33 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % one_is_add
% 5.12/5.33 thf(fact_2716_less__natE,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_nat @ M2 @ N )
% 5.12/5.33 => ~ ! [Q3: nat] :
% 5.12/5.33 ( N
% 5.12/5.33 != ( suc @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_natE
% 5.12/5.33 thf(fact_2717_less__add__Suc1,axiom,
% 5.12/5.33 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_Suc1
% 5.12/5.33 thf(fact_2718_less__add__Suc2,axiom,
% 5.12/5.33 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_add_Suc2
% 5.12/5.33 thf(fact_2719_less__iff__Suc__add,axiom,
% 5.12/5.33 ( ord_less_nat
% 5.12/5.33 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.33 ? [K3: nat] :
% 5.12/5.33 ( N4
% 5.12/5.33 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_iff_Suc_add
% 5.12/5.33 thf(fact_2720_less__imp__Suc__add,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ( ord_less_nat @ M2 @ N )
% 5.12/5.33 => ? [K2: nat] :
% 5.12/5.33 ( N
% 5.12/5.33 = ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_imp_Suc_add
% 5.12/5.33 thf(fact_2721_less__imp__add__positive,axiom,
% 5.12/5.33 ! [I: nat,J2: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.33 => ? [K2: nat] :
% 5.12/5.33 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.12/5.33 & ( ( plus_plus_nat @ I @ K2 )
% 5.12/5.33 = J2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_imp_add_positive
% 5.12/5.33 thf(fact_2722_mono__nat__linear__lb,axiom,
% 5.12/5.33 ! [F: nat > nat,M2: nat,K: nat] :
% 5.12/5.33 ( ! [M3: nat,N2: nat] :
% 5.12/5.33 ( ( ord_less_nat @ M3 @ N2 )
% 5.12/5.33 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
% 5.12/5.33 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M2 ) @ K ) @ ( F @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % mono_nat_linear_lb
% 5.12/5.33 thf(fact_2723_diff__add__0,axiom,
% 5.12/5.33 ! [N: nat,M2: nat] :
% 5.12/5.33 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.33 = zero_zero_nat ) ).
% 5.12/5.33
% 5.12/5.33 % diff_add_0
% 5.12/5.33 thf(fact_2724_less__diff__conv,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.33 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J2 @ K ) )
% 5.12/5.33 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J2 ) ) ).
% 5.12/5.33
% 5.12/5.33 % less_diff_conv
% 5.12/5.33 thf(fact_2725_add__diff__inverse__nat,axiom,
% 5.12/5.33 ! [M2: nat,N: nat] :
% 5.12/5.33 ( ~ ( ord_less_nat @ M2 @ N )
% 5.12/5.33 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.33 = M2 ) ) ).
% 5.12/5.33
% 5.12/5.33 % add_diff_inverse_nat
% 5.12/5.33 thf(fact_2726_Suc__eq__plus1,axiom,
% 5.12/5.33 ( suc
% 5.12/5.33 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Suc_eq_plus1
% 5.12/5.33 thf(fact_2727_plus__1__eq__Suc,axiom,
% 5.12/5.33 ( ( plus_plus_nat @ one_one_nat )
% 5.12/5.33 = suc ) ).
% 5.12/5.33
% 5.12/5.33 % plus_1_eq_Suc
% 5.12/5.33 thf(fact_2728_Suc__eq__plus1__left,axiom,
% 5.12/5.33 ( suc
% 5.12/5.33 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.12/5.33
% 5.12/5.33 % Suc_eq_plus1_left
% 5.12/5.33 thf(fact_2729_odd__nonzero,axiom,
% 5.12/5.33 ! [Z2: int] :
% 5.12/5.33 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 )
% 5.12/5.33 != zero_zero_int ) ).
% 5.12/5.33
% 5.12/5.33 % odd_nonzero
% 5.12/5.33 thf(fact_2730_le__diff__conv,axiom,
% 5.12/5.33 ! [J2: nat,K: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K ) @ I )
% 5.12/5.33 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % le_diff_conv
% 5.12/5.33 thf(fact_2731_Nat_Ole__diff__conv2,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J2 @ K ) )
% 5.12/5.33 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.le_diff_conv2
% 5.12/5.33 thf(fact_2732_Nat_Odiff__add__assoc,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J2 ) @ K )
% 5.12/5.33 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J2 @ K ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.diff_add_assoc
% 5.12/5.33 thf(fact_2733_Nat_Odiff__add__assoc2,axiom,
% 5.12/5.33 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.33 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I ) @ K )
% 5.12/5.33 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K ) @ I ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.diff_add_assoc2
% 5.12/5.33 thf(fact_2734_Nat_Ole__imp__diff__is__add,axiom,
% 5.12/5.33 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.33 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.33 => ( ( ( minus_minus_nat @ J2 @ I )
% 5.12/5.33 = K )
% 5.12/5.33 = ( J2
% 5.12/5.33 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % Nat.le_imp_diff_is_add
% 5.12/5.33 thf(fact_2735_int__ge__induct,axiom,
% 5.12/5.33 ! [K: int,I: int,P: int > $o] :
% 5.12/5.33 ( ( ord_less_eq_int @ K @ I )
% 5.12/5.33 => ( ( P @ K )
% 5.12/5.33 => ( ! [I3: int] :
% 5.12/5.33 ( ( ord_less_eq_int @ K @ I3 )
% 5.12/5.33 => ( ( P @ I3 )
% 5.12/5.33 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.12/5.33 => ( P @ I ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % int_ge_induct
% 5.12/5.33 thf(fact_2736_int__gr__induct,axiom,
% 5.12/5.33 ! [K: int,I: int,P: int > $o] :
% 5.12/5.33 ( ( ord_less_int @ K @ I )
% 5.12/5.33 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.12/5.33 => ( ! [I3: int] :
% 5.12/5.33 ( ( ord_less_int @ K @ I3 )
% 5.12/5.33 => ( ( P @ I3 )
% 5.12/5.33 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.12/5.33 => ( P @ I ) ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % int_gr_induct
% 5.12/5.33 thf(fact_2737_zless__add1__eq,axiom,
% 5.12/5.33 ! [W: int,Z2: int] :
% 5.12/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z2 @ one_one_int ) )
% 5.12/5.33 = ( ( ord_less_int @ W @ Z2 )
% 5.12/5.33 | ( W = Z2 ) ) ) ).
% 5.12/5.33
% 5.12/5.33 % zless_add1_eq
% 5.12/5.33 thf(fact_2738_zle__iff__zadd,axiom,
% 5.12/5.33 ( ord_less_eq_int
% 5.12/5.33 = ( ^ [W3: int,Z6: int] :
% 5.12/5.33 ? [N4: nat] :
% 5.12/5.34 ( Z6
% 5.12/5.34 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % zle_iff_zadd
% 5.12/5.34 thf(fact_2739_minus__log__eq__powr,axiom,
% 5.12/5.34 ! [B: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.34 => ( ( B != one_one_real )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( minus_minus_real @ Y @ ( log2 @ B @ X ) )
% 5.12/5.34 = ( log2 @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_log_eq_powr
% 5.12/5.34 thf(fact_2740_minus__real__def,axiom,
% 5.12/5.34 ( minus_minus_real
% 5.12/5.34 = ( ^ [X2: real,Y6: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y6 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_real_def
% 5.12/5.34 thf(fact_2741_dbl__inc__def,axiom,
% 5.12/5.34 ( neg_nu8557863876264182079omplex
% 5.12/5.34 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_inc_def
% 5.12/5.34 thf(fact_2742_dbl__inc__def,axiom,
% 5.12/5.34 ( neg_nu8295874005876285629c_real
% 5.12/5.34 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_inc_def
% 5.12/5.34 thf(fact_2743_dbl__inc__def,axiom,
% 5.12/5.34 ( neg_nu5219082963157363817nc_rat
% 5.12/5.34 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_inc_def
% 5.12/5.34 thf(fact_2744_dbl__inc__def,axiom,
% 5.12/5.34 ( neg_nu5851722552734809277nc_int
% 5.12/5.34 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_inc_def
% 5.12/5.34 thf(fact_2745_powr__less__mono2,axiom,
% 5.12/5.34 ! [A: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_real @ X @ Y )
% 5.12/5.34 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_less_mono2
% 5.12/5.34 thf(fact_2746_powr__mono2_H,axiom,
% 5.12/5.34 ! [A: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.34 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_mono2'
% 5.12/5.34 thf(fact_2747_powr__inj,axiom,
% 5.12/5.34 ! [A: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( A != one_one_real )
% 5.12/5.34 => ( ( ( powr_real @ A @ X )
% 5.12/5.34 = ( powr_real @ A @ Y ) )
% 5.12/5.34 = ( X = Y ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_inj
% 5.12/5.34 thf(fact_2748_gr__one__powr,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.34 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % gr_one_powr
% 5.12/5.34 thf(fact_2749_ge__one__powr__ge__zero,axiom,
% 5.12/5.34 ! [X: real,A: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ge_one_powr_ge_zero
% 5.12/5.34 thf(fact_2750_powr__mono__both,axiom,
% 5.12/5.34 ! [A: real,B: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_eq_real @ A @ B )
% 5.12/5.34 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.34 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_mono_both
% 5.12/5.34 thf(fact_2751_powr__le1,axiom,
% 5.12/5.34 ! [A: real,X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.34 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_le1
% 5.12/5.34 thf(fact_2752_powr__divide,axiom,
% 5.12/5.34 ! [X: real,Y: real,A: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.34 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 5.12/5.34 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_divide
% 5.12/5.34 thf(fact_2753_field__le__epsilon,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ! [E: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ E )
% 5.12/5.34 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
% 5.12/5.34 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % field_le_epsilon
% 5.12/5.34 thf(fact_2754_field__le__epsilon,axiom,
% 5.12/5.34 ! [X: rat,Y: rat] :
% 5.12/5.34 ( ! [E: rat] :
% 5.12/5.34 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.12/5.34 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E ) ) )
% 5.12/5.34 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % field_le_epsilon
% 5.12/5.34 thf(fact_2755_add__strict__increasing2,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_real @ B @ C )
% 5.12/5.34 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing2
% 5.12/5.34 thf(fact_2756_add__strict__increasing2,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.34 => ( ( ord_less_rat @ B @ C )
% 5.12/5.34 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing2
% 5.12/5.34 thf(fact_2757_add__strict__increasing2,axiom,
% 5.12/5.34 ! [A: nat,B: nat,C: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.34 => ( ( ord_less_nat @ B @ C )
% 5.12/5.34 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing2
% 5.12/5.34 thf(fact_2758_add__strict__increasing2,axiom,
% 5.12/5.34 ! [A: int,B: int,C: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.34 => ( ( ord_less_int @ B @ C )
% 5.12/5.34 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing2
% 5.12/5.34 thf(fact_2759_add__strict__increasing,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_eq_real @ B @ C )
% 5.12/5.34 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing
% 5.12/5.34 thf(fact_2760_add__strict__increasing,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.34 => ( ( ord_less_eq_rat @ B @ C )
% 5.12/5.34 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing
% 5.12/5.34 thf(fact_2761_add__strict__increasing,axiom,
% 5.12/5.34 ! [A: nat,B: nat,C: nat] :
% 5.12/5.34 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.34 => ( ( ord_less_eq_nat @ B @ C )
% 5.12/5.34 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing
% 5.12/5.34 thf(fact_2762_add__strict__increasing,axiom,
% 5.12/5.34 ! [A: int,B: int,C: int] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.34 => ( ( ord_less_eq_int @ B @ C )
% 5.12/5.34 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_strict_increasing
% 5.12/5.34 thf(fact_2763_add__pos__nonneg,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.34 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_pos_nonneg
% 5.12/5.34 thf(fact_2764_add__pos__nonneg,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.34 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.34 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_pos_nonneg
% 5.12/5.34 thf(fact_2765_add__pos__nonneg,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.34 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.34 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_pos_nonneg
% 5.12/5.34 thf(fact_2766_add__pos__nonneg,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.34 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_pos_nonneg
% 5.12/5.34 thf(fact_2767_add__nonpos__neg,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.34 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.34 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonpos_neg
% 5.12/5.34 thf(fact_2768_add__nonpos__neg,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.34 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.34 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonpos_neg
% 5.12/5.34 thf(fact_2769_add__nonpos__neg,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.12/5.34 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.12/5.34 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonpos_neg
% 5.12/5.34 thf(fact_2770_add__nonpos__neg,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.34 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.34 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonpos_neg
% 5.12/5.34 thf(fact_2771_add__nonneg__pos,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.34 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonneg_pos
% 5.12/5.34 thf(fact_2772_add__nonneg__pos,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.34 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.34 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonneg_pos
% 5.12/5.34 thf(fact_2773_add__nonneg__pos,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.34 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.34 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonneg_pos
% 5.12/5.34 thf(fact_2774_add__nonneg__pos,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.34 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.34 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_nonneg_pos
% 5.12/5.34 thf(fact_2775_add__neg__nonpos,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.34 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.12/5.34 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_neg_nonpos
% 5.12/5.34 thf(fact_2776_add__neg__nonpos,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.34 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.12/5.34 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_neg_nonpos
% 5.12/5.34 thf(fact_2777_add__neg__nonpos,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.12/5.34 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.12/5.34 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_neg_nonpos
% 5.12/5.34 thf(fact_2778_add__neg__nonpos,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.34 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.34 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_neg_nonpos
% 5.12/5.34 thf(fact_2779_discrete,axiom,
% 5.12/5.34 ( ord_less_nat
% 5.12/5.34 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % discrete
% 5.12/5.34 thf(fact_2780_discrete,axiom,
% 5.12/5.34 ( ord_less_int
% 5.12/5.34 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % discrete
% 5.12/5.34 thf(fact_2781_zero__less__two,axiom,
% 5.12/5.34 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_two
% 5.12/5.34 thf(fact_2782_zero__less__two,axiom,
% 5.12/5.34 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_two
% 5.12/5.34 thf(fact_2783_zero__less__two,axiom,
% 5.12/5.34 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_two
% 5.12/5.34 thf(fact_2784_zero__less__two,axiom,
% 5.12/5.34 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_two
% 5.12/5.34 thf(fact_2785_abs__real__def,axiom,
% 5.12/5.34 ( abs_abs_real
% 5.12/5.34 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_real_def
% 5.12/5.34 thf(fact_2786_div__add__self2,axiom,
% 5.12/5.34 ! [B: nat,A: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_add_self2
% 5.12/5.34 thf(fact_2787_div__add__self2,axiom,
% 5.12/5.34 ! [B: int,A: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.12/5.34 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_add_self2
% 5.12/5.34 thf(fact_2788_div__add__self1,axiom,
% 5.12/5.34 ! [B: nat,A: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_add_self1
% 5.12/5.34 thf(fact_2789_div__add__self1,axiom,
% 5.12/5.34 ! [B: int,A: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.12/5.34 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_add_self1
% 5.12/5.34 thf(fact_2790_less__half__sum,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ B )
% 5.12/5.34 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % less_half_sum
% 5.12/5.34 thf(fact_2791_less__half__sum,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_rat @ A @ B )
% 5.12/5.34 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % less_half_sum
% 5.12/5.34 thf(fact_2792_gt__half__sum,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ B )
% 5.12/5.34 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % gt_half_sum
% 5.12/5.34 thf(fact_2793_gt__half__sum,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ord_less_rat @ A @ B )
% 5.12/5.34 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % gt_half_sum
% 5.12/5.34 thf(fact_2794_abs__diff__triangle__ineq,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_triangle_ineq
% 5.12/5.34 thf(fact_2795_abs__diff__triangle__ineq,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_triangle_ineq
% 5.12/5.34 thf(fact_2796_abs__diff__triangle__ineq,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_triangle_ineq
% 5.12/5.34 thf(fact_2797_abs__diff__triangle__ineq,axiom,
% 5.12/5.34 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_triangle_ineq
% 5.12/5.34 thf(fact_2798_abs__triangle__ineq4,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_triangle_ineq4
% 5.12/5.34 thf(fact_2799_abs__triangle__ineq4,axiom,
% 5.12/5.34 ! [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 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_triangle_ineq4
% 5.12/5.34 thf(fact_2800_abs__triangle__ineq4,axiom,
% 5.12/5.34 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_triangle_ineq4
% 5.12/5.34 thf(fact_2801_abs__triangle__ineq4,axiom,
% 5.12/5.34 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_triangle_ineq4
% 5.12/5.34 thf(fact_2802_abs__diff__le__iff,axiom,
% 5.12/5.34 ! [X: code_integer,A: code_integer,R4: code_integer] :
% 5.12/5.34 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_le_iff
% 5.12/5.34 thf(fact_2803_abs__diff__le__iff,axiom,
% 5.12/5.34 ! [X: real,A: real,R4: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_le_iff
% 5.12/5.34 thf(fact_2804_abs__diff__le__iff,axiom,
% 5.12/5.34 ! [X: rat,A: rat,R4: rat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_le_iff
% 5.12/5.34 thf(fact_2805_abs__diff__le__iff,axiom,
% 5.12/5.34 ! [X: int,A: int,R4: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_le_iff
% 5.12/5.34 thf(fact_2806_log__ln,axiom,
% 5.12/5.34 ( ln_ln_real
% 5.12/5.34 = ( log2 @ ( exp_real @ one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_ln
% 5.12/5.34 thf(fact_2807_real__root__abs,axiom,
% 5.12/5.34 ! [N: nat,X: real] :
% 5.12/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.34 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.12/5.34 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_root_abs
% 5.12/5.34 thf(fact_2808_abs__diff__less__iff,axiom,
% 5.12/5.34 ! [X: code_integer,A: code_integer,R4: code_integer] :
% 5.12/5.34 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_less_iff
% 5.12/5.34 thf(fact_2809_abs__diff__less__iff,axiom,
% 5.12/5.34 ! [X: real,A: real,R4: real] :
% 5.12/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_real @ ( minus_minus_real @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_less_iff
% 5.12/5.34 thf(fact_2810_abs__diff__less__iff,axiom,
% 5.12/5.34 ! [X: rat,A: rat,R4: rat] :
% 5.12/5.34 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_less_iff
% 5.12/5.34 thf(fact_2811_abs__diff__less__iff,axiom,
% 5.12/5.34 ! [X: int,A: int,R4: int] :
% 5.12/5.34 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R4 )
% 5.12/5.34 = ( ( ord_less_int @ ( minus_minus_int @ A @ R4 ) @ X )
% 5.12/5.34 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_diff_less_iff
% 5.12/5.34 thf(fact_2812_powr__diff,axiom,
% 5.12/5.34 ! [W: real,Z1: real,Z22: real] :
% 5.12/5.34 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.12/5.34 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_diff
% 5.12/5.34 thf(fact_2813_ex__gt__or__lt,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ? [B3: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ B3 )
% 5.12/5.34 | ( ord_less_real @ B3 @ A ) ) ).
% 5.12/5.34
% 5.12/5.34 % ex_gt_or_lt
% 5.12/5.34 thf(fact_2814_nat__diff__split__asm,axiom,
% 5.12/5.34 ! [P: nat > $o,A: nat,B: nat] :
% 5.12/5.34 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.12/5.34 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.12/5.34 & ~ ( P @ zero_zero_nat ) )
% 5.12/5.34 | ? [D4: nat] :
% 5.12/5.34 ( ( A
% 5.12/5.34 = ( plus_plus_nat @ B @ D4 ) )
% 5.12/5.34 & ~ ( P @ D4 ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nat_diff_split_asm
% 5.12/5.34 thf(fact_2815_nat__diff__split,axiom,
% 5.12/5.34 ! [P: nat > $o,A: nat,B: nat] :
% 5.12/5.34 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.12/5.34 = ( ( ( ord_less_nat @ A @ B )
% 5.12/5.34 => ( P @ zero_zero_nat ) )
% 5.12/5.34 & ! [D4: nat] :
% 5.12/5.34 ( ( A
% 5.12/5.34 = ( plus_plus_nat @ B @ D4 ) )
% 5.12/5.34 => ( P @ D4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nat_diff_split
% 5.12/5.34 thf(fact_2816_real__add__less__0__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_add_less_0_iff
% 5.12/5.34 thf(fact_2817_real__0__less__add__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.34 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_0_less_add_iff
% 5.12/5.34 thf(fact_2818_real__0__le__add__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.34 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_0_le_add_iff
% 5.12/5.34 thf(fact_2819_real__add__le__0__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_add_le_0_iff
% 5.12/5.34 thf(fact_2820_less__diff__conv2,axiom,
% 5.12/5.34 ! [K: nat,J2: nat,I: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ J2 )
% 5.12/5.34 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K ) @ I )
% 5.12/5.34 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % less_diff_conv2
% 5.12/5.34 thf(fact_2821_int__ops_I4_J,axiom,
% 5.12/5.34 ! [A: nat] :
% 5.12/5.34 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.12/5.34 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % int_ops(4)
% 5.12/5.34 thf(fact_2822_int__Suc,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.12/5.34 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % int_Suc
% 5.12/5.34 thf(fact_2823_zless__iff__Suc__zadd,axiom,
% 5.12/5.34 ( ord_less_int
% 5.12/5.34 = ( ^ [W3: int,Z6: int] :
% 5.12/5.34 ? [N4: nat] :
% 5.12/5.34 ( Z6
% 5.12/5.34 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % zless_iff_Suc_zadd
% 5.12/5.34 thf(fact_2824_odd__less__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z2 ) @ Z2 ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % odd_less_0_iff
% 5.12/5.34 thf(fact_2825_add1__zle__eq,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z2 )
% 5.12/5.34 = ( ord_less_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % add1_zle_eq
% 5.12/5.34 thf(fact_2826_zless__imp__add1__zle,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ W @ Z2 )
% 5.12/5.34 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % zless_imp_add1_zle
% 5.12/5.34 thf(fact_2827_int__induct,axiom,
% 5.12/5.34 ! [P: int > $o,K: int,I: int] :
% 5.12/5.34 ( ( P @ K )
% 5.12/5.34 => ( ! [I3: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ K @ I3 )
% 5.12/5.34 => ( ( P @ I3 )
% 5.12/5.34 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.12/5.34 => ( ! [I3: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ I3 @ K )
% 5.12/5.34 => ( ( P @ I3 )
% 5.12/5.34 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.12/5.34 => ( P @ I ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % int_induct
% 5.12/5.34 thf(fact_2828_exp__ge__add__one__self,axiom,
% 5.12/5.34 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % exp_ge_add_one_self
% 5.12/5.34 thf(fact_2829_dbl__dec__def,axiom,
% 5.12/5.34 ( neg_nu6511756317524482435omplex
% 5.12/5.34 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_dec_def
% 5.12/5.34 thf(fact_2830_dbl__dec__def,axiom,
% 5.12/5.34 ( neg_nu6075765906172075777c_real
% 5.12/5.34 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_dec_def
% 5.12/5.34 thf(fact_2831_dbl__dec__def,axiom,
% 5.12/5.34 ( neg_nu3179335615603231917ec_rat
% 5.12/5.34 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_dec_def
% 5.12/5.34 thf(fact_2832_dbl__dec__def,axiom,
% 5.12/5.34 ( neg_nu3811975205180677377ec_int
% 5.12/5.34 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % dbl_dec_def
% 5.12/5.34 thf(fact_2833_log__base__change,axiom,
% 5.12/5.34 ! [A: real,B: real,X: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( A != one_one_real )
% 5.12/5.34 => ( ( log2 @ B @ X )
% 5.12/5.34 = ( divide_divide_real @ ( log2 @ A @ X ) @ ( log2 @ A @ B ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_base_change
% 5.12/5.34 thf(fact_2834_powr__realpow,axiom,
% 5.12/5.34 ! [X: real,N: nat] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.34 = ( power_power_real @ X @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_realpow
% 5.12/5.34 thf(fact_2835_less__log__of__power,axiom,
% 5.12/5.34 ! [B: real,N: nat,M2: real] :
% 5.12/5.34 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M2 )
% 5.12/5.34 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.34 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ M2 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % less_log_of_power
% 5.12/5.34 thf(fact_2836_log__of__power__eq,axiom,
% 5.12/5.34 ! [M2: nat,B: real,N: nat] :
% 5.12/5.34 ( ( ( semiri5074537144036343181t_real @ M2 )
% 5.12/5.34 = ( power_power_real @ B @ N ) )
% 5.12/5.34 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.34 => ( ( semiri5074537144036343181t_real @ N )
% 5.12/5.34 = ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_of_power_eq
% 5.12/5.34 thf(fact_2837_abs__add__one__gt__zero,axiom,
% 5.12/5.34 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_add_one_gt_zero
% 5.12/5.34 thf(fact_2838_abs__add__one__gt__zero,axiom,
% 5.12/5.34 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_add_one_gt_zero
% 5.12/5.34 thf(fact_2839_abs__add__one__gt__zero,axiom,
% 5.12/5.34 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_add_one_gt_zero
% 5.12/5.34 thf(fact_2840_abs__add__one__gt__zero,axiom,
% 5.12/5.34 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_add_one_gt_zero
% 5.12/5.34 thf(fact_2841_root__abs__power,axiom,
% 5.12/5.34 ! [N: nat,Y: real] :
% 5.12/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.34 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 5.12/5.34 = ( abs_abs_real @ Y ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % root_abs_power
% 5.12/5.34 thf(fact_2842_add__eq__if,axiom,
% 5.12/5.34 ( plus_plus_nat
% 5.12/5.34 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_eq_if
% 5.12/5.34 thf(fact_2843_nat__less__real__le,axiom,
% 5.12/5.34 ( ord_less_nat
% 5.12/5.34 = ( ^ [N4: nat,M5: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N4 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M5 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nat_less_real_le
% 5.12/5.34 thf(fact_2844_nat__le__real__less,axiom,
% 5.12/5.34 ( ord_less_eq_nat
% 5.12/5.34 = ( ^ [N4: nat,M5: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nat_le_real_less
% 5.12/5.34 thf(fact_2845_le__imp__0__less,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % le_imp_0_less
% 5.12/5.34 thf(fact_2846_ln__add__one__self__le__self,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % ln_add_one_self_le_self
% 5.12/5.34 thf(fact_2847_Suc__as__int,axiom,
% 5.12/5.34 ( suc
% 5.12/5.34 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % Suc_as_int
% 5.12/5.34 thf(fact_2848_exp__ge__add__one__self__aux,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % exp_ge_add_one_self_aux
% 5.12/5.34 thf(fact_2849_mod__pos__neg__trivial,axiom,
% 5.12/5.34 ! [K: int,L: int] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.34 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.12/5.34 => ( ( modulo_modulo_int @ K @ L )
% 5.12/5.34 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mod_pos_neg_trivial
% 5.12/5.34 thf(fact_2850_real__of__nat__div__aux,axiom,
% 5.12/5.34 ! [X: nat,D: nat] :
% 5.12/5.34 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.12/5.34 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_of_nat_div_aux
% 5.12/5.34 thf(fact_2851_powr__minus__divide,axiom,
% 5.12/5.34 ! [X: real,A: real] :
% 5.12/5.34 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 5.12/5.34 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_minus_divide
% 5.12/5.34 thf(fact_2852_powr__neg__one,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.34 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_neg_one
% 5.12/5.34 thf(fact_2853_log__divide,axiom,
% 5.12/5.34 ! [A: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( A != one_one_real )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.34 => ( ( log2 @ A @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.34 = ( minus_minus_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_divide
% 5.12/5.34 thf(fact_2854_le__log__of__power,axiom,
% 5.12/5.34 ! [B: real,N: nat,M2: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M2 )
% 5.12/5.34 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.34 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ M2 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % le_log_of_power
% 5.12/5.34 thf(fact_2855_log__base__pow,axiom,
% 5.12/5.34 ! [A: real,N: nat,X: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ( log2 @ ( power_power_real @ A @ N ) @ X )
% 5.12/5.34 = ( divide_divide_real @ ( log2 @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_base_pow
% 5.12/5.34 thf(fact_2856_Suc__nat__eq__nat__zadd1,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ( suc @ ( nat2 @ Z2 ) )
% 5.12/5.34 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z2 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % Suc_nat_eq_nat_zadd1
% 5.12/5.34 thf(fact_2857_ln__add__one__self__le__self2,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.34 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % ln_add_one_self_le_self2
% 5.12/5.34 thf(fact_2858_log__of__power__less,axiom,
% 5.12/5.34 ! [M2: nat,B: real,N: nat] :
% 5.12/5.34 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 5.12/5.34 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.34 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.34 => ( ord_less_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_of_power_less
% 5.12/5.34 thf(fact_2859_ln__powr__bound,axiom,
% 5.12/5.34 ! [X: real,A: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.34 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ln_powr_bound
% 5.12/5.34 thf(fact_2860_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.12/5.34 ! [K: nat,N: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.34 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.34 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % neg_one_power_add_eq_neg_one_power_diff
% 5.12/5.34 thf(fact_2861_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.12/5.34 ! [K: nat,N: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.34 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.34 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % neg_one_power_add_eq_neg_one_power_diff
% 5.12/5.34 thf(fact_2862_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.12/5.34 ! [K: nat,N: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.34 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.34 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % neg_one_power_add_eq_neg_one_power_diff
% 5.12/5.34 thf(fact_2863_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.12/5.34 ! [K: nat,N: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.34 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.34 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % neg_one_power_add_eq_neg_one_power_diff
% 5.12/5.34 thf(fact_2864_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.12/5.34 ! [K: nat,N: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.34 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.12/5.34 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % neg_one_power_add_eq_neg_one_power_diff
% 5.12/5.34 thf(fact_2865_lemma__interval,axiom,
% 5.12/5.34 ! [A: real,X: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ X )
% 5.12/5.34 => ( ( ord_less_real @ X @ B )
% 5.12/5.34 => ? [D5: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.34 & ! [Y5: real] :
% 5.12/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D5 )
% 5.12/5.34 => ( ( ord_less_eq_real @ A @ Y5 )
% 5.12/5.34 & ( ord_less_eq_real @ Y5 @ B ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % lemma_interval
% 5.12/5.34 thf(fact_2866_ceiling__log__eq__powr__iff,axiom,
% 5.12/5.34 ! [X: real,B: real,K: nat] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.34 => ( ( ( archim7802044766580827645g_real @ ( log2 @ B @ X ) )
% 5.12/5.34 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.12/5.34 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.12/5.34 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_log_eq_powr_iff
% 5.12/5.34 thf(fact_2867_sin__bound__lemma,axiom,
% 5.12/5.34 ! [X: real,Y: real,U: real,V: real] :
% 5.12/5.34 ( ( X = Y )
% 5.12/5.34 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.12/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % sin_bound_lemma
% 5.12/5.34 thf(fact_2868_lemma__interval__lt,axiom,
% 5.12/5.34 ! [A: real,X: real,B: real] :
% 5.12/5.34 ( ( ord_less_real @ A @ X )
% 5.12/5.34 => ( ( ord_less_real @ X @ B )
% 5.12/5.34 => ? [D5: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.34 & ! [Y5: real] :
% 5.12/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D5 )
% 5.12/5.34 => ( ( ord_less_real @ A @ Y5 )
% 5.12/5.34 & ( ord_less_real @ Y5 @ B ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % lemma_interval_lt
% 5.12/5.34 thf(fact_2869_ceiling__zero,axiom,
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_zero
% 5.12/5.34 thf(fact_2870_ceiling__zero,axiom,
% 5.12/5.34 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_zero
% 5.12/5.34 thf(fact_2871_ceiling__one,axiom,
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.12/5.34 = one_one_int ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_one
% 5.12/5.34 thf(fact_2872_ceiling__one,axiom,
% 5.12/5.34 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.12/5.34 = one_one_int ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_one
% 5.12/5.34 thf(fact_2873_ceiling__of__nat,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.34 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_of_nat
% 5.12/5.34 thf(fact_2874_ceiling__of__nat,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.12/5.34 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_of_nat
% 5.12/5.34 thf(fact_2875_ceiling__le__zero,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_le_zero
% 5.12/5.34 thf(fact_2876_ceiling__le__zero,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_le_zero
% 5.12/5.34 thf(fact_2877_zero__less__ceiling,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.34 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_ceiling
% 5.12/5.34 thf(fact_2878_zero__less__ceiling,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.34 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % zero_less_ceiling
% 5.12/5.34 thf(fact_2879_ceiling__less__one,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.12/5.34 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_one
% 5.12/5.34 thf(fact_2880_ceiling__less__one,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.12/5.34 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_one
% 5.12/5.34 thf(fact_2881_one__le__ceiling,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.34 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % one_le_ceiling
% 5.12/5.34 thf(fact_2882_one__le__ceiling,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.34 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % one_le_ceiling
% 5.12/5.34 thf(fact_2883_ceiling__le__one,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.12/5.34 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_le_one
% 5.12/5.34 thf(fact_2884_ceiling__le__one,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.12/5.34 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_le_one
% 5.12/5.34 thf(fact_2885_one__less__ceiling,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.34 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % one_less_ceiling
% 5.12/5.34 thf(fact_2886_one__less__ceiling,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.34 = ( ord_less_real @ one_one_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % one_less_ceiling
% 5.12/5.34 thf(fact_2887_ceiling__add__one,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 5.12/5.34 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_one
% 5.12/5.34 thf(fact_2888_ceiling__add__one,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.12/5.34 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_one
% 5.12/5.34 thf(fact_2889_ceiling__diff__one,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.12/5.34 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_diff_one
% 5.12/5.34 thf(fact_2890_ceiling__diff__one,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.12/5.34 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_diff_one
% 5.12/5.34 thf(fact_2891_nat__ceiling__le__eq,axiom,
% 5.12/5.34 ! [X: real,A: nat] :
% 5.12/5.34 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.12/5.34 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nat_ceiling_le_eq
% 5.12/5.34 thf(fact_2892_ceiling__less__zero,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_zero
% 5.12/5.34 thf(fact_2893_ceiling__less__zero,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_zero
% 5.12/5.34 thf(fact_2894_zero__le__ceiling,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.34 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % zero_le_ceiling
% 5.12/5.34 thf(fact_2895_zero__le__ceiling,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.34 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % zero_le_ceiling
% 5.12/5.34 thf(fact_2896_ceiling__mono,axiom,
% 5.12/5.34 ! [Y: real,X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ Y @ X )
% 5.12/5.34 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_mono
% 5.12/5.34 thf(fact_2897_ceiling__mono,axiom,
% 5.12/5.34 ! [Y: rat,X: rat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ Y @ X )
% 5.12/5.34 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_mono
% 5.12/5.34 thf(fact_2898_ceiling__less__cancel,axiom,
% 5.12/5.34 ! [X: rat,Y: rat] :
% 5.12/5.34 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 5.12/5.34 => ( ord_less_rat @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_cancel
% 5.12/5.34 thf(fact_2899_ceiling__less__cancel,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 5.12/5.34 => ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_less_cancel
% 5.12/5.34 thf(fact_2900_of__nat__ceiling,axiom,
% 5.12/5.34 ! [R4: real] : ( ord_less_eq_real @ R4 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_ceiling
% 5.12/5.34 thf(fact_2901_of__nat__ceiling,axiom,
% 5.12/5.34 ! [R4: rat] : ( ord_less_eq_rat @ R4 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_ceiling
% 5.12/5.34 thf(fact_2902_ceiling__add__le,axiom,
% 5.12/5.34 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_le
% 5.12/5.34 thf(fact_2903_ceiling__add__le,axiom,
% 5.12/5.34 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_le
% 5.12/5.34 thf(fact_2904_real__nat__ceiling__ge,axiom,
% 5.12/5.34 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_nat_ceiling_ge
% 5.12/5.34 thf(fact_2905_length__induct,axiom,
% 5.12/5.34 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.12/5.34 ( ! [Xs2: list_VEBT_VEBT] :
% 5.12/5.34 ( ! [Ys: list_VEBT_VEBT] :
% 5.12/5.34 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.12/5.34 => ( P @ Ys ) )
% 5.12/5.34 => ( P @ Xs2 ) )
% 5.12/5.34 => ( P @ Xs ) ) ).
% 5.12/5.34
% 5.12/5.34 % length_induct
% 5.12/5.34 thf(fact_2906_length__induct,axiom,
% 5.12/5.34 ! [P: list_o > $o,Xs: list_o] :
% 5.12/5.34 ( ! [Xs2: list_o] :
% 5.12/5.34 ( ! [Ys: list_o] :
% 5.12/5.34 ( ( ord_less_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs2 ) )
% 5.12/5.34 => ( P @ Ys ) )
% 5.12/5.34 => ( P @ Xs2 ) )
% 5.12/5.34 => ( P @ Xs ) ) ).
% 5.12/5.34
% 5.12/5.34 % length_induct
% 5.12/5.34 thf(fact_2907_length__induct,axiom,
% 5.12/5.34 ! [P: list_nat > $o,Xs: list_nat] :
% 5.12/5.34 ( ! [Xs2: list_nat] :
% 5.12/5.34 ( ! [Ys: list_nat] :
% 5.12/5.34 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs2 ) )
% 5.12/5.34 => ( P @ Ys ) )
% 5.12/5.34 => ( P @ Xs2 ) )
% 5.12/5.34 => ( P @ Xs ) ) ).
% 5.12/5.34
% 5.12/5.34 % length_induct
% 5.12/5.34 thf(fact_2908_length__induct,axiom,
% 5.12/5.34 ! [P: list_int > $o,Xs: list_int] :
% 5.12/5.34 ( ! [Xs2: list_int] :
% 5.12/5.34 ( ! [Ys: list_int] :
% 5.12/5.34 ( ( ord_less_nat @ ( size_size_list_int @ Ys ) @ ( size_size_list_int @ Xs2 ) )
% 5.12/5.34 => ( P @ Ys ) )
% 5.12/5.34 => ( P @ Xs2 ) )
% 5.12/5.34 => ( P @ Xs ) ) ).
% 5.12/5.34
% 5.12/5.34 % length_induct
% 5.12/5.34 thf(fact_2909_eq__diff__eq_H,axiom,
% 5.12/5.34 ! [X: real,Y: real,Z2: real] :
% 5.12/5.34 ( ( X
% 5.12/5.34 = ( minus_minus_real @ Y @ Z2 ) )
% 5.12/5.34 = ( Y
% 5.12/5.34 = ( plus_plus_real @ X @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % eq_diff_eq'
% 5.12/5.34 thf(fact_2910_powr__int,axiom,
% 5.12/5.34 ! [X: real,I: int] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.12/5.34 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.12/5.34 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 5.12/5.34 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.12/5.34 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.12/5.34 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % powr_int
% 5.12/5.34 thf(fact_2911_log__minus__eq__powr,axiom,
% 5.12/5.34 ! [B: real,X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.34 => ( ( B != one_one_real )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.34 => ( ( minus_minus_real @ ( log2 @ B @ X ) @ Y )
% 5.12/5.34 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_minus_eq_powr
% 5.12/5.34 thf(fact_2912_log__base__root,axiom,
% 5.12/5.34 ! [N: nat,B: real,X: real] :
% 5.12/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.34 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.34 => ( ( log2 @ ( root @ N @ B ) @ X )
% 5.12/5.34 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % log_base_root
% 5.12/5.34 thf(fact_2913_tanh__altdef,axiom,
% 5.12/5.34 ( tanh_real
% 5.12/5.34 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_altdef
% 5.12/5.34 thf(fact_2914_tanh__altdef,axiom,
% 5.12/5.34 ( tanh_complex
% 5.12/5.34 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_altdef
% 5.12/5.34 thf(fact_2915_triangle__Suc,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( nat_triangle @ ( suc @ N ) )
% 5.12/5.34 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % triangle_Suc
% 5.12/5.34 thf(fact_2916_ceiling__eq,axiom,
% 5.12/5.34 ! [N: int,X: real] :
% 5.12/5.34 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.12/5.34 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.12/5.34 => ( ( archim7802044766580827645g_real @ X )
% 5.12/5.34 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_eq
% 5.12/5.34 thf(fact_2917_ceiling__eq,axiom,
% 5.12/5.34 ! [N: int,X: rat] :
% 5.12/5.34 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 5.12/5.34 => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.12/5.34 => ( ( archim2889992004027027881ng_rat @ X )
% 5.12/5.34 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_eq
% 5.12/5.34 thf(fact_2918_add__0__iff,axiom,
% 5.12/5.34 ! [B: real,A: real] :
% 5.12/5.34 ( ( B
% 5.12/5.34 = ( plus_plus_real @ B @ A ) )
% 5.12/5.34 = ( A = zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_0_iff
% 5.12/5.34 thf(fact_2919_add__0__iff,axiom,
% 5.12/5.34 ! [B: rat,A: rat] :
% 5.12/5.34 ( ( B
% 5.12/5.34 = ( plus_plus_rat @ B @ A ) )
% 5.12/5.34 = ( A = zero_zero_rat ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_0_iff
% 5.12/5.34 thf(fact_2920_add__0__iff,axiom,
% 5.12/5.34 ! [B: nat,A: nat] :
% 5.12/5.34 ( ( B
% 5.12/5.34 = ( plus_plus_nat @ B @ A ) )
% 5.12/5.34 = ( A = zero_zero_nat ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_0_iff
% 5.12/5.34 thf(fact_2921_add__0__iff,axiom,
% 5.12/5.34 ! [B: int,A: int] :
% 5.12/5.34 ( ( B
% 5.12/5.34 = ( plus_plus_int @ B @ A ) )
% 5.12/5.34 = ( A = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % add_0_iff
% 5.12/5.34 thf(fact_2922_split__neg__lemma,axiom,
% 5.12/5.34 ! [K: int,P: int > int > $o,N: int] :
% 5.12/5.34 ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.34 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.12/5.34 = ( ! [I2: int,J3: int] :
% 5.12/5.34 ( ( ( ord_less_int @ K @ J3 )
% 5.12/5.34 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.12/5.34 & ( N
% 5.12/5.34 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.34 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % split_neg_lemma
% 5.12/5.34 thf(fact_2923_tanh__real__zero__iff,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ( tanh_real @ X )
% 5.12/5.34 = zero_zero_real )
% 5.12/5.34 = ( X = zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_zero_iff
% 5.12/5.34 thf(fact_2924_tanh__real__less__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.12/5.34 = ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_less_iff
% 5.12/5.34 thf(fact_2925_tanh__real__le__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.12/5.34 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_le_iff
% 5.12/5.34 thf(fact_2926_of__int__eq__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_real @ W )
% 5.12/5.34 = ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( W = Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_iff
% 5.12/5.34 thf(fact_2927_of__int__eq__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_rat @ W )
% 5.12/5.34 = ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( W = Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_iff
% 5.12/5.34 thf(fact_2928_tanh__real__abs,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( tanh_real @ ( abs_abs_real @ X ) )
% 5.12/5.34 = ( abs_abs_real @ ( tanh_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_abs
% 5.12/5.34 thf(fact_2929_mult__cancel__right,axiom,
% 5.12/5.34 ! [A: real,C: real,B: real] :
% 5.12/5.34 ( ( ( times_times_real @ A @ C )
% 5.12/5.34 = ( times_times_real @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right
% 5.12/5.34 thf(fact_2930_mult__cancel__right,axiom,
% 5.12/5.34 ! [A: rat,C: rat,B: rat] :
% 5.12/5.34 ( ( ( times_times_rat @ A @ C )
% 5.12/5.34 = ( times_times_rat @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right
% 5.12/5.34 thf(fact_2931_mult__cancel__right,axiom,
% 5.12/5.34 ! [A: nat,C: nat,B: nat] :
% 5.12/5.34 ( ( ( times_times_nat @ A @ C )
% 5.12/5.34 = ( times_times_nat @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_nat )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right
% 5.12/5.34 thf(fact_2932_mult__cancel__right,axiom,
% 5.12/5.34 ! [A: int,C: int,B: int] :
% 5.12/5.34 ( ( ( times_times_int @ A @ C )
% 5.12/5.34 = ( times_times_int @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right
% 5.12/5.34 thf(fact_2933_mult__cancel__left,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( ( times_times_real @ C @ A )
% 5.12/5.34 = ( times_times_real @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left
% 5.12/5.34 thf(fact_2934_mult__cancel__left,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( ( times_times_rat @ C @ A )
% 5.12/5.34 = ( times_times_rat @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left
% 5.12/5.34 thf(fact_2935_mult__cancel__left,axiom,
% 5.12/5.34 ! [C: nat,A: nat,B: nat] :
% 5.12/5.34 ( ( ( times_times_nat @ C @ A )
% 5.12/5.34 = ( times_times_nat @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_nat )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left
% 5.12/5.34 thf(fact_2936_mult__cancel__left,axiom,
% 5.12/5.34 ! [C: int,A: int,B: int] :
% 5.12/5.34 ( ( ( times_times_int @ C @ A )
% 5.12/5.34 = ( times_times_int @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( A = B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left
% 5.12/5.34 thf(fact_2937_mult__eq__0__iff,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( ( times_times_real @ A @ B )
% 5.12/5.34 = zero_zero_real )
% 5.12/5.34 = ( ( A = zero_zero_real )
% 5.12/5.34 | ( B = zero_zero_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_eq_0_iff
% 5.12/5.34 thf(fact_2938_mult__eq__0__iff,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( ( times_times_rat @ A @ B )
% 5.12/5.34 = zero_zero_rat )
% 5.12/5.34 = ( ( A = zero_zero_rat )
% 5.12/5.34 | ( B = zero_zero_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_eq_0_iff
% 5.12/5.34 thf(fact_2939_mult__eq__0__iff,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( ( times_times_nat @ A @ B )
% 5.12/5.34 = zero_zero_nat )
% 5.12/5.34 = ( ( A = zero_zero_nat )
% 5.12/5.34 | ( B = zero_zero_nat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_eq_0_iff
% 5.12/5.34 thf(fact_2940_mult__eq__0__iff,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( ( times_times_int @ A @ B )
% 5.12/5.34 = zero_zero_int )
% 5.12/5.34 = ( ( A = zero_zero_int )
% 5.12/5.34 | ( B = zero_zero_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_eq_0_iff
% 5.12/5.34 thf(fact_2941_mult__zero__right,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ( ( times_times_real @ A @ zero_zero_real )
% 5.12/5.34 = zero_zero_real ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_right
% 5.12/5.34 thf(fact_2942_mult__zero__right,axiom,
% 5.12/5.34 ! [A: rat] :
% 5.12/5.34 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.12/5.34 = zero_zero_rat ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_right
% 5.12/5.34 thf(fact_2943_mult__zero__right,axiom,
% 5.12/5.34 ! [A: nat] :
% 5.12/5.34 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.12/5.34 = zero_zero_nat ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_right
% 5.12/5.34 thf(fact_2944_mult__zero__right,axiom,
% 5.12/5.34 ! [A: int] :
% 5.12/5.34 ( ( times_times_int @ A @ zero_zero_int )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_right
% 5.12/5.34 thf(fact_2945_mult__zero__left,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ( ( times_times_real @ zero_zero_real @ A )
% 5.12/5.34 = zero_zero_real ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_left
% 5.12/5.34 thf(fact_2946_mult__zero__left,axiom,
% 5.12/5.34 ! [A: rat] :
% 5.12/5.34 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.12/5.34 = zero_zero_rat ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_left
% 5.12/5.34 thf(fact_2947_mult__zero__left,axiom,
% 5.12/5.34 ! [A: nat] :
% 5.12/5.34 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.12/5.34 = zero_zero_nat ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_left
% 5.12/5.34 thf(fact_2948_mult__zero__left,axiom,
% 5.12/5.34 ! [A: int] :
% 5.12/5.34 ( ( times_times_int @ zero_zero_int @ A )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % mult_zero_left
% 5.12/5.34 thf(fact_2949_mult_Oright__neutral,axiom,
% 5.12/5.34 ! [A: complex] :
% 5.12/5.34 ( ( times_times_complex @ A @ one_one_complex )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult.right_neutral
% 5.12/5.34 thf(fact_2950_mult_Oright__neutral,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ( ( times_times_real @ A @ one_one_real )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult.right_neutral
% 5.12/5.34 thf(fact_2951_mult_Oright__neutral,axiom,
% 5.12/5.34 ! [A: rat] :
% 5.12/5.34 ( ( times_times_rat @ A @ one_one_rat )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult.right_neutral
% 5.12/5.34 thf(fact_2952_mult_Oright__neutral,axiom,
% 5.12/5.34 ! [A: nat] :
% 5.12/5.34 ( ( times_times_nat @ A @ one_one_nat )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult.right_neutral
% 5.12/5.34 thf(fact_2953_mult_Oright__neutral,axiom,
% 5.12/5.34 ! [A: int] :
% 5.12/5.34 ( ( times_times_int @ A @ one_one_int )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult.right_neutral
% 5.12/5.34 thf(fact_2954_mult__1,axiom,
% 5.12/5.34 ! [A: complex] :
% 5.12/5.34 ( ( times_times_complex @ one_one_complex @ A )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult_1
% 5.12/5.34 thf(fact_2955_mult__1,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ( ( times_times_real @ one_one_real @ A )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult_1
% 5.12/5.34 thf(fact_2956_mult__1,axiom,
% 5.12/5.34 ! [A: rat] :
% 5.12/5.34 ( ( times_times_rat @ one_one_rat @ A )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult_1
% 5.12/5.34 thf(fact_2957_mult__1,axiom,
% 5.12/5.34 ! [A: nat] :
% 5.12/5.34 ( ( times_times_nat @ one_one_nat @ A )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult_1
% 5.12/5.34 thf(fact_2958_mult__1,axiom,
% 5.12/5.34 ! [A: int] :
% 5.12/5.34 ( ( times_times_int @ one_one_int @ A )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % mult_1
% 5.12/5.34 thf(fact_2959_times__divide__eq__right,axiom,
% 5.12/5.34 ! [A: complex,B: complex,C: complex] :
% 5.12/5.34 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_right
% 5.12/5.34 thf(fact_2960_times__divide__eq__right,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.34 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_right
% 5.12/5.34 thf(fact_2961_times__divide__eq__right,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.34 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_right
% 5.12/5.34 thf(fact_2962_divide__divide__eq__right,axiom,
% 5.12/5.34 ! [A: complex,B: complex,C: complex] :
% 5.12/5.34 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_right
% 5.12/5.34 thf(fact_2963_divide__divide__eq__right,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.34 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_right
% 5.12/5.34 thf(fact_2964_divide__divide__eq__right,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.34 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_right
% 5.12/5.34 thf(fact_2965_divide__divide__eq__left,axiom,
% 5.12/5.34 ! [A: complex,B: complex,C: complex] :
% 5.12/5.34 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_left
% 5.12/5.34 thf(fact_2966_divide__divide__eq__left,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.12/5.34 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_left
% 5.12/5.34 thf(fact_2967_divide__divide__eq__left,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.12/5.34 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % divide_divide_eq_left
% 5.12/5.34 thf(fact_2968_times__divide__eq__left,axiom,
% 5.12/5.34 ! [B: complex,C: complex,A: complex] :
% 5.12/5.34 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.12/5.34 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_left
% 5.12/5.34 thf(fact_2969_times__divide__eq__left,axiom,
% 5.12/5.34 ! [B: real,C: real,A: real] :
% 5.12/5.34 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.34 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_left
% 5.12/5.34 thf(fact_2970_times__divide__eq__left,axiom,
% 5.12/5.34 ! [B: rat,C: rat,A: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.34 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.12/5.34
% 5.12/5.34 % times_divide_eq_left
% 5.12/5.34 thf(fact_2971_mult__minus__left,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.34 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_left
% 5.12/5.34 thf(fact_2972_mult__minus__left,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.12/5.34 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_left
% 5.12/5.34 thf(fact_2973_mult__minus__left,axiom,
% 5.12/5.34 ! [A: complex,B: complex] :
% 5.12/5.34 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_left
% 5.12/5.34 thf(fact_2974_mult__minus__left,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.12/5.34 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_left
% 5.12/5.34 thf(fact_2975_mult__minus__left,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.12/5.34 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_left
% 5.12/5.34 thf(fact_2976_minus__mult__minus,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.12/5.34 = ( times_times_int @ A @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_mult_minus
% 5.12/5.34 thf(fact_2977_minus__mult__minus,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.12/5.34 = ( times_times_real @ A @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_mult_minus
% 5.12/5.34 thf(fact_2978_minus__mult__minus,axiom,
% 5.12/5.34 ! [A: complex,B: complex] :
% 5.12/5.34 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.12/5.34 = ( times_times_complex @ A @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_mult_minus
% 5.12/5.34 thf(fact_2979_minus__mult__minus,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.12/5.34 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_mult_minus
% 5.12/5.34 thf(fact_2980_minus__mult__minus,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.12/5.34 = ( times_times_rat @ A @ B ) ) ).
% 5.12/5.34
% 5.12/5.34 % minus_mult_minus
% 5.12/5.34 thf(fact_2981_mult__minus__right,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.12/5.34 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_right
% 5.12/5.34 thf(fact_2982_mult__minus__right,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.12/5.34 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_right
% 5.12/5.34 thf(fact_2983_mult__minus__right,axiom,
% 5.12/5.34 ! [A: complex,B: complex] :
% 5.12/5.34 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_right
% 5.12/5.34 thf(fact_2984_mult__minus__right,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.12/5.34 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_right
% 5.12/5.34 thf(fact_2985_mult__minus__right,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.12/5.34 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus_right
% 5.12/5.34 thf(fact_2986_of__nat__mult,axiom,
% 5.12/5.34 ! [M2: nat,N: nat] :
% 5.12/5.34 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.34 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_mult
% 5.12/5.34 thf(fact_2987_of__nat__mult,axiom,
% 5.12/5.34 ! [M2: nat,N: nat] :
% 5.12/5.34 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.34 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_mult
% 5.12/5.34 thf(fact_2988_of__nat__mult,axiom,
% 5.12/5.34 ! [M2: nat,N: nat] :
% 5.12/5.34 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.34 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_mult
% 5.12/5.34 thf(fact_2989_of__nat__mult,axiom,
% 5.12/5.34 ! [M2: nat,N: nat] :
% 5.12/5.34 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.34 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_mult
% 5.12/5.34 thf(fact_2990_of__nat__mult,axiom,
% 5.12/5.34 ! [M2: nat,N: nat] :
% 5.12/5.34 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.34 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_mult
% 5.12/5.34 thf(fact_2991_abs__mult__self__eq,axiom,
% 5.12/5.34 ! [A: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.34 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_mult_self_eq
% 5.12/5.34 thf(fact_2992_abs__mult__self__eq,axiom,
% 5.12/5.34 ! [A: real] :
% 5.12/5.34 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.12/5.34 = ( times_times_real @ A @ A ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_mult_self_eq
% 5.12/5.34 thf(fact_2993_abs__mult__self__eq,axiom,
% 5.12/5.34 ! [A: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.12/5.34 = ( times_times_rat @ A @ A ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_mult_self_eq
% 5.12/5.34 thf(fact_2994_abs__mult__self__eq,axiom,
% 5.12/5.34 ! [A: int] :
% 5.12/5.34 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.12/5.34 = ( times_times_int @ A @ A ) ) ).
% 5.12/5.34
% 5.12/5.34 % abs_mult_self_eq
% 5.12/5.34 thf(fact_2995_tanh__real__neg__iff,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_neg_iff
% 5.12/5.34 thf(fact_2996_tanh__real__pos__iff,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.12/5.34 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_pos_iff
% 5.12/5.34 thf(fact_2997_tanh__real__nonpos__iff,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_nonpos_iff
% 5.12/5.34 thf(fact_2998_tanh__real__nonneg__iff,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.12/5.34 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_real_nonneg_iff
% 5.12/5.34 thf(fact_2999_real__divide__square__eq,axiom,
% 5.12/5.34 ! [R4: real,A: real] :
% 5.12/5.34 ( ( divide_divide_real @ ( times_times_real @ R4 @ A ) @ ( times_times_real @ R4 @ R4 ) )
% 5.12/5.34 = ( divide_divide_real @ A @ R4 ) ) ).
% 5.12/5.34
% 5.12/5.34 % real_divide_square_eq
% 5.12/5.34 thf(fact_3000_tanh__0,axiom,
% 5.12/5.34 ( ( tanh_real @ zero_zero_real )
% 5.12/5.34 = zero_zero_real ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_0
% 5.12/5.34 thf(fact_3001_of__int__ceiling__cancel,axiom,
% 5.12/5.34 ! [X: rat] :
% 5.12/5.34 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.34 = X )
% 5.12/5.34 = ( ? [N4: int] :
% 5.12/5.34 ( X
% 5.12/5.34 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_ceiling_cancel
% 5.12/5.34 thf(fact_3002_of__int__ceiling__cancel,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.34 = X )
% 5.12/5.34 = ( ? [N4: int] :
% 5.12/5.34 ( X
% 5.12/5.34 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_ceiling_cancel
% 5.12/5.34 thf(fact_3003_ceiling__of__int,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = Z2 ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_of_int
% 5.12/5.34 thf(fact_3004_ceiling__of__int,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = Z2 ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_of_int
% 5.12/5.34 thf(fact_3005_tanh__minus,axiom,
% 5.12/5.34 ! [X: real] :
% 5.12/5.34 ( ( tanh_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.34 = ( uminus_uminus_real @ ( tanh_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_minus
% 5.12/5.34 thf(fact_3006_tanh__minus,axiom,
% 5.12/5.34 ! [X: complex] :
% 5.12/5.34 ( ( tanh_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ ( tanh_complex @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % tanh_minus
% 5.12/5.34 thf(fact_3007_triangle__0,axiom,
% 5.12/5.34 ( ( nat_triangle @ zero_zero_nat )
% 5.12/5.34 = zero_zero_nat ) ).
% 5.12/5.34
% 5.12/5.34 % triangle_0
% 5.12/5.34 thf(fact_3008_mult__cancel__right2,axiom,
% 5.12/5.34 ! [A: complex,C: complex] :
% 5.12/5.34 ( ( ( times_times_complex @ A @ C )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_complex )
% 5.12/5.34 | ( A = one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right2
% 5.12/5.34 thf(fact_3009_mult__cancel__right2,axiom,
% 5.12/5.34 ! [A: real,C: real] :
% 5.12/5.34 ( ( ( times_times_real @ A @ C )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( A = one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right2
% 5.12/5.34 thf(fact_3010_mult__cancel__right2,axiom,
% 5.12/5.34 ! [A: rat,C: rat] :
% 5.12/5.34 ( ( ( times_times_rat @ A @ C )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( A = one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right2
% 5.12/5.34 thf(fact_3011_mult__cancel__right2,axiom,
% 5.12/5.34 ! [A: int,C: int] :
% 5.12/5.34 ( ( ( times_times_int @ A @ C )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( A = one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right2
% 5.12/5.34 thf(fact_3012_mult__cancel__right1,axiom,
% 5.12/5.34 ! [C: complex,B: complex] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_complex @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_complex )
% 5.12/5.34 | ( B = one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right1
% 5.12/5.34 thf(fact_3013_mult__cancel__right1,axiom,
% 5.12/5.34 ! [C: real,B: real] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_real @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( B = one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right1
% 5.12/5.34 thf(fact_3014_mult__cancel__right1,axiom,
% 5.12/5.34 ! [C: rat,B: rat] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_rat @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( B = one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right1
% 5.12/5.34 thf(fact_3015_mult__cancel__right1,axiom,
% 5.12/5.34 ! [C: int,B: int] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_int @ B @ C ) )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( B = one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_right1
% 5.12/5.34 thf(fact_3016_mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: complex,A: complex] :
% 5.12/5.34 ( ( ( times_times_complex @ C @ A )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_complex )
% 5.12/5.34 | ( A = one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left2
% 5.12/5.34 thf(fact_3017_mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: real,A: real] :
% 5.12/5.34 ( ( ( times_times_real @ C @ A )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( A = one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left2
% 5.12/5.34 thf(fact_3018_mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: rat,A: rat] :
% 5.12/5.34 ( ( ( times_times_rat @ C @ A )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( A = one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left2
% 5.12/5.34 thf(fact_3019_mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: int,A: int] :
% 5.12/5.34 ( ( ( times_times_int @ C @ A )
% 5.12/5.34 = C )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( A = one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left2
% 5.12/5.34 thf(fact_3020_mult__cancel__left1,axiom,
% 5.12/5.34 ! [C: complex,B: complex] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_complex @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_complex )
% 5.12/5.34 | ( B = one_one_complex ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left1
% 5.12/5.34 thf(fact_3021_mult__cancel__left1,axiom,
% 5.12/5.34 ! [C: real,B: real] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_real @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_real )
% 5.12/5.34 | ( B = one_one_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left1
% 5.12/5.34 thf(fact_3022_mult__cancel__left1,axiom,
% 5.12/5.34 ! [C: rat,B: rat] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_rat @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_rat )
% 5.12/5.34 | ( B = one_one_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left1
% 5.12/5.34 thf(fact_3023_mult__cancel__left1,axiom,
% 5.12/5.34 ! [C: int,B: int] :
% 5.12/5.34 ( ( C
% 5.12/5.34 = ( times_times_int @ C @ B ) )
% 5.12/5.34 = ( ( C = zero_zero_int )
% 5.12/5.34 | ( B = one_one_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_cancel_left1
% 5.12/5.34 thf(fact_3024_sum__squares__eq__zero__iff,axiom,
% 5.12/5.34 ! [X: real,Y: real] :
% 5.12/5.34 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.12/5.34 = zero_zero_real )
% 5.12/5.34 = ( ( X = zero_zero_real )
% 5.12/5.34 & ( Y = zero_zero_real ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % sum_squares_eq_zero_iff
% 5.12/5.34 thf(fact_3025_sum__squares__eq__zero__iff,axiom,
% 5.12/5.34 ! [X: rat,Y: rat] :
% 5.12/5.34 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.12/5.34 = zero_zero_rat )
% 5.12/5.34 = ( ( X = zero_zero_rat )
% 5.12/5.34 & ( Y = zero_zero_rat ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % sum_squares_eq_zero_iff
% 5.12/5.34 thf(fact_3026_sum__squares__eq__zero__iff,axiom,
% 5.12/5.34 ! [X: int,Y: int] :
% 5.12/5.34 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.12/5.34 = zero_zero_int )
% 5.12/5.34 = ( ( X = zero_zero_int )
% 5.12/5.34 & ( Y = zero_zero_int ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % sum_squares_eq_zero_iff
% 5.12/5.34 thf(fact_3027_mult__divide__mult__cancel__left__if,axiom,
% 5.12/5.34 ! [C: complex,A: complex,B: complex] :
% 5.12/5.34 ( ( ( C = zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.12/5.34 = zero_zero_complex ) )
% 5.12/5.34 & ( ( C != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_divide_mult_cancel_left_if
% 5.12/5.34 thf(fact_3028_mult__divide__mult__cancel__left__if,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( ( C = zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.34 = zero_zero_real ) )
% 5.12/5.34 & ( ( C != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.34 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_divide_mult_cancel_left_if
% 5.12/5.34 thf(fact_3029_mult__divide__mult__cancel__left__if,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( ( C = zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.34 = zero_zero_rat ) )
% 5.12/5.34 & ( ( C != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.34 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_divide_mult_cancel_left_if
% 5.12/5.34 thf(fact_3030_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [C: complex,A: complex,B: complex] :
% 5.12/5.34 ( ( C != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3031_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( C != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.34 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3032_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( C != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.34 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3033_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: complex,A: complex,B: complex] :
% 5.12/5.34 ( ( C != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left2
% 5.12/5.34 thf(fact_3034_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( C != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.12/5.34 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left2
% 5.12/5.34 thf(fact_3035_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( C != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.34 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_left2
% 5.12/5.34 thf(fact_3036_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [C: complex,A: complex,B: complex] :
% 5.12/5.34 ( ( C != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3037_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( C != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.34 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3038_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( C != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.34 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3039_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.12/5.34 ! [C: complex,A: complex,B: complex] :
% 5.12/5.34 ( ( C != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right2
% 5.12/5.34 thf(fact_3040_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.12/5.34 ! [C: real,A: real,B: real] :
% 5.12/5.34 ( ( C != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.12/5.34 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right2
% 5.12/5.34 thf(fact_3041_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.12/5.34 ! [C: rat,A: rat,B: rat] :
% 5.12/5.34 ( ( C != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.34 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_divide_mult_cancel_right2
% 5.12/5.34 thf(fact_3042_div__mult__mult1,axiom,
% 5.12/5.34 ! [C: nat,A: nat,B: nat] :
% 5.12/5.34 ( ( C != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.12/5.34 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult1
% 5.12/5.34 thf(fact_3043_div__mult__mult1,axiom,
% 5.12/5.34 ! [C: int,A: int,B: int] :
% 5.12/5.34 ( ( C != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.34 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult1
% 5.12/5.34 thf(fact_3044_div__mult__mult2,axiom,
% 5.12/5.34 ! [C: nat,A: nat,B: nat] :
% 5.12/5.34 ( ( C != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.12/5.34 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult2
% 5.12/5.34 thf(fact_3045_div__mult__mult2,axiom,
% 5.12/5.34 ! [C: int,A: int,B: int] :
% 5.12/5.34 ( ( C != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.34 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult2
% 5.12/5.34 thf(fact_3046_div__mult__mult1__if,axiom,
% 5.12/5.34 ! [C: nat,A: nat,B: nat] :
% 5.12/5.34 ( ( ( C = zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.12/5.34 = zero_zero_nat ) )
% 5.12/5.34 & ( ( C != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.12/5.34 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult1_if
% 5.12/5.34 thf(fact_3047_div__mult__mult1__if,axiom,
% 5.12/5.34 ! [C: int,A: int,B: int] :
% 5.12/5.34 ( ( ( C = zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.34 = zero_zero_int ) )
% 5.12/5.34 & ( ( C != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.34 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_mult1_if
% 5.12/5.34 thf(fact_3048_nonzero__mult__div__cancel__right,axiom,
% 5.12/5.34 ! [B: complex,A: complex] :
% 5.12/5.34 ( ( B != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.12/5.34 = A ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_right
% 5.12/5.34 thf(fact_3049_nonzero__mult__div__cancel__right,axiom,
% 5.12/5.34 ! [B: real,A: real] :
% 5.12/5.34 ( ( B != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.12/5.34 = A ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_right
% 5.12/5.34 thf(fact_3050_nonzero__mult__div__cancel__right,axiom,
% 5.12/5.34 ! [B: rat,A: rat] :
% 5.12/5.34 ( ( B != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.12/5.34 = A ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_right
% 5.12/5.34 thf(fact_3051_nonzero__mult__div__cancel__right,axiom,
% 5.12/5.34 ! [B: nat,A: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.12/5.34 = A ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_right
% 5.12/5.34 thf(fact_3052_nonzero__mult__div__cancel__right,axiom,
% 5.12/5.34 ! [B: int,A: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.12/5.34 = A ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_right
% 5.12/5.34 thf(fact_3053_nonzero__mult__div__cancel__left,axiom,
% 5.12/5.34 ! [A: complex,B: complex] :
% 5.12/5.34 ( ( A != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.12/5.34 = B ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_left
% 5.12/5.34 thf(fact_3054_nonzero__mult__div__cancel__left,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( A != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.12/5.34 = B ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_left
% 5.12/5.34 thf(fact_3055_nonzero__mult__div__cancel__left,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( A != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.12/5.34 = B ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_left
% 5.12/5.34 thf(fact_3056_nonzero__mult__div__cancel__left,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( A != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.12/5.34 = B ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_left
% 5.12/5.34 thf(fact_3057_nonzero__mult__div__cancel__left,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( A != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.12/5.34 = B ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_mult_div_cancel_left
% 5.12/5.34 thf(fact_3058_mult__minus1__right,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( times_times_int @ Z2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.34 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1_right
% 5.12/5.34 thf(fact_3059_mult__minus1__right,axiom,
% 5.12/5.34 ! [Z2: real] :
% 5.12/5.34 ( ( times_times_real @ Z2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.34 = ( uminus_uminus_real @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1_right
% 5.12/5.34 thf(fact_3060_mult__minus1__right,axiom,
% 5.12/5.34 ! [Z2: complex] :
% 5.12/5.34 ( ( times_times_complex @ Z2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1_right
% 5.12/5.34 thf(fact_3061_mult__minus1__right,axiom,
% 5.12/5.34 ! [Z2: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ Z2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.34 = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1_right
% 5.12/5.34 thf(fact_3062_mult__minus1__right,axiom,
% 5.12/5.34 ! [Z2: rat] :
% 5.12/5.34 ( ( times_times_rat @ Z2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.34 = ( uminus_uminus_rat @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1_right
% 5.12/5.34 thf(fact_3063_mult__minus1,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z2 )
% 5.12/5.34 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1
% 5.12/5.34 thf(fact_3064_mult__minus1,axiom,
% 5.12/5.34 ! [Z2: real] :
% 5.12/5.34 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z2 )
% 5.12/5.34 = ( uminus_uminus_real @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1
% 5.12/5.34 thf(fact_3065_mult__minus1,axiom,
% 5.12/5.34 ! [Z2: complex] :
% 5.12/5.34 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z2 )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1
% 5.12/5.34 thf(fact_3066_mult__minus1,axiom,
% 5.12/5.34 ! [Z2: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z2 )
% 5.12/5.34 = ( uminus1351360451143612070nteger @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1
% 5.12/5.34 thf(fact_3067_mult__minus1,axiom,
% 5.12/5.34 ! [Z2: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z2 )
% 5.12/5.34 = ( uminus_uminus_rat @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult_minus1
% 5.12/5.34 thf(fact_3068_mod__mult__self1__is__0,axiom,
% 5.12/5.34 ! [B: int,A: int] :
% 5.12/5.34 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self1_is_0
% 5.12/5.34 thf(fact_3069_mod__mult__self1__is__0,axiom,
% 5.12/5.34 ! [B: nat,A: nat] :
% 5.12/5.34 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.12/5.34 = zero_zero_nat ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self1_is_0
% 5.12/5.34 thf(fact_3070_mod__mult__self1__is__0,axiom,
% 5.12/5.34 ! [B: code_integer,A: code_integer] :
% 5.12/5.34 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.12/5.34 = zero_z3403309356797280102nteger ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self1_is_0
% 5.12/5.34 thf(fact_3071_mod__mult__self1__is__0,axiom,
% 5.12/5.34 ! [B: code_natural,A: code_natural] :
% 5.12/5.34 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 5.12/5.34 = zero_z2226904508553997617atural ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self1_is_0
% 5.12/5.34 thf(fact_3072_mod__mult__self2__is__0,axiom,
% 5.12/5.34 ! [A: int,B: int] :
% 5.12/5.34 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self2_is_0
% 5.12/5.34 thf(fact_3073_mod__mult__self2__is__0,axiom,
% 5.12/5.34 ! [A: nat,B: nat] :
% 5.12/5.34 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.12/5.34 = zero_zero_nat ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self2_is_0
% 5.12/5.34 thf(fact_3074_mod__mult__self2__is__0,axiom,
% 5.12/5.34 ! [A: code_integer,B: code_integer] :
% 5.12/5.34 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.12/5.34 = zero_z3403309356797280102nteger ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self2_is_0
% 5.12/5.34 thf(fact_3075_mod__mult__self2__is__0,axiom,
% 5.12/5.34 ! [A: code_natural,B: code_natural] :
% 5.12/5.34 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 5.12/5.34 = zero_z2226904508553997617atural ) ).
% 5.12/5.34
% 5.12/5.34 % mod_mult_self2_is_0
% 5.12/5.34 thf(fact_3076_of__int__eq__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_int @ Z2 )
% 5.12/5.34 = zero_zero_int )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_0_iff
% 5.12/5.34 thf(fact_3077_of__int__eq__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_real @ Z2 )
% 5.12/5.34 = zero_zero_real )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_0_iff
% 5.12/5.34 thf(fact_3078_of__int__eq__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_rat @ Z2 )
% 5.12/5.34 = zero_zero_rat )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_0_iff
% 5.12/5.34 thf(fact_3079_of__int__0__eq__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( zero_zero_int
% 5.12/5.34 = ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_eq_iff
% 5.12/5.34 thf(fact_3080_of__int__0__eq__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( zero_zero_real
% 5.12/5.34 = ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_eq_iff
% 5.12/5.34 thf(fact_3081_of__int__0__eq__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( zero_zero_rat
% 5.12/5.34 = ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( Z2 = zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_eq_iff
% 5.12/5.34 thf(fact_3082_of__int__0,axiom,
% 5.12/5.34 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.12/5.34 = zero_zero_int ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0
% 5.12/5.34 thf(fact_3083_of__int__0,axiom,
% 5.12/5.34 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.12/5.34 = zero_zero_real ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0
% 5.12/5.34 thf(fact_3084_of__int__0,axiom,
% 5.12/5.34 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.12/5.34 = zero_zero_rat ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0
% 5.12/5.34 thf(fact_3085_of__int__le__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_iff
% 5.12/5.34 thf(fact_3086_of__int__le__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_iff
% 5.12/5.34 thf(fact_3087_of__int__le__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_iff
% 5.12/5.34 thf(fact_3088_of__int__less__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_iff
% 5.12/5.34 thf(fact_3089_of__int__less__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_iff
% 5.12/5.34 thf(fact_3090_of__int__less__iff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ W @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_iff
% 5.12/5.34 thf(fact_3091_of__int__eq__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_17405671764205052669omplex @ Z2 )
% 5.12/5.34 = one_one_complex )
% 5.12/5.34 = ( Z2 = one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_1_iff
% 5.12/5.34 thf(fact_3092_of__int__eq__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_int @ Z2 )
% 5.12/5.34 = one_one_int )
% 5.12/5.34 = ( Z2 = one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_1_iff
% 5.12/5.34 thf(fact_3093_of__int__eq__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_real @ Z2 )
% 5.12/5.34 = one_one_real )
% 5.12/5.34 = ( Z2 = one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_1_iff
% 5.12/5.34 thf(fact_3094_of__int__eq__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ( ring_1_of_int_rat @ Z2 )
% 5.12/5.34 = one_one_rat )
% 5.12/5.34 = ( Z2 = one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_1_iff
% 5.12/5.34 thf(fact_3095_of__int__1,axiom,
% 5.12/5.34 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.12/5.34 = one_one_complex ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1
% 5.12/5.34 thf(fact_3096_of__int__1,axiom,
% 5.12/5.34 ( ( ring_1_of_int_int @ one_one_int )
% 5.12/5.34 = one_one_int ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1
% 5.12/5.34 thf(fact_3097_of__int__1,axiom,
% 5.12/5.34 ( ( ring_1_of_int_real @ one_one_int )
% 5.12/5.34 = one_one_real ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1
% 5.12/5.34 thf(fact_3098_of__int__1,axiom,
% 5.12/5.34 ( ( ring_1_of_int_rat @ one_one_int )
% 5.12/5.34 = one_one_rat ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1
% 5.12/5.34 thf(fact_3099_of__int__mult,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z2 ) )
% 5.12/5.34 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_mult
% 5.12/5.34 thf(fact_3100_of__int__mult,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z2 ) )
% 5.12/5.34 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_mult
% 5.12/5.34 thf(fact_3101_of__int__mult,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z2 ) )
% 5.12/5.34 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_mult
% 5.12/5.34 thf(fact_3102_of__int__add,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z2 ) )
% 5.12/5.34 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_add
% 5.12/5.34 thf(fact_3103_of__int__add,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z2 ) )
% 5.12/5.34 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_add
% 5.12/5.34 thf(fact_3104_of__int__add,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z2 ) )
% 5.12/5.34 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_add
% 5.12/5.34 thf(fact_3105_of__int__minus,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z2 ) )
% 5.12/5.34 = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_minus
% 5.12/5.34 thf(fact_3106_of__int__minus,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z2 ) )
% 5.12/5.34 = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_minus
% 5.12/5.34 thf(fact_3107_of__int__minus,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z2 ) )
% 5.12/5.34 = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_minus
% 5.12/5.34 thf(fact_3108_of__int__minus,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z2 ) )
% 5.12/5.34 = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_minus
% 5.12/5.34 thf(fact_3109_of__int__minus,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z2 ) )
% 5.12/5.34 = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_minus
% 5.12/5.34 thf(fact_3110_of__int__diff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z2 ) )
% 5.12/5.34 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_diff
% 5.12/5.34 thf(fact_3111_of__int__diff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z2 ) )
% 5.12/5.34 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_diff
% 5.12/5.34 thf(fact_3112_of__int__diff,axiom,
% 5.12/5.34 ! [W: int,Z2: int] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z2 ) )
% 5.12/5.34 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_diff
% 5.12/5.34 thf(fact_3113_of__int__of__nat__eq,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( ring_17405671764205052669omplex @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.34 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_of_nat_eq
% 5.12/5.34 thf(fact_3114_of__int__of__nat__eq,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.34 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_of_nat_eq
% 5.12/5.34 thf(fact_3115_of__int__of__nat__eq,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.34 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_of_nat_eq
% 5.12/5.34 thf(fact_3116_of__int__of__nat__eq,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.34 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_of_nat_eq
% 5.12/5.34 thf(fact_3117_of__int__abs,axiom,
% 5.12/5.34 ! [X: int] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
% 5.12/5.34 = ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_abs
% 5.12/5.34 thf(fact_3118_of__int__abs,axiom,
% 5.12/5.34 ! [X: int] :
% 5.12/5.34 ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X ) )
% 5.12/5.34 = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_abs
% 5.12/5.34 thf(fact_3119_of__int__abs,axiom,
% 5.12/5.34 ! [X: int] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
% 5.12/5.34 = ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_abs
% 5.12/5.34 thf(fact_3120_of__int__abs,axiom,
% 5.12/5.34 ! [X: int] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( abs_abs_int @ X ) )
% 5.12/5.34 = ( abs_abs_rat @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_abs
% 5.12/5.34 thf(fact_3121_of__int__power,axiom,
% 5.12/5.34 ! [Z2: int,N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_rat @ ( power_power_int @ Z2 @ N ) )
% 5.12/5.34 = ( power_power_rat @ ( ring_1_of_int_rat @ Z2 ) @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power
% 5.12/5.34 thf(fact_3122_of__int__power,axiom,
% 5.12/5.34 ! [Z2: int,N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_int @ ( power_power_int @ Z2 @ N ) )
% 5.12/5.34 = ( power_power_int @ ( ring_1_of_int_int @ Z2 ) @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power
% 5.12/5.34 thf(fact_3123_of__int__power,axiom,
% 5.12/5.34 ! [Z2: int,N: nat] :
% 5.12/5.34 ( ( ring_1_of_int_real @ ( power_power_int @ Z2 @ N ) )
% 5.12/5.34 = ( power_power_real @ ( ring_1_of_int_real @ Z2 ) @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power
% 5.12/5.34 thf(fact_3124_of__int__power,axiom,
% 5.12/5.34 ! [Z2: int,N: nat] :
% 5.12/5.34 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z2 @ N ) )
% 5.12/5.34 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z2 ) @ N ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power
% 5.12/5.34 thf(fact_3125_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.12/5.34 = ( ring_1_of_int_rat @ X ) )
% 5.12/5.34 = ( ( power_power_int @ B @ W )
% 5.12/5.34 = X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3126_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.12/5.34 = ( ring_1_of_int_int @ X ) )
% 5.12/5.34 = ( ( power_power_int @ B @ W )
% 5.12/5.34 = X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3127_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.12/5.34 = ( ring_1_of_int_real @ X ) )
% 5.12/5.34 = ( ( power_power_int @ B @ W )
% 5.12/5.34 = X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3128_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.12/5.34 = ( ring_17405671764205052669omplex @ X ) )
% 5.12/5.34 = ( ( power_power_int @ B @ W )
% 5.12/5.34 = X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_eq_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3129_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ( ring_1_of_int_rat @ X )
% 5.12/5.34 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.12/5.34 = ( X
% 5.12/5.34 = ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_eq_of_int_cancel_iff
% 5.12/5.34 thf(fact_3130_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ( ring_1_of_int_int @ X )
% 5.12/5.34 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.12/5.34 = ( X
% 5.12/5.34 = ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_eq_of_int_cancel_iff
% 5.12/5.34 thf(fact_3131_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ( ring_1_of_int_real @ X )
% 5.12/5.34 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.12/5.34 = ( X
% 5.12/5.34 = ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_eq_of_int_cancel_iff
% 5.12/5.34 thf(fact_3132_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ( ring_17405671764205052669omplex @ X )
% 5.12/5.34 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.12/5.34 = ( X
% 5.12/5.34 = ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_eq_of_int_cancel_iff
% 5.12/5.34 thf(fact_3133_nonzero__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [B: complex,A: complex] :
% 5.12/5.34 ( ( B != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3134_nonzero__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [B: real,A: real] :
% 5.12/5.34 ( ( B != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.12/5.34 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3135_nonzero__divide__mult__cancel__right,axiom,
% 5.12/5.34 ! [B: rat,A: rat] :
% 5.12/5.34 ( ( B != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.12/5.34 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_right
% 5.12/5.34 thf(fact_3136_nonzero__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [A: complex,B: complex] :
% 5.12/5.34 ( ( A != zero_zero_complex )
% 5.12/5.34 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.12/5.34 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3137_nonzero__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [A: real,B: real] :
% 5.12/5.34 ( ( A != zero_zero_real )
% 5.12/5.34 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.12/5.34 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3138_nonzero__divide__mult__cancel__left,axiom,
% 5.12/5.34 ! [A: rat,B: rat] :
% 5.12/5.34 ( ( A != zero_zero_rat )
% 5.12/5.34 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.12/5.34 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % nonzero_divide_mult_cancel_left
% 5.12/5.34 thf(fact_3139_div__mult__self1,axiom,
% 5.12/5.34 ! [B: nat,A: nat,C: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self1
% 5.12/5.34 thf(fact_3140_div__mult__self1,axiom,
% 5.12/5.34 ! [B: int,A: int,C: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.12/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self1
% 5.12/5.34 thf(fact_3141_div__mult__self2,axiom,
% 5.12/5.34 ! [B: nat,A: nat,C: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self2
% 5.12/5.34 thf(fact_3142_div__mult__self2,axiom,
% 5.12/5.34 ! [B: int,A: int,C: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.12/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self2
% 5.12/5.34 thf(fact_3143_div__mult__self3,axiom,
% 5.12/5.34 ! [B: nat,C: nat,A: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self3
% 5.12/5.34 thf(fact_3144_div__mult__self3,axiom,
% 5.12/5.34 ! [B: int,C: int,A: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.12/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self3
% 5.12/5.34 thf(fact_3145_div__mult__self4,axiom,
% 5.12/5.34 ! [B: nat,C: nat,A: nat] :
% 5.12/5.34 ( ( B != zero_zero_nat )
% 5.12/5.34 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.12/5.34 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self4
% 5.12/5.34 thf(fact_3146_div__mult__self4,axiom,
% 5.12/5.34 ! [B: int,C: int,A: int] :
% 5.12/5.34 ( ( B != zero_zero_int )
% 5.12/5.34 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.12/5.34 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % div_mult_self4
% 5.12/5.34 thf(fact_3147_left__minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat,A: int] :
% 5.12/5.34 ( ( 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 ) )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % left_minus_one_mult_self
% 5.12/5.34 thf(fact_3148_left__minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat,A: real] :
% 5.12/5.34 ( ( 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 ) )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % left_minus_one_mult_self
% 5.12/5.34 thf(fact_3149_left__minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat,A: complex] :
% 5.12/5.34 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % left_minus_one_mult_self
% 5.12/5.34 thf(fact_3150_left__minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat,A: code_integer] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % left_minus_one_mult_self
% 5.12/5.34 thf(fact_3151_left__minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat,A: rat] :
% 5.12/5.34 ( ( 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 ) )
% 5.12/5.34 = A ) ).
% 5.12/5.34
% 5.12/5.34 % left_minus_one_mult_self
% 5.12/5.34 thf(fact_3152_minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.12/5.34 = one_one_int ) ).
% 5.12/5.34
% 5.12/5.34 % minus_one_mult_self
% 5.12/5.34 thf(fact_3153_minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.12/5.34 = one_one_real ) ).
% 5.12/5.34
% 5.12/5.34 % minus_one_mult_self
% 5.12/5.34 thf(fact_3154_minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.12/5.34 = one_one_complex ) ).
% 5.12/5.34
% 5.12/5.34 % minus_one_mult_self
% 5.12/5.34 thf(fact_3155_minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.12/5.34 = one_one_Code_integer ) ).
% 5.12/5.34
% 5.12/5.34 % minus_one_mult_self
% 5.12/5.34 thf(fact_3156_minus__one__mult__self,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.12/5.34 = one_one_rat ) ).
% 5.12/5.34
% 5.12/5.34 % minus_one_mult_self
% 5.12/5.34 thf(fact_3157_ceiling__add__of__int,axiom,
% 5.12/5.34 ! [X: rat,Z2: int] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) )
% 5.12/5.34 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_of_int
% 5.12/5.34 thf(fact_3158_ceiling__add__of__int,axiom,
% 5.12/5.34 ! [X: real,Z2: int] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
% 5.12/5.34 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_add_of_int
% 5.12/5.34 thf(fact_3159_ceiling__diff__of__int,axiom,
% 5.12/5.34 ! [X: rat,Z2: int] :
% 5.12/5.34 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) )
% 5.12/5.34 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_diff_of_int
% 5.12/5.34 thf(fact_3160_ceiling__diff__of__int,axiom,
% 5.12/5.34 ! [X: real,Z2: int] :
% 5.12/5.34 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
% 5.12/5.34 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % ceiling_diff_of_int
% 5.12/5.34 thf(fact_3161_of__int__le__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_0_iff
% 5.12/5.34 thf(fact_3162_of__int__le__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_0_iff
% 5.12/5.34 thf(fact_3163_of__int__le__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_0_iff
% 5.12/5.34 thf(fact_3164_of__int__0__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_le_iff
% 5.12/5.34 thf(fact_3165_of__int__0__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_le_iff
% 5.12/5.34 thf(fact_3166_of__int__0__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_le_iff
% 5.12/5.34 thf(fact_3167_of__int__less__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ zero_zero_real )
% 5.12/5.34 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_0_iff
% 5.12/5.34 thf(fact_3168_of__int__less__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ zero_zero_rat )
% 5.12/5.34 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_0_iff
% 5.12/5.34 thf(fact_3169_of__int__less__0__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 5.12/5.34 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_0_iff
% 5.12/5.34 thf(fact_3170_of__int__0__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_less_iff
% 5.12/5.34 thf(fact_3171_of__int__0__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_less_iff
% 5.12/5.34 thf(fact_3172_of__int__0__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_0_less_iff
% 5.12/5.34 thf(fact_3173_of__int__le__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_1_iff
% 5.12/5.34 thf(fact_3174_of__int__le__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_1_iff
% 5.12/5.34 thf(fact_3175_of__int__le__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 5.12/5.34 = ( ord_less_eq_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_1_iff
% 5.12/5.34 thf(fact_3176_of__int__1__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_le_iff
% 5.12/5.34 thf(fact_3177_of__int__1__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_le_iff
% 5.12/5.34 thf(fact_3178_of__int__1__le__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_eq_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_le_iff
% 5.12/5.34 thf(fact_3179_of__int__less__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real )
% 5.12/5.34 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_1_iff
% 5.12/5.34 thf(fact_3180_of__int__less__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat )
% 5.12/5.34 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_1_iff
% 5.12/5.34 thf(fact_3181_of__int__less__1__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 5.12/5.34 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_1_iff
% 5.12/5.34 thf(fact_3182_of__int__1__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_less_iff
% 5.12/5.34 thf(fact_3183_of__int__1__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_less_iff
% 5.12/5.34 thf(fact_3184_of__int__1__less__iff,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.34 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_1_less_iff
% 5.12/5.34 thf(fact_3185_of__int__le__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.12/5.34 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3186_of__int__le__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.12/5.34 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3187_of__int__le__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.12/5.34 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_le_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3188_of__int__power__le__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_le_of_int_cancel_iff
% 5.12/5.34 thf(fact_3189_of__int__power__le__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_le_of_int_cancel_iff
% 5.12/5.34 thf(fact_3190_of__int__power__le__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_le_of_int_cancel_iff
% 5.12/5.34 thf(fact_3191_of__int__power__less__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_less_of_int_cancel_iff
% 5.12/5.34 thf(fact_3192_of__int__power__less__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_less_of_int_cancel_iff
% 5.12/5.34 thf(fact_3193_of__int__power__less__of__int__cancel__iff,axiom,
% 5.12/5.34 ! [X: int,B: int,W: nat] :
% 5.12/5.34 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.12/5.34 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_power_less_of_int_cancel_iff
% 5.12/5.34 thf(fact_3194_of__int__less__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.12/5.34 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3195_of__int__less__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.12/5.34 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3196_of__int__less__of__int__power__cancel__iff,axiom,
% 5.12/5.34 ! [B: int,W: nat,X: int] :
% 5.12/5.34 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.12/5.34 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_int_less_of_int_power_cancel_iff
% 5.12/5.34 thf(fact_3197_of__nat__nat,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z2 ) )
% 5.12/5.34 = ( ring_17405671764205052669omplex @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_nat
% 5.12/5.34 thf(fact_3198_of__nat__nat,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z2 ) )
% 5.12/5.34 = ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_nat
% 5.12/5.34 thf(fact_3199_of__nat__nat,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z2 ) )
% 5.12/5.34 = ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_nat
% 5.12/5.34 thf(fact_3200_of__nat__nat,axiom,
% 5.12/5.34 ! [Z2: int] :
% 5.12/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.34 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z2 ) )
% 5.12/5.34 = ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % of_nat_nat
% 5.12/5.34 thf(fact_3201_neq__if__length__neq,axiom,
% 5.12/5.34 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.12/5.34 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.12/5.34 != ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.12/5.34 => ( Xs != Ys2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % neq_if_length_neq
% 5.12/5.34 thf(fact_3202_neq__if__length__neq,axiom,
% 5.12/5.34 ! [Xs: list_o,Ys2: list_o] :
% 5.12/5.34 ( ( ( size_size_list_o @ Xs )
% 5.12/5.34 != ( size_size_list_o @ Ys2 ) )
% 5.12/5.34 => ( Xs != Ys2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % neq_if_length_neq
% 5.12/5.34 thf(fact_3203_neq__if__length__neq,axiom,
% 5.12/5.34 ! [Xs: list_nat,Ys2: list_nat] :
% 5.12/5.34 ( ( ( size_size_list_nat @ Xs )
% 5.12/5.34 != ( size_size_list_nat @ Ys2 ) )
% 5.12/5.34 => ( Xs != Ys2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % neq_if_length_neq
% 5.12/5.34 thf(fact_3204_neq__if__length__neq,axiom,
% 5.12/5.34 ! [Xs: list_int,Ys2: list_int] :
% 5.12/5.34 ( ( ( size_size_list_int @ Xs )
% 5.12/5.34 != ( size_size_list_int @ Ys2 ) )
% 5.12/5.34 => ( Xs != Ys2 ) ) ).
% 5.12/5.34
% 5.12/5.34 % neq_if_length_neq
% 5.12/5.34 thf(fact_3205_Ex__list__of__length,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ? [Xs2: list_VEBT_VEBT] :
% 5.12/5.34 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.12/5.34 = N ) ).
% 5.12/5.34
% 5.12/5.34 % Ex_list_of_length
% 5.12/5.34 thf(fact_3206_Ex__list__of__length,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ? [Xs2: list_o] :
% 5.12/5.34 ( ( size_size_list_o @ Xs2 )
% 5.12/5.34 = N ) ).
% 5.12/5.34
% 5.12/5.34 % Ex_list_of_length
% 5.12/5.34 thf(fact_3207_Ex__list__of__length,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ? [Xs2: list_nat] :
% 5.12/5.34 ( ( size_size_list_nat @ Xs2 )
% 5.12/5.34 = N ) ).
% 5.12/5.34
% 5.12/5.34 % Ex_list_of_length
% 5.12/5.34 thf(fact_3208_Ex__list__of__length,axiom,
% 5.12/5.34 ! [N: nat] :
% 5.12/5.34 ? [Xs2: list_int] :
% 5.12/5.34 ( ( size_size_list_int @ Xs2 )
% 5.12/5.34 = N ) ).
% 5.12/5.34
% 5.12/5.34 % Ex_list_of_length
% 5.12/5.34 thf(fact_3209_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ab_semigroup_mult_class.mult_ac(1)
% 5.12/5.34 thf(fact_3210_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ab_semigroup_mult_class.mult_ac(1)
% 5.12/5.34 thf(fact_3211_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.12/5.34 ! [A: nat,B: nat,C: nat] :
% 5.12/5.34 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ab_semigroup_mult_class.mult_ac(1)
% 5.12/5.34 thf(fact_3212_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.12/5.34 ! [A: int,B: int,C: int] :
% 5.12/5.34 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % ab_semigroup_mult_class.mult_ac(1)
% 5.12/5.34 thf(fact_3213_mult_Oassoc,axiom,
% 5.12/5.34 ! [A: real,B: real,C: real] :
% 5.12/5.34 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.assoc
% 5.12/5.34 thf(fact_3214_mult_Oassoc,axiom,
% 5.12/5.34 ! [A: rat,B: rat,C: rat] :
% 5.12/5.34 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.assoc
% 5.12/5.34 thf(fact_3215_mult_Oassoc,axiom,
% 5.12/5.34 ! [A: nat,B: nat,C: nat] :
% 5.12/5.34 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.assoc
% 5.12/5.34 thf(fact_3216_mult_Oassoc,axiom,
% 5.12/5.34 ! [A: int,B: int,C: int] :
% 5.12/5.34 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.34 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.assoc
% 5.12/5.34 thf(fact_3217_mult_Ocommute,axiom,
% 5.12/5.34 ( times_times_real
% 5.12/5.34 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.commute
% 5.12/5.34 thf(fact_3218_mult_Ocommute,axiom,
% 5.12/5.34 ( times_times_rat
% 5.12/5.34 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.commute
% 5.12/5.34 thf(fact_3219_mult_Ocommute,axiom,
% 5.12/5.34 ( times_times_nat
% 5.12/5.34 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.12/5.34
% 5.12/5.34 % mult.commute
% 5.12/5.35 thf(fact_3220_mult_Ocommute,axiom,
% 5.12/5.35 ( times_times_int
% 5.12/5.35 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult.commute
% 5.12/5.35 thf(fact_3221_mult_Oleft__commute,axiom,
% 5.12/5.35 ! [B: real,A: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.12/5.35 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult.left_commute
% 5.12/5.35 thf(fact_3222_mult_Oleft__commute,axiom,
% 5.12/5.35 ! [B: rat,A: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.12/5.35 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult.left_commute
% 5.12/5.35 thf(fact_3223_mult_Oleft__commute,axiom,
% 5.12/5.35 ! [B: nat,A: nat,C: nat] :
% 5.12/5.35 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.12/5.35 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult.left_commute
% 5.12/5.35 thf(fact_3224_mult_Oleft__commute,axiom,
% 5.12/5.35 ! [B: int,A: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.12/5.35 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult.left_commute
% 5.12/5.35 thf(fact_3225_mult__of__int__commute,axiom,
% 5.12/5.35 ! [X: int,Y: real] :
% 5.12/5.35 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 5.12/5.35 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_int_commute
% 5.12/5.35 thf(fact_3226_mult__of__int__commute,axiom,
% 5.12/5.35 ! [X: int,Y: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 5.12/5.35 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_int_commute
% 5.12/5.35 thf(fact_3227_mult__of__int__commute,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 5.12/5.35 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_int_commute
% 5.12/5.35 thf(fact_3228_ex__le__of__int,axiom,
% 5.12/5.35 ! [X: real] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ex_le_of_int
% 5.12/5.35 thf(fact_3229_ex__le__of__int,axiom,
% 5.12/5.35 ! [X: rat] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ex_le_of_int
% 5.12/5.35 thf(fact_3230_ex__of__int__less,axiom,
% 5.12/5.35 ! [X: real] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z4 ) @ X ) ).
% 5.12/5.35
% 5.12/5.35 % ex_of_int_less
% 5.12/5.35 thf(fact_3231_ex__of__int__less,axiom,
% 5.12/5.35 ! [X: rat] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z4 ) @ X ) ).
% 5.12/5.35
% 5.12/5.35 % ex_of_int_less
% 5.12/5.35 thf(fact_3232_ex__less__of__int,axiom,
% 5.12/5.35 ! [X: real] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ex_less_of_int
% 5.12/5.35 thf(fact_3233_ex__less__of__int,axiom,
% 5.12/5.35 ! [X: rat] :
% 5.12/5.35 ? [Z4: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ex_less_of_int
% 5.12/5.35 thf(fact_3234_mult__right__cancel,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( ( times_times_real @ A @ C )
% 5.12/5.35 = ( times_times_real @ B @ C ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_cancel
% 5.12/5.35 thf(fact_3235_mult__right__cancel,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( ( times_times_rat @ A @ C )
% 5.12/5.35 = ( times_times_rat @ B @ C ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_cancel
% 5.12/5.35 thf(fact_3236_mult__right__cancel,axiom,
% 5.12/5.35 ! [C: nat,A: nat,B: nat] :
% 5.12/5.35 ( ( C != zero_zero_nat )
% 5.12/5.35 => ( ( ( times_times_nat @ A @ C )
% 5.12/5.35 = ( times_times_nat @ B @ C ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_cancel
% 5.12/5.35 thf(fact_3237_mult__right__cancel,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( C != zero_zero_int )
% 5.12/5.35 => ( ( ( times_times_int @ A @ C )
% 5.12/5.35 = ( times_times_int @ B @ C ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_cancel
% 5.12/5.35 thf(fact_3238_mult__left__cancel,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( ( times_times_real @ C @ A )
% 5.12/5.35 = ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_cancel
% 5.12/5.35 thf(fact_3239_mult__left__cancel,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( ( times_times_rat @ C @ A )
% 5.12/5.35 = ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_cancel
% 5.12/5.35 thf(fact_3240_mult__left__cancel,axiom,
% 5.12/5.35 ! [C: nat,A: nat,B: nat] :
% 5.12/5.35 ( ( C != zero_zero_nat )
% 5.12/5.35 => ( ( ( times_times_nat @ C @ A )
% 5.12/5.35 = ( times_times_nat @ C @ B ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_cancel
% 5.12/5.35 thf(fact_3241_mult__left__cancel,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( C != zero_zero_int )
% 5.12/5.35 => ( ( ( times_times_int @ C @ A )
% 5.12/5.35 = ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( A = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_cancel
% 5.12/5.35 thf(fact_3242_no__zero__divisors,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( A != zero_zero_real )
% 5.12/5.35 => ( ( B != zero_zero_real )
% 5.12/5.35 => ( ( times_times_real @ A @ B )
% 5.12/5.35 != zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % no_zero_divisors
% 5.12/5.35 thf(fact_3243_no__zero__divisors,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( A != zero_zero_rat )
% 5.12/5.35 => ( ( B != zero_zero_rat )
% 5.12/5.35 => ( ( times_times_rat @ A @ B )
% 5.12/5.35 != zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % no_zero_divisors
% 5.12/5.35 thf(fact_3244_no__zero__divisors,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( A != zero_zero_nat )
% 5.12/5.35 => ( ( B != zero_zero_nat )
% 5.12/5.35 => ( ( times_times_nat @ A @ B )
% 5.12/5.35 != zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % no_zero_divisors
% 5.12/5.35 thf(fact_3245_no__zero__divisors,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( A != zero_zero_int )
% 5.12/5.35 => ( ( B != zero_zero_int )
% 5.12/5.35 => ( ( times_times_int @ A @ B )
% 5.12/5.35 != zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % no_zero_divisors
% 5.12/5.35 thf(fact_3246_divisors__zero,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ( times_times_real @ A @ B )
% 5.12/5.35 = zero_zero_real )
% 5.12/5.35 => ( ( A = zero_zero_real )
% 5.12/5.35 | ( B = zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divisors_zero
% 5.12/5.35 thf(fact_3247_divisors__zero,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ( times_times_rat @ A @ B )
% 5.12/5.35 = zero_zero_rat )
% 5.12/5.35 => ( ( A = zero_zero_rat )
% 5.12/5.35 | ( B = zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divisors_zero
% 5.12/5.35 thf(fact_3248_divisors__zero,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ( times_times_nat @ A @ B )
% 5.12/5.35 = zero_zero_nat )
% 5.12/5.35 => ( ( A = zero_zero_nat )
% 5.12/5.35 | ( B = zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divisors_zero
% 5.12/5.35 thf(fact_3249_divisors__zero,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ( times_times_int @ A @ B )
% 5.12/5.35 = zero_zero_int )
% 5.12/5.35 => ( ( A = zero_zero_int )
% 5.12/5.35 | ( B = zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divisors_zero
% 5.12/5.35 thf(fact_3250_mult__not__zero,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ( times_times_real @ A @ B )
% 5.12/5.35 != zero_zero_real )
% 5.12/5.35 => ( ( A != zero_zero_real )
% 5.12/5.35 & ( B != zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_not_zero
% 5.12/5.35 thf(fact_3251_mult__not__zero,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ( times_times_rat @ A @ B )
% 5.12/5.35 != zero_zero_rat )
% 5.12/5.35 => ( ( A != zero_zero_rat )
% 5.12/5.35 & ( B != zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_not_zero
% 5.12/5.35 thf(fact_3252_mult__not__zero,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ( times_times_nat @ A @ B )
% 5.12/5.35 != zero_zero_nat )
% 5.12/5.35 => ( ( A != zero_zero_nat )
% 5.12/5.35 & ( B != zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_not_zero
% 5.12/5.35 thf(fact_3253_mult__not__zero,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ( times_times_int @ A @ B )
% 5.12/5.35 != zero_zero_int )
% 5.12/5.35 => ( ( A != zero_zero_int )
% 5.12/5.35 & ( B != zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_not_zero
% 5.12/5.35 thf(fact_3254_comm__monoid__mult__class_Omult__1,axiom,
% 5.12/5.35 ! [A: complex] :
% 5.12/5.35 ( ( times_times_complex @ one_one_complex @ A )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % comm_monoid_mult_class.mult_1
% 5.12/5.35 thf(fact_3255_comm__monoid__mult__class_Omult__1,axiom,
% 5.12/5.35 ! [A: real] :
% 5.12/5.35 ( ( times_times_real @ one_one_real @ A )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % comm_monoid_mult_class.mult_1
% 5.12/5.35 thf(fact_3256_comm__monoid__mult__class_Omult__1,axiom,
% 5.12/5.35 ! [A: rat] :
% 5.12/5.35 ( ( times_times_rat @ one_one_rat @ A )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % comm_monoid_mult_class.mult_1
% 5.12/5.35 thf(fact_3257_comm__monoid__mult__class_Omult__1,axiom,
% 5.12/5.35 ! [A: nat] :
% 5.12/5.35 ( ( times_times_nat @ one_one_nat @ A )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % comm_monoid_mult_class.mult_1
% 5.12/5.35 thf(fact_3258_comm__monoid__mult__class_Omult__1,axiom,
% 5.12/5.35 ! [A: int] :
% 5.12/5.35 ( ( times_times_int @ one_one_int @ A )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % comm_monoid_mult_class.mult_1
% 5.12/5.35 thf(fact_3259_mult_Ocomm__neutral,axiom,
% 5.12/5.35 ! [A: complex] :
% 5.12/5.35 ( ( times_times_complex @ A @ one_one_complex )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % mult.comm_neutral
% 5.12/5.35 thf(fact_3260_mult_Ocomm__neutral,axiom,
% 5.12/5.35 ! [A: real] :
% 5.12/5.35 ( ( times_times_real @ A @ one_one_real )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % mult.comm_neutral
% 5.12/5.35 thf(fact_3261_mult_Ocomm__neutral,axiom,
% 5.12/5.35 ! [A: rat] :
% 5.12/5.35 ( ( times_times_rat @ A @ one_one_rat )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % mult.comm_neutral
% 5.12/5.35 thf(fact_3262_mult_Ocomm__neutral,axiom,
% 5.12/5.35 ! [A: nat] :
% 5.12/5.35 ( ( times_times_nat @ A @ one_one_nat )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % mult.comm_neutral
% 5.12/5.35 thf(fact_3263_mult_Ocomm__neutral,axiom,
% 5.12/5.35 ! [A: int] :
% 5.12/5.35 ( ( times_times_int @ A @ one_one_int )
% 5.12/5.35 = A ) ).
% 5.12/5.35
% 5.12/5.35 % mult.comm_neutral
% 5.12/5.35 thf(fact_3264_ring__class_Oring__distribs_I2_J,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(2)
% 5.12/5.35 thf(fact_3265_ring__class_Oring__distribs_I2_J,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(2)
% 5.12/5.35 thf(fact_3266_ring__class_Oring__distribs_I2_J,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(2)
% 5.12/5.35 thf(fact_3267_ring__class_Oring__distribs_I1_J,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(1)
% 5.12/5.35 thf(fact_3268_ring__class_Oring__distribs_I1_J,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(1)
% 5.12/5.35 thf(fact_3269_ring__class_Oring__distribs_I1_J,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ring_class.ring_distribs(1)
% 5.12/5.35 thf(fact_3270_comm__semiring__class_Odistrib,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % comm_semiring_class.distrib
% 5.12/5.35 thf(fact_3271_comm__semiring__class_Odistrib,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % comm_semiring_class.distrib
% 5.12/5.35 thf(fact_3272_comm__semiring__class_Odistrib,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % comm_semiring_class.distrib
% 5.12/5.35 thf(fact_3273_comm__semiring__class_Odistrib,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % comm_semiring_class.distrib
% 5.12/5.35 thf(fact_3274_distrib__left,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_left
% 5.12/5.35 thf(fact_3275_distrib__left,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_left
% 5.12/5.35 thf(fact_3276_distrib__left,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_left
% 5.12/5.35 thf(fact_3277_distrib__left,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_left
% 5.12/5.35 thf(fact_3278_distrib__right,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_right
% 5.12/5.35 thf(fact_3279_distrib__right,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_right
% 5.12/5.35 thf(fact_3280_distrib__right,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_right
% 5.12/5.35 thf(fact_3281_distrib__right,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % distrib_right
% 5.12/5.35 thf(fact_3282_combine__common__factor,axiom,
% 5.12/5.35 ! [A: real,E2: real,B: real,C: real] :
% 5.12/5.35 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 5.12/5.35
% 5.12/5.35 % combine_common_factor
% 5.12/5.35 thf(fact_3283_combine__common__factor,axiom,
% 5.12/5.35 ! [A: rat,E2: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.12/5.35
% 5.12/5.35 % combine_common_factor
% 5.12/5.35 thf(fact_3284_combine__common__factor,axiom,
% 5.12/5.35 ! [A: nat,E2: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 5.12/5.35 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.12/5.35
% 5.12/5.35 % combine_common_factor
% 5.12/5.35 thf(fact_3285_combine__common__factor,axiom,
% 5.12/5.35 ! [A: int,E2: int,B: int,C: int] :
% 5.12/5.35 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 5.12/5.35
% 5.12/5.35 % combine_common_factor
% 5.12/5.35 thf(fact_3286_inf__period_I1_J,axiom,
% 5.12/5.35 ! [P: real > $o,D6: real,Q: real > $o] :
% 5.12/5.35 ( ! [X3: real,K2: real] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: real,K2: real] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: real,K4: real] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 & ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) )
% 5.12/5.35 & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(1)
% 5.12/5.35 thf(fact_3287_inf__period_I1_J,axiom,
% 5.12/5.35 ! [P: rat > $o,D6: rat,Q: rat > $o] :
% 5.12/5.35 ( ! [X3: rat,K2: rat] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: rat,K2: rat] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: rat,K4: rat] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 & ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) )
% 5.12/5.35 & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(1)
% 5.12/5.35 thf(fact_3288_inf__period_I1_J,axiom,
% 5.12/5.35 ! [P: int > $o,D6: int,Q: int > $o] :
% 5.12/5.35 ( ! [X3: int,K2: int] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: int,K2: int] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: int,K4: int] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 & ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) )
% 5.12/5.35 & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(1)
% 5.12/5.35 thf(fact_3289_inf__period_I2_J,axiom,
% 5.12/5.35 ! [P: real > $o,D6: real,Q: real > $o] :
% 5.12/5.35 ( ! [X3: real,K2: real] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: real,K2: real] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: real,K4: real] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 | ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) )
% 5.12/5.35 | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(2)
% 5.12/5.35 thf(fact_3290_inf__period_I2_J,axiom,
% 5.12/5.35 ! [P: rat > $o,D6: rat,Q: rat > $o] :
% 5.12/5.35 ( ! [X3: rat,K2: rat] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: rat,K2: rat] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: rat,K4: rat] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 | ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) )
% 5.12/5.35 | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(2)
% 5.12/5.35 thf(fact_3291_inf__period_I2_J,axiom,
% 5.12/5.35 ! [P: int > $o,D6: int,Q: int > $o] :
% 5.12/5.35 ( ! [X3: int,K2: int] :
% 5.12/5.35 ( ( P @ X3 )
% 5.12/5.35 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ( ! [X3: int,K2: int] :
% 5.12/5.35 ( ( Q @ X3 )
% 5.12/5.35 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.35 => ! [X4: int,K4: int] :
% 5.12/5.35 ( ( ( P @ X4 )
% 5.12/5.35 | ( Q @ X4 ) )
% 5.12/5.35 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) )
% 5.12/5.35 | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % inf_period(2)
% 5.12/5.35 thf(fact_3292_right__diff__distrib_H,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.12/5.35 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib'
% 5.12/5.35 thf(fact_3293_right__diff__distrib_H,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.12/5.35 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib'
% 5.12/5.35 thf(fact_3294_right__diff__distrib_H,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.12/5.35 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib'
% 5.12/5.35 thf(fact_3295_right__diff__distrib_H,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib'
% 5.12/5.35 thf(fact_3296_left__diff__distrib_H,axiom,
% 5.12/5.35 ! [B: real,C: real,A: real] :
% 5.12/5.35 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.12/5.35 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib'
% 5.12/5.35 thf(fact_3297_left__diff__distrib_H,axiom,
% 5.12/5.35 ! [B: rat,C: rat,A: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.12/5.35 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib'
% 5.12/5.35 thf(fact_3298_left__diff__distrib_H,axiom,
% 5.12/5.35 ! [B: nat,C: nat,A: nat] :
% 5.12/5.35 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.12/5.35 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib'
% 5.12/5.35 thf(fact_3299_left__diff__distrib_H,axiom,
% 5.12/5.35 ! [B: int,C: int,A: int] :
% 5.12/5.35 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib'
% 5.12/5.35 thf(fact_3300_right__diff__distrib,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.12/5.35 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib
% 5.12/5.35 thf(fact_3301_right__diff__distrib,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.12/5.35 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib
% 5.12/5.35 thf(fact_3302_right__diff__distrib,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % right_diff_distrib
% 5.12/5.35 thf(fact_3303_left__diff__distrib,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.12/5.35 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib
% 5.12/5.35 thf(fact_3304_left__diff__distrib,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.12/5.35 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib
% 5.12/5.35 thf(fact_3305_left__diff__distrib,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_diff_distrib
% 5.12/5.35 thf(fact_3306_divide__divide__eq__left_H,axiom,
% 5.12/5.35 ! [A: complex,B: complex,C: complex] :
% 5.12/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.12/5.35 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_eq_left'
% 5.12/5.35 thf(fact_3307_divide__divide__eq__left_H,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.12/5.35 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_eq_left'
% 5.12/5.35 thf(fact_3308_divide__divide__eq__left_H,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.12/5.35 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_eq_left'
% 5.12/5.35 thf(fact_3309_divide__divide__times__eq,axiom,
% 5.12/5.35 ! [X: complex,Y: complex,Z2: complex,W: complex] :
% 5.12/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z2 @ W ) )
% 5.12/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_times_eq
% 5.12/5.35 thf(fact_3310_divide__divide__times__eq,axiom,
% 5.12/5.35 ! [X: real,Y: real,Z2: real,W: real] :
% 5.12/5.35 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 5.12/5.35 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_times_eq
% 5.12/5.35 thf(fact_3311_divide__divide__times__eq,axiom,
% 5.12/5.35 ! [X: rat,Y: rat,Z2: rat,W: rat] :
% 5.12/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z2 @ W ) )
% 5.12/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_divide_times_eq
% 5.12/5.35 thf(fact_3312_times__divide__times__eq,axiom,
% 5.12/5.35 ! [X: complex,Y: complex,Z2: complex,W: complex] :
% 5.12/5.35 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z2 @ W ) )
% 5.12/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % times_divide_times_eq
% 5.12/5.35 thf(fact_3313_times__divide__times__eq,axiom,
% 5.12/5.35 ! [X: real,Y: real,Z2: real,W: real] :
% 5.12/5.35 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z2 @ W ) )
% 5.12/5.35 = ( divide_divide_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % times_divide_times_eq
% 5.12/5.35 thf(fact_3314_times__divide__times__eq,axiom,
% 5.12/5.35 ! [X: rat,Y: rat,Z2: rat,W: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z2 @ W ) )
% 5.12/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % times_divide_times_eq
% 5.12/5.35 thf(fact_3315_square__eq__iff,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ( times_times_int @ A @ A )
% 5.12/5.35 = ( times_times_int @ B @ B ) )
% 5.12/5.35 = ( ( A = B )
% 5.12/5.35 | ( A
% 5.12/5.35 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_iff
% 5.12/5.35 thf(fact_3316_square__eq__iff,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ( times_times_real @ A @ A )
% 5.12/5.35 = ( times_times_real @ B @ B ) )
% 5.12/5.35 = ( ( A = B )
% 5.12/5.35 | ( A
% 5.12/5.35 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_iff
% 5.12/5.35 thf(fact_3317_square__eq__iff,axiom,
% 5.12/5.35 ! [A: complex,B: complex] :
% 5.12/5.35 ( ( ( times_times_complex @ A @ A )
% 5.12/5.35 = ( times_times_complex @ B @ B ) )
% 5.12/5.35 = ( ( A = B )
% 5.12/5.35 | ( A
% 5.12/5.35 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_iff
% 5.12/5.35 thf(fact_3318_square__eq__iff,axiom,
% 5.12/5.35 ! [A: code_integer,B: code_integer] :
% 5.12/5.35 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.12/5.35 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.12/5.35 = ( ( A = B )
% 5.12/5.35 | ( A
% 5.12/5.35 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_iff
% 5.12/5.35 thf(fact_3319_square__eq__iff,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ( times_times_rat @ A @ A )
% 5.12/5.35 = ( times_times_rat @ B @ B ) )
% 5.12/5.35 = ( ( A = B )
% 5.12/5.35 | ( A
% 5.12/5.35 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_iff
% 5.12/5.35 thf(fact_3320_minus__mult__commute,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.35 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % minus_mult_commute
% 5.12/5.35 thf(fact_3321_minus__mult__commute,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.12/5.35 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % minus_mult_commute
% 5.12/5.35 thf(fact_3322_minus__mult__commute,axiom,
% 5.12/5.35 ! [A: complex,B: complex] :
% 5.12/5.35 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.12/5.35 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % minus_mult_commute
% 5.12/5.35 thf(fact_3323_minus__mult__commute,axiom,
% 5.12/5.35 ! [A: code_integer,B: code_integer] :
% 5.12/5.35 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.12/5.35 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % minus_mult_commute
% 5.12/5.35 thf(fact_3324_minus__mult__commute,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.12/5.35 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % minus_mult_commute
% 5.12/5.35 thf(fact_3325_mult__of__nat__commute,axiom,
% 5.12/5.35 ! [X: nat,Y: complex] :
% 5.12/5.35 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 5.12/5.35 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_nat_commute
% 5.12/5.35 thf(fact_3326_mult__of__nat__commute,axiom,
% 5.12/5.35 ! [X: nat,Y: real] :
% 5.12/5.35 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.12/5.35 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_nat_commute
% 5.12/5.35 thf(fact_3327_mult__of__nat__commute,axiom,
% 5.12/5.35 ! [X: nat,Y: rat] :
% 5.12/5.35 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.12/5.35 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_nat_commute
% 5.12/5.35 thf(fact_3328_mult__of__nat__commute,axiom,
% 5.12/5.35 ! [X: nat,Y: nat] :
% 5.12/5.35 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.12/5.35 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_nat_commute
% 5.12/5.35 thf(fact_3329_mult__of__nat__commute,axiom,
% 5.12/5.35 ! [X: nat,Y: int] :
% 5.12/5.35 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.12/5.35 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_of_nat_commute
% 5.12/5.35 thf(fact_3330_times__int__code_I1_J,axiom,
% 5.12/5.35 ! [K: int] :
% 5.12/5.35 ( ( times_times_int @ K @ zero_zero_int )
% 5.12/5.35 = zero_zero_int ) ).
% 5.12/5.35
% 5.12/5.35 % times_int_code(1)
% 5.12/5.35 thf(fact_3331_times__int__code_I2_J,axiom,
% 5.12/5.35 ! [L: int] :
% 5.12/5.35 ( ( times_times_int @ zero_zero_int @ L )
% 5.12/5.35 = zero_zero_int ) ).
% 5.12/5.35
% 5.12/5.35 % times_int_code(2)
% 5.12/5.35 thf(fact_3332_abs__mult,axiom,
% 5.12/5.35 ! [A: code_integer,B: code_integer] :
% 5.12/5.35 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.12/5.35 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult
% 5.12/5.35 thf(fact_3333_abs__mult,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.12/5.35 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult
% 5.12/5.35 thf(fact_3334_abs__mult,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult
% 5.12/5.35 thf(fact_3335_abs__mult,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.12/5.35 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult
% 5.12/5.35 thf(fact_3336_int__distrib_I2_J,axiom,
% 5.12/5.35 ! [W: int,Z1: int,Z22: int] :
% 5.12/5.35 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % int_distrib(2)
% 5.12/5.35 thf(fact_3337_int__distrib_I1_J,axiom,
% 5.12/5.35 ! [Z1: int,Z22: int,W: int] :
% 5.12/5.35 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % int_distrib(1)
% 5.12/5.35 thf(fact_3338_int__distrib_I3_J,axiom,
% 5.12/5.35 ! [Z1: int,Z22: int,W: int] :
% 5.12/5.35 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % int_distrib(3)
% 5.12/5.35 thf(fact_3339_int__distrib_I4_J,axiom,
% 5.12/5.35 ! [W: int,Z1: int,Z22: int] :
% 5.12/5.35 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.12/5.35 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % int_distrib(4)
% 5.12/5.35 thf(fact_3340_exp__times__arg__commute,axiom,
% 5.12/5.35 ! [A2: complex] :
% 5.12/5.35 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.12/5.35 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % exp_times_arg_commute
% 5.12/5.35 thf(fact_3341_exp__times__arg__commute,axiom,
% 5.12/5.35 ! [A2: real] :
% 5.12/5.35 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.12/5.35 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % exp_times_arg_commute
% 5.12/5.35 thf(fact_3342_powr__powr,axiom,
% 5.12/5.35 ! [X: real,A: real,B: real] :
% 5.12/5.35 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.12/5.35 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % powr_powr
% 5.12/5.35 thf(fact_3343_add__scale__eq__noteq,axiom,
% 5.12/5.35 ! [R4: real,A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( R4 != zero_zero_real )
% 5.12/5.35 => ( ( ( A = B )
% 5.12/5.35 & ( C != D ) )
% 5.12/5.35 => ( ( plus_plus_real @ A @ ( times_times_real @ R4 @ C ) )
% 5.12/5.35 != ( plus_plus_real @ B @ ( times_times_real @ R4 @ D ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % add_scale_eq_noteq
% 5.12/5.35 thf(fact_3344_add__scale__eq__noteq,axiom,
% 5.12/5.35 ! [R4: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( R4 != zero_zero_rat )
% 5.12/5.35 => ( ( ( A = B )
% 5.12/5.35 & ( C != D ) )
% 5.12/5.35 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R4 @ C ) )
% 5.12/5.35 != ( plus_plus_rat @ B @ ( times_times_rat @ R4 @ D ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % add_scale_eq_noteq
% 5.12/5.35 thf(fact_3345_add__scale__eq__noteq,axiom,
% 5.12/5.35 ! [R4: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( R4 != zero_zero_nat )
% 5.12/5.35 => ( ( ( A = B )
% 5.12/5.35 & ( C != D ) )
% 5.12/5.35 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R4 @ C ) )
% 5.12/5.35 != ( plus_plus_nat @ B @ ( times_times_nat @ R4 @ D ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % add_scale_eq_noteq
% 5.12/5.35 thf(fact_3346_add__scale__eq__noteq,axiom,
% 5.12/5.35 ! [R4: int,A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( R4 != zero_zero_int )
% 5.12/5.35 => ( ( ( A = B )
% 5.12/5.35 & ( C != D ) )
% 5.12/5.35 => ( ( plus_plus_int @ A @ ( times_times_int @ R4 @ C ) )
% 5.12/5.35 != ( plus_plus_int @ B @ ( times_times_int @ R4 @ D ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % add_scale_eq_noteq
% 5.12/5.35 thf(fact_3347_artanh__tanh__real,axiom,
% 5.12/5.35 ! [X: real] :
% 5.12/5.35 ( ( artanh_real @ ( tanh_real @ X ) )
% 5.12/5.35 = X ) ).
% 5.12/5.35
% 5.12/5.35 % artanh_tanh_real
% 5.12/5.35 thf(fact_3348_mult__ceiling__le,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_ceiling_le
% 5.12/5.35 thf(fact_3349_mult__ceiling__le,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_ceiling_le
% 5.12/5.35 thf(fact_3350_le__of__int__ceiling,axiom,
% 5.12/5.35 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % le_of_int_ceiling
% 5.12/5.35 thf(fact_3351_le__of__int__ceiling,axiom,
% 5.12/5.35 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % le_of_int_ceiling
% 5.12/5.35 thf(fact_3352_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.12/5.35 thf(fact_3353_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.12/5.35 thf(fact_3354_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.12/5.35 thf(fact_3355_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.12/5.35 thf(fact_3356_zero__le__mult__iff,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_mult_iff
% 5.12/5.35 thf(fact_3357_zero__le__mult__iff,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_mult_iff
% 5.12/5.35 thf(fact_3358_zero__le__mult__iff,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_mult_iff
% 5.12/5.35 thf(fact_3359_mult__nonneg__nonpos2,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos2
% 5.12/5.35 thf(fact_3360_mult__nonneg__nonpos2,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos2
% 5.12/5.35 thf(fact_3361_mult__nonneg__nonpos2,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos2
% 5.12/5.35 thf(fact_3362_mult__nonneg__nonpos2,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos2
% 5.12/5.35 thf(fact_3363_mult__nonpos__nonneg,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonneg
% 5.12/5.35 thf(fact_3364_mult__nonpos__nonneg,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonneg
% 5.12/5.35 thf(fact_3365_mult__nonpos__nonneg,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonneg
% 5.12/5.35 thf(fact_3366_mult__nonpos__nonneg,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonneg
% 5.12/5.35 thf(fact_3367_mult__nonneg__nonpos,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos
% 5.12/5.35 thf(fact_3368_mult__nonneg__nonpos,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos
% 5.12/5.35 thf(fact_3369_mult__nonneg__nonpos,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos
% 5.12/5.35 thf(fact_3370_mult__nonneg__nonpos,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonpos
% 5.12/5.35 thf(fact_3371_mult__nonneg__nonneg,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonneg
% 5.12/5.35 thf(fact_3372_mult__nonneg__nonneg,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonneg
% 5.12/5.35 thf(fact_3373_mult__nonneg__nonneg,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonneg
% 5.12/5.35 thf(fact_3374_mult__nonneg__nonneg,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonneg_nonneg
% 5.12/5.35 thf(fact_3375_split__mult__neg__le,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.12/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_neg_le
% 5.12/5.35 thf(fact_3376_split__mult__neg__le,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.12/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_neg_le
% 5.12/5.35 thf(fact_3377_split__mult__neg__le,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.12/5.35 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.12/5.35 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_neg_le
% 5.12/5.35 thf(fact_3378_split__mult__neg__le,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.12/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_neg_le
% 5.12/5.35 thf(fact_3379_mult__le__0__iff,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.12/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.12/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_0_iff
% 5.12/5.35 thf(fact_3380_mult__le__0__iff,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.12/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.12/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_0_iff
% 5.12/5.35 thf(fact_3381_mult__le__0__iff,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.12/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.12/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_0_iff
% 5.12/5.35 thf(fact_3382_mult__right__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono
% 5.12/5.35 thf(fact_3383_mult__right__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono
% 5.12/5.35 thf(fact_3384_mult__right__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono
% 5.12/5.35 thf(fact_3385_mult__right__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono
% 5.12/5.35 thf(fact_3386_mult__right__mono__neg,axiom,
% 5.12/5.35 ! [B: real,A: real,C: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono_neg
% 5.12/5.35 thf(fact_3387_mult__right__mono__neg,axiom,
% 5.12/5.35 ! [B: rat,A: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono_neg
% 5.12/5.35 thf(fact_3388_mult__right__mono__neg,axiom,
% 5.12/5.35 ! [B: int,A: int,C: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_mono_neg
% 5.12/5.35 thf(fact_3389_mult__left__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono
% 5.12/5.35 thf(fact_3390_mult__left__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono
% 5.12/5.35 thf(fact_3391_mult__left__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono
% 5.12/5.35 thf(fact_3392_mult__left__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono
% 5.12/5.35 thf(fact_3393_mult__nonpos__nonpos,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonpos
% 5.12/5.35 thf(fact_3394_mult__nonpos__nonpos,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonpos
% 5.12/5.35 thf(fact_3395_mult__nonpos__nonpos,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_nonpos_nonpos
% 5.12/5.35 thf(fact_3396_mult__left__mono__neg,axiom,
% 5.12/5.35 ! [B: real,A: real,C: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono_neg
% 5.12/5.35 thf(fact_3397_mult__left__mono__neg,axiom,
% 5.12/5.35 ! [B: rat,A: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono_neg
% 5.12/5.35 thf(fact_3398_mult__left__mono__neg,axiom,
% 5.12/5.35 ! [B: int,A: int,C: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ B @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_mono_neg
% 5.12/5.35 thf(fact_3399_split__mult__pos__le,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.12/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_pos_le
% 5.12/5.35 thf(fact_3400_split__mult__pos__le,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.12/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_pos_le
% 5.12/5.35 thf(fact_3401_split__mult__pos__le,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.12/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.12/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % split_mult_pos_le
% 5.12/5.35 thf(fact_3402_zero__le__square,axiom,
% 5.12/5.35 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_square
% 5.12/5.35 thf(fact_3403_zero__le__square,axiom,
% 5.12/5.35 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_square
% 5.12/5.35 thf(fact_3404_zero__le__square,axiom,
% 5.12/5.35 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_le_square
% 5.12/5.35 thf(fact_3405_mult__mono_H,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono'
% 5.12/5.35 thf(fact_3406_mult__mono_H,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono'
% 5.12/5.35 thf(fact_3407_mult__mono_H,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono'
% 5.12/5.35 thf(fact_3408_mult__mono_H,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono'
% 5.12/5.35 thf(fact_3409_mult__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono
% 5.12/5.35 thf(fact_3410_mult__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono
% 5.12/5.35 thf(fact_3411_mult__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono
% 5.12/5.35 thf(fact_3412_mult__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_mono
% 5.12/5.35 thf(fact_3413_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.12/5.35 thf(fact_3414_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.12/5.35 thf(fact_3415_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.12/5.35 thf(fact_3416_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.12/5.35 thf(fact_3417_mult__less__cancel__right__disj,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 & ( ord_less_real @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right_disj
% 5.12/5.35 thf(fact_3418_mult__less__cancel__right__disj,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 & ( ord_less_rat @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right_disj
% 5.12/5.35 thf(fact_3419_mult__less__cancel__right__disj,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 & ( ord_less_int @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right_disj
% 5.12/5.35 thf(fact_3420_mult__strict__right__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono
% 5.12/5.35 thf(fact_3421_mult__strict__right__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono
% 5.12/5.35 thf(fact_3422_mult__strict__right__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono
% 5.12/5.35 thf(fact_3423_mult__strict__right__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono
% 5.12/5.35 thf(fact_3424_mult__strict__right__mono__neg,axiom,
% 5.12/5.35 ! [B: real,A: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ B @ A )
% 5.12/5.35 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono_neg
% 5.12/5.35 thf(fact_3425_mult__strict__right__mono__neg,axiom,
% 5.12/5.35 ! [B: rat,A: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ B @ A )
% 5.12/5.35 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono_neg
% 5.12/5.35 thf(fact_3426_mult__strict__right__mono__neg,axiom,
% 5.12/5.35 ! [B: int,A: int,C: int] :
% 5.12/5.35 ( ( ord_less_int @ B @ A )
% 5.12/5.35 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_right_mono_neg
% 5.12/5.35 thf(fact_3427_mult__less__cancel__left__disj,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 & ( ord_less_real @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_disj
% 5.12/5.35 thf(fact_3428_mult__less__cancel__left__disj,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 & ( ord_less_rat @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_disj
% 5.12/5.35 thf(fact_3429_mult__less__cancel__left__disj,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 & ( ord_less_int @ A @ B ) )
% 5.12/5.35 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_disj
% 5.12/5.35 thf(fact_3430_mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono
% 5.12/5.35 thf(fact_3431_mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono
% 5.12/5.35 thf(fact_3432_mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono
% 5.12/5.35 thf(fact_3433_mult__strict__left__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono
% 5.12/5.35 thf(fact_3434_mult__strict__left__mono__neg,axiom,
% 5.12/5.35 ! [B: real,A: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ B @ A )
% 5.12/5.35 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono_neg
% 5.12/5.35 thf(fact_3435_mult__strict__left__mono__neg,axiom,
% 5.12/5.35 ! [B: rat,A: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ B @ A )
% 5.12/5.35 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono_neg
% 5.12/5.35 thf(fact_3436_mult__strict__left__mono__neg,axiom,
% 5.12/5.35 ! [B: int,A: int,C: int] :
% 5.12/5.35 ( ( ord_less_int @ B @ A )
% 5.12/5.35 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_left_mono_neg
% 5.12/5.35 thf(fact_3437_mult__less__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_pos
% 5.12/5.35 thf(fact_3438_mult__less__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_pos
% 5.12/5.35 thf(fact_3439_mult__less__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_pos
% 5.12/5.35 thf(fact_3440_mult__less__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ord_less_real @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_neg
% 5.12/5.35 thf(fact_3441_mult__less__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_neg
% 5.12/5.35 thf(fact_3442_mult__less__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ord_less_int @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left_neg
% 5.12/5.35 thf(fact_3443_zero__less__mult__pos2,axiom,
% 5.12/5.35 ! [B: real,A: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos2
% 5.12/5.35 thf(fact_3444_zero__less__mult__pos2,axiom,
% 5.12/5.35 ! [B: rat,A: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos2
% 5.12/5.35 thf(fact_3445_zero__less__mult__pos2,axiom,
% 5.12/5.35 ! [B: nat,A: nat] :
% 5.12/5.35 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos2
% 5.12/5.35 thf(fact_3446_zero__less__mult__pos2,axiom,
% 5.12/5.35 ! [B: int,A: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos2
% 5.12/5.35 thf(fact_3447_zero__less__mult__pos,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos
% 5.12/5.35 thf(fact_3448_zero__less__mult__pos,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos
% 5.12/5.35 thf(fact_3449_zero__less__mult__pos,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos
% 5.12/5.35 thf(fact_3450_zero__less__mult__pos,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_pos
% 5.12/5.35 thf(fact_3451_zero__less__mult__iff,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.12/5.35 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_iff
% 5.12/5.35 thf(fact_3452_zero__less__mult__iff,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.12/5.35 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_iff
% 5.12/5.35 thf(fact_3453_zero__less__mult__iff,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.12/5.35 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zero_less_mult_iff
% 5.12/5.35 thf(fact_3454_mult__pos__neg2,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg2
% 5.12/5.35 thf(fact_3455_mult__pos__neg2,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg2
% 5.12/5.35 thf(fact_3456_mult__pos__neg2,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg2
% 5.12/5.35 thf(fact_3457_mult__pos__neg2,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg2
% 5.12/5.35 thf(fact_3458_mult__pos__pos,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_pos
% 5.12/5.35 thf(fact_3459_mult__pos__pos,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_pos
% 5.12/5.35 thf(fact_3460_mult__pos__pos,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_pos
% 5.12/5.35 thf(fact_3461_mult__pos__pos,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_pos
% 5.12/5.35 thf(fact_3462_mult__pos__neg,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg
% 5.12/5.35 thf(fact_3463_mult__pos__neg,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg
% 5.12/5.35 thf(fact_3464_mult__pos__neg,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg
% 5.12/5.35 thf(fact_3465_mult__pos__neg,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_pos_neg
% 5.12/5.35 thf(fact_3466_mult__neg__pos,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_pos
% 5.12/5.35 thf(fact_3467_mult__neg__pos,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_pos
% 5.12/5.35 thf(fact_3468_mult__neg__pos,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_pos
% 5.12/5.35 thf(fact_3469_mult__neg__pos,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_pos
% 5.12/5.35 thf(fact_3470_mult__less__0__iff,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.12/5.35 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.35 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_0_iff
% 5.12/5.35 thf(fact_3471_mult__less__0__iff,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.12/5.35 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.35 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_0_iff
% 5.12/5.35 thf(fact_3472_mult__less__0__iff,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.12/5.35 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.35 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_0_iff
% 5.12/5.35 thf(fact_3473_not__square__less__zero,axiom,
% 5.12/5.35 ! [A: real] :
% 5.12/5.35 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.12/5.35
% 5.12/5.35 % not_square_less_zero
% 5.12/5.35 thf(fact_3474_not__square__less__zero,axiom,
% 5.12/5.35 ! [A: rat] :
% 5.12/5.35 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.12/5.35
% 5.12/5.35 % not_square_less_zero
% 5.12/5.35 thf(fact_3475_not__square__less__zero,axiom,
% 5.12/5.35 ! [A: int] :
% 5.12/5.35 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.12/5.35
% 5.12/5.35 % not_square_less_zero
% 5.12/5.35 thf(fact_3476_mult__neg__neg,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_neg
% 5.12/5.35 thf(fact_3477_mult__neg__neg,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_neg
% 5.12/5.35 thf(fact_3478_mult__neg__neg,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_neg_neg
% 5.12/5.35 thf(fact_3479_less__1__mult,axiom,
% 5.12/5.35 ! [M2: real,N: real] :
% 5.12/5.35 ( ( ord_less_real @ one_one_real @ M2 )
% 5.12/5.35 => ( ( ord_less_real @ one_one_real @ N )
% 5.12/5.35 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_1_mult
% 5.12/5.35 thf(fact_3480_less__1__mult,axiom,
% 5.12/5.35 ! [M2: rat,N: rat] :
% 5.12/5.35 ( ( ord_less_rat @ one_one_rat @ M2 )
% 5.12/5.35 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.12/5.35 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_1_mult
% 5.12/5.35 thf(fact_3481_less__1__mult,axiom,
% 5.12/5.35 ! [M2: nat,N: nat] :
% 5.12/5.35 ( ( ord_less_nat @ one_one_nat @ M2 )
% 5.12/5.35 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.12/5.35 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_1_mult
% 5.12/5.35 thf(fact_3482_less__1__mult,axiom,
% 5.12/5.35 ! [M2: int,N: int] :
% 5.12/5.35 ( ( ord_less_int @ one_one_int @ M2 )
% 5.12/5.35 => ( ( ord_less_int @ one_one_int @ N )
% 5.12/5.35 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_1_mult
% 5.12/5.35 thf(fact_3483_frac__eq__eq,axiom,
% 5.12/5.35 ! [Y: complex,Z2: complex,X: complex,W: complex] :
% 5.12/5.35 ( ( Y != zero_zero_complex )
% 5.12/5.35 => ( ( Z2 != zero_zero_complex )
% 5.12/5.35 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.12/5.35 = ( divide1717551699836669952omplex @ W @ Z2 ) )
% 5.12/5.35 = ( ( times_times_complex @ X @ Z2 )
% 5.12/5.35 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % frac_eq_eq
% 5.12/5.35 thf(fact_3484_frac__eq__eq,axiom,
% 5.12/5.35 ! [Y: real,Z2: real,X: real,W: real] :
% 5.12/5.35 ( ( Y != zero_zero_real )
% 5.12/5.35 => ( ( Z2 != zero_zero_real )
% 5.12/5.35 => ( ( ( divide_divide_real @ X @ Y )
% 5.12/5.35 = ( divide_divide_real @ W @ Z2 ) )
% 5.12/5.35 = ( ( times_times_real @ X @ Z2 )
% 5.12/5.35 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % frac_eq_eq
% 5.12/5.35 thf(fact_3485_frac__eq__eq,axiom,
% 5.12/5.35 ! [Y: rat,Z2: rat,X: rat,W: rat] :
% 5.12/5.35 ( ( Y != zero_zero_rat )
% 5.12/5.35 => ( ( Z2 != zero_zero_rat )
% 5.12/5.35 => ( ( ( divide_divide_rat @ X @ Y )
% 5.12/5.35 = ( divide_divide_rat @ W @ Z2 ) )
% 5.12/5.35 = ( ( times_times_rat @ X @ Z2 )
% 5.12/5.35 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % frac_eq_eq
% 5.12/5.35 thf(fact_3486_divide__eq__eq,axiom,
% 5.12/5.35 ! [B: complex,C: complex,A: complex] :
% 5.12/5.35 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( ( ( C != zero_zero_complex )
% 5.12/5.35 => ( B
% 5.12/5.35 = ( times_times_complex @ A @ C ) ) )
% 5.12/5.35 & ( ( C = zero_zero_complex )
% 5.12/5.35 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_eq
% 5.12/5.35 thf(fact_3487_divide__eq__eq,axiom,
% 5.12/5.35 ! [B: real,C: real,A: real] :
% 5.12/5.35 ( ( ( divide_divide_real @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( ( ( C != zero_zero_real )
% 5.12/5.35 => ( B
% 5.12/5.35 = ( times_times_real @ A @ C ) ) )
% 5.12/5.35 & ( ( C = zero_zero_real )
% 5.12/5.35 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_eq
% 5.12/5.35 thf(fact_3488_divide__eq__eq,axiom,
% 5.12/5.35 ! [B: rat,C: rat,A: rat] :
% 5.12/5.35 ( ( ( divide_divide_rat @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( ( ( C != zero_zero_rat )
% 5.12/5.35 => ( B
% 5.12/5.35 = ( times_times_rat @ A @ C ) ) )
% 5.12/5.35 & ( ( C = zero_zero_rat )
% 5.12/5.35 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_eq
% 5.12/5.35 thf(fact_3489_eq__divide__eq,axiom,
% 5.12/5.35 ! [A: complex,B: complex,C: complex] :
% 5.12/5.35 ( ( A
% 5.12/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.35 = ( ( ( C != zero_zero_complex )
% 5.12/5.35 => ( ( times_times_complex @ A @ C )
% 5.12/5.35 = B ) )
% 5.12/5.35 & ( ( C = zero_zero_complex )
% 5.12/5.35 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_eq
% 5.12/5.35 thf(fact_3490_eq__divide__eq,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( A
% 5.12/5.35 = ( divide_divide_real @ B @ C ) )
% 5.12/5.35 = ( ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( times_times_real @ A @ C )
% 5.12/5.35 = B ) )
% 5.12/5.35 & ( ( C = zero_zero_real )
% 5.12/5.35 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_eq
% 5.12/5.35 thf(fact_3491_eq__divide__eq,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( A
% 5.12/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.35 = ( ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( times_times_rat @ A @ C )
% 5.12/5.35 = B ) )
% 5.12/5.35 & ( ( C = zero_zero_rat )
% 5.12/5.35 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_eq
% 5.12/5.35 thf(fact_3492_divide__eq__imp,axiom,
% 5.12/5.35 ! [C: complex,B: complex,A: complex] :
% 5.12/5.35 ( ( C != zero_zero_complex )
% 5.12/5.35 => ( ( B
% 5.12/5.35 = ( times_times_complex @ A @ C ) )
% 5.12/5.35 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.12/5.35 = A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_imp
% 5.12/5.35 thf(fact_3493_divide__eq__imp,axiom,
% 5.12/5.35 ! [C: real,B: real,A: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( B
% 5.12/5.35 = ( times_times_real @ A @ C ) )
% 5.12/5.35 => ( ( divide_divide_real @ B @ C )
% 5.12/5.35 = A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_imp
% 5.12/5.35 thf(fact_3494_divide__eq__imp,axiom,
% 5.12/5.35 ! [C: rat,B: rat,A: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( B
% 5.12/5.35 = ( times_times_rat @ A @ C ) )
% 5.12/5.35 => ( ( divide_divide_rat @ B @ C )
% 5.12/5.35 = A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_eq_imp
% 5.12/5.35 thf(fact_3495_eq__divide__imp,axiom,
% 5.12/5.35 ! [C: complex,A: complex,B: complex] :
% 5.12/5.35 ( ( C != zero_zero_complex )
% 5.12/5.35 => ( ( ( times_times_complex @ A @ C )
% 5.12/5.35 = B )
% 5.12/5.35 => ( A
% 5.12/5.35 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_imp
% 5.12/5.35 thf(fact_3496_eq__divide__imp,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( ( times_times_real @ A @ C )
% 5.12/5.35 = B )
% 5.12/5.35 => ( A
% 5.12/5.35 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_imp
% 5.12/5.35 thf(fact_3497_eq__divide__imp,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( ( times_times_rat @ A @ C )
% 5.12/5.35 = B )
% 5.12/5.35 => ( A
% 5.12/5.35 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_divide_imp
% 5.12/5.35 thf(fact_3498_nonzero__divide__eq__eq,axiom,
% 5.12/5.35 ! [C: complex,B: complex,A: complex] :
% 5.12/5.35 ( ( C != zero_zero_complex )
% 5.12/5.35 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( B
% 5.12/5.35 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_divide_eq_eq
% 5.12/5.35 thf(fact_3499_nonzero__divide__eq__eq,axiom,
% 5.12/5.35 ! [C: real,B: real,A: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( ( divide_divide_real @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( B
% 5.12/5.35 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_divide_eq_eq
% 5.12/5.35 thf(fact_3500_nonzero__divide__eq__eq,axiom,
% 5.12/5.35 ! [C: rat,B: rat,A: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( ( divide_divide_rat @ B @ C )
% 5.12/5.35 = A )
% 5.12/5.35 = ( B
% 5.12/5.35 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_divide_eq_eq
% 5.12/5.35 thf(fact_3501_nonzero__eq__divide__eq,axiom,
% 5.12/5.35 ! [C: complex,A: complex,B: complex] :
% 5.12/5.35 ( ( C != zero_zero_complex )
% 5.12/5.35 => ( ( A
% 5.12/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.35 = ( ( times_times_complex @ A @ C )
% 5.12/5.35 = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_eq_divide_eq
% 5.12/5.35 thf(fact_3502_nonzero__eq__divide__eq,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( C != zero_zero_real )
% 5.12/5.35 => ( ( A
% 5.12/5.35 = ( divide_divide_real @ B @ C ) )
% 5.12/5.35 = ( ( times_times_real @ A @ C )
% 5.12/5.35 = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_eq_divide_eq
% 5.12/5.35 thf(fact_3503_nonzero__eq__divide__eq,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( C != zero_zero_rat )
% 5.12/5.35 => ( ( A
% 5.12/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.35 = ( ( times_times_rat @ A @ C )
% 5.12/5.35 = B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % nonzero_eq_divide_eq
% 5.12/5.35 thf(fact_3504_eq__add__iff1,axiom,
% 5.12/5.35 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.35 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 5.12/5.35 = D ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff1
% 5.12/5.35 thf(fact_3505_eq__add__iff1,axiom,
% 5.12/5.35 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.35 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 5.12/5.35 = D ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff1
% 5.12/5.35 thf(fact_3506_eq__add__iff1,axiom,
% 5.12/5.35 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.35 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 5.12/5.35 = D ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff1
% 5.12/5.35 thf(fact_3507_eq__add__iff2,axiom,
% 5.12/5.35 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.35 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( C
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff2
% 5.12/5.35 thf(fact_3508_eq__add__iff2,axiom,
% 5.12/5.35 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.35 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( C
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff2
% 5.12/5.35 thf(fact_3509_eq__add__iff2,axiom,
% 5.12/5.35 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.35 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.35 = ( C
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % eq_add_iff2
% 5.12/5.35 thf(fact_3510_square__diff__square__factored,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.12/5.35 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_diff_square_factored
% 5.12/5.35 thf(fact_3511_square__diff__square__factored,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.12/5.35 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_diff_square_factored
% 5.12/5.35 thf(fact_3512_square__diff__square__factored,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.12/5.35 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_diff_square_factored
% 5.12/5.35 thf(fact_3513_mult__diff__mult,axiom,
% 5.12/5.35 ! [X: real,Y: real,A: real,B: real] :
% 5.12/5.35 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.12/5.35 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_diff_mult
% 5.12/5.35 thf(fact_3514_mult__diff__mult,axiom,
% 5.12/5.35 ! [X: rat,Y: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_diff_mult
% 5.12/5.35 thf(fact_3515_mult__diff__mult,axiom,
% 5.12/5.35 ! [X: int,Y: int,A: int,B: int] :
% 5.12/5.35 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.12/5.35 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_diff_mult
% 5.12/5.35 thf(fact_3516_square__eq__1__iff,axiom,
% 5.12/5.35 ! [X: int] :
% 5.12/5.35 ( ( ( times_times_int @ X @ X )
% 5.12/5.35 = one_one_int )
% 5.12/5.35 = ( ( X = one_one_int )
% 5.12/5.35 | ( X
% 5.12/5.35 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_1_iff
% 5.12/5.35 thf(fact_3517_square__eq__1__iff,axiom,
% 5.12/5.35 ! [X: real] :
% 5.12/5.35 ( ( ( times_times_real @ X @ X )
% 5.12/5.35 = one_one_real )
% 5.12/5.35 = ( ( X = one_one_real )
% 5.12/5.35 | ( X
% 5.12/5.35 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_1_iff
% 5.12/5.35 thf(fact_3518_square__eq__1__iff,axiom,
% 5.12/5.35 ! [X: complex] :
% 5.12/5.35 ( ( ( times_times_complex @ X @ X )
% 5.12/5.35 = one_one_complex )
% 5.12/5.35 = ( ( X = one_one_complex )
% 5.12/5.35 | ( X
% 5.12/5.35 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_1_iff
% 5.12/5.35 thf(fact_3519_square__eq__1__iff,axiom,
% 5.12/5.35 ! [X: code_integer] :
% 5.12/5.35 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.12/5.35 = one_one_Code_integer )
% 5.12/5.35 = ( ( X = one_one_Code_integer )
% 5.12/5.35 | ( X
% 5.12/5.35 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_1_iff
% 5.12/5.35 thf(fact_3520_square__eq__1__iff,axiom,
% 5.12/5.35 ! [X: rat] :
% 5.12/5.35 ( ( ( times_times_rat @ X @ X )
% 5.12/5.35 = one_one_rat )
% 5.12/5.35 = ( ( X = one_one_rat )
% 5.12/5.35 | ( X
% 5.12/5.35 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % square_eq_1_iff
% 5.12/5.35 thf(fact_3521_left__right__inverse__power,axiom,
% 5.12/5.35 ! [X: complex,Y: complex,N: nat] :
% 5.12/5.35 ( ( ( times_times_complex @ X @ Y )
% 5.12/5.35 = one_one_complex )
% 5.12/5.35 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.12/5.35 = one_one_complex ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_right_inverse_power
% 5.12/5.35 thf(fact_3522_left__right__inverse__power,axiom,
% 5.12/5.35 ! [X: real,Y: real,N: nat] :
% 5.12/5.35 ( ( ( times_times_real @ X @ Y )
% 5.12/5.35 = one_one_real )
% 5.12/5.35 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 5.12/5.35 = one_one_real ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_right_inverse_power
% 5.12/5.35 thf(fact_3523_left__right__inverse__power,axiom,
% 5.12/5.35 ! [X: rat,Y: rat,N: nat] :
% 5.12/5.35 ( ( ( times_times_rat @ X @ Y )
% 5.12/5.35 = one_one_rat )
% 5.12/5.35 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.12/5.35 = one_one_rat ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_right_inverse_power
% 5.12/5.35 thf(fact_3524_left__right__inverse__power,axiom,
% 5.12/5.35 ! [X: nat,Y: nat,N: nat] :
% 5.12/5.35 ( ( ( times_times_nat @ X @ Y )
% 5.12/5.35 = one_one_nat )
% 5.12/5.35 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 5.12/5.35 = one_one_nat ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_right_inverse_power
% 5.12/5.35 thf(fact_3525_left__right__inverse__power,axiom,
% 5.12/5.35 ! [X: int,Y: int,N: nat] :
% 5.12/5.35 ( ( ( times_times_int @ X @ Y )
% 5.12/5.35 = one_one_int )
% 5.12/5.35 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 5.12/5.35 = one_one_int ) ) ).
% 5.12/5.35
% 5.12/5.35 % left_right_inverse_power
% 5.12/5.35 thf(fact_3526_power__Suc,axiom,
% 5.12/5.35 ! [A: complex,N: nat] :
% 5.12/5.35 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc
% 5.12/5.35 thf(fact_3527_power__Suc,axiom,
% 5.12/5.35 ! [A: real,N: nat] :
% 5.12/5.35 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc
% 5.12/5.35 thf(fact_3528_power__Suc,axiom,
% 5.12/5.35 ! [A: rat,N: nat] :
% 5.12/5.35 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc
% 5.12/5.35 thf(fact_3529_power__Suc,axiom,
% 5.12/5.35 ! [A: nat,N: nat] :
% 5.12/5.35 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc
% 5.12/5.35 thf(fact_3530_power__Suc,axiom,
% 5.12/5.35 ! [A: int,N: nat] :
% 5.12/5.35 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc
% 5.12/5.35 thf(fact_3531_power__Suc2,axiom,
% 5.12/5.35 ! [A: complex,N: nat] :
% 5.12/5.35 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc2
% 5.12/5.35 thf(fact_3532_power__Suc2,axiom,
% 5.12/5.35 ! [A: real,N: nat] :
% 5.12/5.35 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc2
% 5.12/5.35 thf(fact_3533_power__Suc2,axiom,
% 5.12/5.35 ! [A: rat,N: nat] :
% 5.12/5.35 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc2
% 5.12/5.35 thf(fact_3534_power__Suc2,axiom,
% 5.12/5.35 ! [A: nat,N: nat] :
% 5.12/5.35 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc2
% 5.12/5.35 thf(fact_3535_power__Suc2,axiom,
% 5.12/5.35 ! [A: int,N: nat] :
% 5.12/5.35 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.12/5.35 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % power_Suc2
% 5.12/5.35 thf(fact_3536_abs__mult__less,axiom,
% 5.12/5.35 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.12/5.35 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.12/5.35 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.12/5.35 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult_less
% 5.12/5.35 thf(fact_3537_abs__mult__less,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real,D: real] :
% 5.12/5.35 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.12/5.35 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult_less
% 5.12/5.35 thf(fact_3538_abs__mult__less,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.12/5.35 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult_less
% 5.12/5.35 thf(fact_3539_abs__mult__less,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int,D: int] :
% 5.12/5.35 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.12/5.35 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_mult_less
% 5.12/5.35 thf(fact_3540_div__mult2__eq_H,axiom,
% 5.12/5.35 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.35 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.12/5.35 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % div_mult2_eq'
% 5.12/5.35 thf(fact_3541_div__mult2__eq_H,axiom,
% 5.12/5.35 ! [A: int,M2: nat,N: nat] :
% 5.12/5.35 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.35 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % div_mult2_eq'
% 5.12/5.35 thf(fact_3542_mult__exp__exp,axiom,
% 5.12/5.35 ! [X: complex,Y: complex] :
% 5.12/5.35 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 5.12/5.35 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_exp_exp
% 5.12/5.35 thf(fact_3543_mult__exp__exp,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.12/5.35 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_exp_exp
% 5.12/5.35 thf(fact_3544_exp__add__commuting,axiom,
% 5.12/5.35 ! [X: complex,Y: complex] :
% 5.12/5.35 ( ( ( times_times_complex @ X @ Y )
% 5.12/5.35 = ( times_times_complex @ Y @ X ) )
% 5.12/5.35 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.12/5.35 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % exp_add_commuting
% 5.12/5.35 thf(fact_3545_exp__add__commuting,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( ( times_times_real @ X @ Y )
% 5.12/5.35 = ( times_times_real @ Y @ X ) )
% 5.12/5.35 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.35 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % exp_add_commuting
% 5.12/5.35 thf(fact_3546_zmult__zless__mono2,axiom,
% 5.12/5.35 ! [I: int,J2: int,K: int] :
% 5.12/5.35 ( ( ord_less_int @ I @ J2 )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J2 ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zmult_zless_mono2
% 5.12/5.35 thf(fact_3547_powr__add,axiom,
% 5.12/5.35 ! [X: real,A: real,B: real] :
% 5.12/5.35 ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 5.12/5.35 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % powr_add
% 5.12/5.35 thf(fact_3548_real__minus__mult__self__le,axiom,
% 5.12/5.35 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.12/5.35
% 5.12/5.35 % real_minus_mult_self_le
% 5.12/5.35 thf(fact_3549_pos__zmult__eq__1__iff__lemma,axiom,
% 5.12/5.35 ! [M2: int,N: int] :
% 5.12/5.35 ( ( ( times_times_int @ M2 @ N )
% 5.12/5.35 = one_one_int )
% 5.12/5.35 => ( ( M2 = one_one_int )
% 5.12/5.35 | ( M2
% 5.12/5.35 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % pos_zmult_eq_1_iff_lemma
% 5.12/5.35 thf(fact_3550_zmult__eq__1__iff,axiom,
% 5.12/5.35 ! [M2: int,N: int] :
% 5.12/5.35 ( ( ( times_times_int @ M2 @ N )
% 5.12/5.35 = one_one_int )
% 5.12/5.35 = ( ( ( M2 = one_one_int )
% 5.12/5.35 & ( N = one_one_int ) )
% 5.12/5.35 | ( ( M2
% 5.12/5.35 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.35 & ( N
% 5.12/5.35 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zmult_eq_1_iff
% 5.12/5.35 thf(fact_3551_abs__zmult__eq__1,axiom,
% 5.12/5.35 ! [M2: int,N: int] :
% 5.12/5.35 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N ) )
% 5.12/5.35 = one_one_int )
% 5.12/5.35 => ( ( abs_abs_int @ M2 )
% 5.12/5.35 = one_one_int ) ) ).
% 5.12/5.35
% 5.12/5.35 % abs_zmult_eq_1
% 5.12/5.35 thf(fact_3552_zmod__eq__0D,axiom,
% 5.12/5.35 ! [M2: int,D: int] :
% 5.12/5.35 ( ( ( modulo_modulo_int @ M2 @ D )
% 5.12/5.35 = zero_zero_int )
% 5.12/5.35 => ? [Q3: int] :
% 5.12/5.35 ( M2
% 5.12/5.35 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zmod_eq_0D
% 5.12/5.35 thf(fact_3553_zmod__eq__0__iff,axiom,
% 5.12/5.35 ! [M2: int,D: int] :
% 5.12/5.35 ( ( ( modulo_modulo_int @ M2 @ D )
% 5.12/5.35 = zero_zero_int )
% 5.12/5.35 = ( ? [Q4: int] :
% 5.12/5.35 ( M2
% 5.12/5.35 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % zmod_eq_0_iff
% 5.12/5.35 thf(fact_3554_ceiling__divide__upper,axiom,
% 5.12/5.35 ! [Q5: real,P4: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ Q5 )
% 5.12/5.35 => ( ord_less_eq_real @ P4 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q5 ) ) ) @ Q5 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_divide_upper
% 5.12/5.35 thf(fact_3555_ceiling__divide__upper,axiom,
% 5.12/5.35 ! [Q5: rat,P4: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ Q5 )
% 5.12/5.35 => ( ord_less_eq_rat @ P4 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q5 ) ) ) @ Q5 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_divide_upper
% 5.12/5.35 thf(fact_3556_tanh__real__lt__1,axiom,
% 5.12/5.35 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 5.12/5.35
% 5.12/5.35 % tanh_real_lt_1
% 5.12/5.35 thf(fact_3557_ceiling__divide__lower,axiom,
% 5.12/5.35 ! [Q5: real,P4: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ Q5 )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q5 ) ) ) @ one_one_real ) @ Q5 ) @ P4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_divide_lower
% 5.12/5.35 thf(fact_3558_ceiling__divide__lower,axiom,
% 5.12/5.35 ! [Q5: rat,P4: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ Q5 )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q5 ) ) ) @ one_one_rat ) @ Q5 ) @ P4 ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_divide_lower
% 5.12/5.35 thf(fact_3559_mult__less__le__imp__less,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_le_imp_less
% 5.12/5.35 thf(fact_3560_mult__less__le__imp__less,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_le_imp_less
% 5.12/5.35 thf(fact_3561_mult__less__le__imp__less,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_le_imp_less
% 5.12/5.35 thf(fact_3562_mult__less__le__imp__less,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_le_imp_less
% 5.12/5.35 thf(fact_3563_mult__le__less__imp__less,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_less_imp_less
% 5.12/5.35 thf(fact_3564_mult__le__less__imp__less,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_less_imp_less
% 5.12/5.35 thf(fact_3565_mult__le__less__imp__less,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_less_imp_less
% 5.12/5.35 thf(fact_3566_mult__le__less__imp__less,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_less_imp_less
% 5.12/5.35 thf(fact_3567_mult__right__le__imp__le,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_imp_le
% 5.12/5.35 thf(fact_3568_mult__right__le__imp__le,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_imp_le
% 5.12/5.35 thf(fact_3569_mult__right__le__imp__le,axiom,
% 5.12/5.35 ! [A: nat,C: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_imp_le
% 5.12/5.35 thf(fact_3570_mult__right__le__imp__le,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_imp_le
% 5.12/5.35 thf(fact_3571_mult__left__le__imp__le,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_imp_le
% 5.12/5.35 thf(fact_3572_mult__left__le__imp__le,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_imp_le
% 5.12/5.35 thf(fact_3573_mult__left__le__imp__le,axiom,
% 5.12/5.35 ! [C: nat,A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_imp_le
% 5.12/5.35 thf(fact_3574_mult__left__le__imp__le,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_imp_le
% 5.12/5.35 thf(fact_3575_mult__le__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_pos
% 5.12/5.35 thf(fact_3576_mult__le__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_pos
% 5.12/5.35 thf(fact_3577_mult__le__cancel__left__pos,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_pos
% 5.12/5.35 thf(fact_3578_mult__le__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_neg
% 5.12/5.35 thf(fact_3579_mult__le__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_neg
% 5.12/5.35 thf(fact_3580_mult__le__cancel__left__neg,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left_neg
% 5.12/5.35 thf(fact_3581_mult__less__cancel__right,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right
% 5.12/5.35 thf(fact_3582_mult__less__cancel__right,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right
% 5.12/5.35 thf(fact_3583_mult__less__cancel__right,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_right
% 5.12/5.35 thf(fact_3584_mult__strict__mono_H,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono'
% 5.12/5.35 thf(fact_3585_mult__strict__mono_H,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono'
% 5.12/5.35 thf(fact_3586_mult__strict__mono_H,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono'
% 5.12/5.35 thf(fact_3587_mult__strict__mono_H,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono'
% 5.12/5.35 thf(fact_3588_mult__right__less__imp__less,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_less_imp_less
% 5.12/5.35 thf(fact_3589_mult__right__less__imp__less,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_less_imp_less
% 5.12/5.35 thf(fact_3590_mult__right__less__imp__less,axiom,
% 5.12/5.35 ! [A: nat,C: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_less_imp_less
% 5.12/5.35 thf(fact_3591_mult__right__less__imp__less,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_less_imp_less
% 5.12/5.35 thf(fact_3592_mult__less__cancel__left,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left
% 5.12/5.35 thf(fact_3593_mult__less__cancel__left,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left
% 5.12/5.35 thf(fact_3594_mult__less__cancel__left,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_less_cancel_left
% 5.12/5.35 thf(fact_3595_mult__strict__mono,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ C @ D )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono
% 5.12/5.35 thf(fact_3596_mult__strict__mono,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ C @ D )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono
% 5.12/5.35 thf(fact_3597_mult__strict__mono,axiom,
% 5.12/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.35 ( ( ord_less_nat @ A @ B )
% 5.12/5.35 => ( ( ord_less_nat @ C @ D )
% 5.12/5.35 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono
% 5.12/5.35 thf(fact_3598_mult__strict__mono,axiom,
% 5.12/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.35 ( ( ord_less_int @ A @ B )
% 5.12/5.35 => ( ( ord_less_int @ C @ D )
% 5.12/5.35 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_strict_mono
% 5.12/5.35 thf(fact_3599_mult__left__less__imp__less,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_real @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_less_imp_less
% 5.12/5.35 thf(fact_3600_mult__left__less__imp__less,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_less_imp_less
% 5.12/5.35 thf(fact_3601_mult__left__less__imp__less,axiom,
% 5.12/5.35 ! [C: nat,A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_less_imp_less
% 5.12/5.35 thf(fact_3602_mult__left__less__imp__less,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_less_imp_less
% 5.12/5.35 thf(fact_3603_mult__le__cancel__right,axiom,
% 5.12/5.35 ! [A: real,C: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_right
% 5.12/5.35 thf(fact_3604_mult__le__cancel__right,axiom,
% 5.12/5.35 ! [A: rat,C: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_right
% 5.12/5.35 thf(fact_3605_mult__le__cancel__right,axiom,
% 5.12/5.35 ! [A: int,C: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_right
% 5.12/5.35 thf(fact_3606_mult__le__cancel__left,axiom,
% 5.12/5.35 ! [C: real,A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.35 => ( ord_less_eq_real @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left
% 5.12/5.35 thf(fact_3607_mult__le__cancel__left,axiom,
% 5.12/5.35 ! [C: rat,A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.35 => ( ord_less_eq_rat @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left
% 5.12/5.35 thf(fact_3608_mult__le__cancel__left,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.35 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ord_less_eq_int @ A @ B ) )
% 5.12/5.35 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.35 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_cancel_left
% 5.12/5.35 thf(fact_3609_ceiling__le__iff,axiom,
% 5.12/5.35 ! [X: real,Z2: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z2 )
% 5.12/5.35 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_le_iff
% 5.12/5.35 thf(fact_3610_ceiling__le__iff,axiom,
% 5.12/5.35 ! [X: rat,Z2: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z2 )
% 5.12/5.35 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_le_iff
% 5.12/5.35 thf(fact_3611_ceiling__le,axiom,
% 5.12/5.35 ! [X: real,A: int] :
% 5.12/5.35 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 5.12/5.35 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_le
% 5.12/5.35 thf(fact_3612_ceiling__le,axiom,
% 5.12/5.35 ! [X: rat,A: int] :
% 5.12/5.35 ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) )
% 5.12/5.35 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ A ) ) ).
% 5.12/5.35
% 5.12/5.35 % ceiling_le
% 5.12/5.35 thf(fact_3613_less__ceiling__iff,axiom,
% 5.12/5.35 ! [Z2: int,X: rat] :
% 5.12/5.35 ( ( ord_less_int @ Z2 @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.35 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_ceiling_iff
% 5.12/5.35 thf(fact_3614_less__ceiling__iff,axiom,
% 5.12/5.35 ! [Z2: int,X: real] :
% 5.12/5.35 ( ( ord_less_int @ Z2 @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.35 = ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X ) ) ).
% 5.12/5.35
% 5.12/5.35 % less_ceiling_iff
% 5.12/5.35 thf(fact_3615_mult__left__le,axiom,
% 5.12/5.35 ! [C: real,A: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le
% 5.12/5.35 thf(fact_3616_mult__left__le,axiom,
% 5.12/5.35 ! [C: rat,A: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le
% 5.12/5.35 thf(fact_3617_mult__left__le,axiom,
% 5.12/5.35 ! [C: nat,A: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le
% 5.12/5.35 thf(fact_3618_mult__left__le,axiom,
% 5.12/5.35 ! [C: int,A: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le
% 5.12/5.35 thf(fact_3619_mult__le__one,axiom,
% 5.12/5.35 ! [A: real,B: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.35 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_one
% 5.12/5.35 thf(fact_3620_mult__le__one,axiom,
% 5.12/5.35 ! [A: rat,B: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.35 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_one
% 5.12/5.35 thf(fact_3621_mult__le__one,axiom,
% 5.12/5.35 ! [A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.12/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.12/5.35 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.12/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_one
% 5.12/5.35 thf(fact_3622_mult__le__one,axiom,
% 5.12/5.35 ! [A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.35 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_le_one
% 5.12/5.35 thf(fact_3623_mult__right__le__one__le,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.35 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_one_le
% 5.12/5.35 thf(fact_3624_mult__right__le__one__le,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.35 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_one_le
% 5.12/5.35 thf(fact_3625_mult__right__le__one__le,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.35 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_right_le_one_le
% 5.12/5.35 thf(fact_3626_mult__left__le__one__le,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.35 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.35 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_one_le
% 5.12/5.35 thf(fact_3627_mult__left__le__one__le,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.35 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.12/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_one_le
% 5.12/5.35 thf(fact_3628_mult__left__le__one__le,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.35 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.12/5.35 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % mult_left_le_one_le
% 5.12/5.35 thf(fact_3629_sum__squares__ge__zero,axiom,
% 5.12/5.35 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_ge_zero
% 5.12/5.35 thf(fact_3630_sum__squares__ge__zero,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_ge_zero
% 5.12/5.35 thf(fact_3631_sum__squares__ge__zero,axiom,
% 5.12/5.35 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_ge_zero
% 5.12/5.35 thf(fact_3632_sum__squares__le__zero__iff,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.12/5.35 = ( ( X = zero_zero_real )
% 5.12/5.35 & ( Y = zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_le_zero_iff
% 5.12/5.35 thf(fact_3633_sum__squares__le__zero__iff,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.12/5.35 = ( ( X = zero_zero_rat )
% 5.12/5.35 & ( Y = zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_le_zero_iff
% 5.12/5.35 thf(fact_3634_sum__squares__le__zero__iff,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.12/5.35 = ( ( X = zero_zero_int )
% 5.12/5.35 & ( Y = zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_le_zero_iff
% 5.12/5.35 thf(fact_3635_not__sum__squares__lt__zero,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.12/5.35
% 5.12/5.35 % not_sum_squares_lt_zero
% 5.12/5.35 thf(fact_3636_not__sum__squares__lt__zero,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.12/5.35
% 5.12/5.35 % not_sum_squares_lt_zero
% 5.12/5.35 thf(fact_3637_not__sum__squares__lt__zero,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.12/5.35
% 5.12/5.35 % not_sum_squares_lt_zero
% 5.12/5.35 thf(fact_3638_sum__squares__gt__zero__iff,axiom,
% 5.12/5.35 ! [X: real,Y: real] :
% 5.12/5.35 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.12/5.35 = ( ( X != zero_zero_real )
% 5.12/5.35 | ( Y != zero_zero_real ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_gt_zero_iff
% 5.12/5.35 thf(fact_3639_sum__squares__gt__zero__iff,axiom,
% 5.12/5.35 ! [X: rat,Y: rat] :
% 5.12/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.12/5.35 = ( ( X != zero_zero_rat )
% 5.12/5.35 | ( Y != zero_zero_rat ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_gt_zero_iff
% 5.12/5.35 thf(fact_3640_sum__squares__gt__zero__iff,axiom,
% 5.12/5.35 ! [X: int,Y: int] :
% 5.12/5.35 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.12/5.35 = ( ( X != zero_zero_int )
% 5.12/5.35 | ( Y != zero_zero_int ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % sum_squares_gt_zero_iff
% 5.12/5.35 thf(fact_3641_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.12/5.35 ! [C: nat,A: nat,B: nat] :
% 5.12/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.35 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.35 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.12/5.35 thf(fact_3642_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.12/5.35 ! [C: int,A: int,B: int] :
% 5.12/5.35 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.35 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.35 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.12/5.35 thf(fact_3643_divide__strict__left__mono__neg,axiom,
% 5.12/5.35 ! [A: real,B: real,C: real] :
% 5.12/5.35 ( ( ord_less_real @ A @ B )
% 5.12/5.35 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.35 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.35 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.12/5.35
% 5.12/5.35 % divide_strict_left_mono_neg
% 5.12/5.35 thf(fact_3644_divide__strict__left__mono__neg,axiom,
% 5.12/5.35 ! [A: rat,B: rat,C: rat] :
% 5.12/5.35 ( ( ord_less_rat @ A @ B )
% 5.12/5.35 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.35 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.35 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_strict_left_mono_neg
% 5.12/5.36 thf(fact_3645_divide__strict__left__mono,axiom,
% 5.12/5.36 ! [B: real,A: real,C: real] :
% 5.12/5.36 ( ( ord_less_real @ B @ A )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.36 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_strict_left_mono
% 5.12/5.36 thf(fact_3646_divide__strict__left__mono,axiom,
% 5.12/5.36 ! [B: rat,A: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_rat @ B @ A )
% 5.12/5.36 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.36 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_strict_left_mono
% 5.12/5.36 thf(fact_3647_mult__imp__less__div__pos,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( ord_less_real @ ( times_times_real @ Z2 @ Y ) @ X )
% 5.12/5.36 => ( ord_less_real @ Z2 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_less_div_pos
% 5.12/5.36 thf(fact_3648_mult__imp__less__div__pos,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.36 => ( ( ord_less_rat @ ( times_times_rat @ Z2 @ Y ) @ X )
% 5.12/5.36 => ( ord_less_rat @ Z2 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_less_div_pos
% 5.12/5.36 thf(fact_3649_mult__imp__div__pos__less,axiom,
% 5.12/5.36 ! [Y: real,X: real,Z2: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( ord_less_real @ X @ ( times_times_real @ Z2 @ Y ) )
% 5.12/5.36 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_div_pos_less
% 5.12/5.36 thf(fact_3650_mult__imp__div__pos__less,axiom,
% 5.12/5.36 ! [Y: rat,X: rat,Z2: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.36 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z2 @ Y ) )
% 5.12/5.36 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_div_pos_less
% 5.12/5.36 thf(fact_3651_pos__less__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_less_divide_eq
% 5.12/5.36 thf(fact_3652_pos__less__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_less_divide_eq
% 5.12/5.36 thf(fact_3653_pos__divide__less__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_divide_less_eq
% 5.12/5.36 thf(fact_3654_pos__divide__less__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_divide_less_eq
% 5.12/5.36 thf(fact_3655_neg__less__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_less_divide_eq
% 5.12/5.36 thf(fact_3656_neg__less__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_less_divide_eq
% 5.12/5.36 thf(fact_3657_neg__divide__less__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_divide_less_eq
% 5.12/5.36 thf(fact_3658_neg__divide__less__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_divide_less_eq
% 5.12/5.36 thf(fact_3659_less__divide__eq,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_divide_eq
% 5.12/5.36 thf(fact_3660_less__divide__eq,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_divide_eq
% 5.12/5.36 thf(fact_3661_divide__less__eq,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_less_eq
% 5.12/5.36 thf(fact_3662_divide__less__eq,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_less_eq
% 5.12/5.36 thf(fact_3663_ordered__ring__class_Ole__add__iff1,axiom,
% 5.12/5.36 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff1
% 5.12/5.36 thf(fact_3664_ordered__ring__class_Ole__add__iff1,axiom,
% 5.12/5.36 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff1
% 5.12/5.36 thf(fact_3665_ordered__ring__class_Ole__add__iff1,axiom,
% 5.12/5.36 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff1
% 5.12/5.36 thf(fact_3666_ordered__ring__class_Ole__add__iff2,axiom,
% 5.12/5.36 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff2
% 5.12/5.36 thf(fact_3667_ordered__ring__class_Ole__add__iff2,axiom,
% 5.12/5.36 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff2
% 5.12/5.36 thf(fact_3668_ordered__ring__class_Ole__add__iff2,axiom,
% 5.12/5.36 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ordered_ring_class.le_add_iff2
% 5.12/5.36 thf(fact_3669_add__divide__eq__if__simps_I2_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(2)
% 5.12/5.36 thf(fact_3670_add__divide__eq__if__simps_I2_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(2)
% 5.12/5.36 thf(fact_3671_add__divide__eq__if__simps_I2_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(2)
% 5.12/5.36 thf(fact_3672_add__divide__eq__if__simps_I1_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(1)
% 5.12/5.36 thf(fact_3673_add__divide__eq__if__simps_I1_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(1)
% 5.12/5.36 thf(fact_3674_add__divide__eq__if__simps_I1_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(1)
% 5.12/5.36 thf(fact_3675_add__frac__eq,axiom,
% 5.12/5.36 ! [Y: complex,Z2: complex,X: complex,W: complex] :
% 5.12/5.36 ( ( Y != zero_zero_complex )
% 5.12/5.36 => ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_eq
% 5.12/5.36 thf(fact_3676_add__frac__eq,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real,W: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_eq
% 5.12/5.36 thf(fact_3677_add__frac__eq,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat,W: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_eq
% 5.12/5.36 thf(fact_3678_add__frac__num,axiom,
% 5.12/5.36 ! [Y: complex,X: complex,Z2: complex] :
% 5.12/5.36 ( ( Y != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z2 )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_num
% 5.12/5.36 thf(fact_3679_add__frac__num,axiom,
% 5.12/5.36 ! [Y: real,X: real,Z2: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z2 )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_num
% 5.12/5.36 thf(fact_3680_add__frac__num,axiom,
% 5.12/5.36 ! [Y: rat,X: rat,Z2: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z2 )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_frac_num
% 5.12/5.36 thf(fact_3681_add__num__frac,axiom,
% 5.12/5.36 ! [Y: complex,Z2: complex,X: complex] :
% 5.12/5.36 ( ( Y != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_num_frac
% 5.12/5.36 thf(fact_3682_add__num__frac,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ Z2 @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_num_frac
% 5.12/5.36 thf(fact_3683_add__num__frac,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ X @ Y ) )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z2 @ Y ) ) @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_num_frac
% 5.12/5.36 thf(fact_3684_add__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_iff
% 5.12/5.36 thf(fact_3685_add__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_iff
% 5.12/5.36 thf(fact_3686_add__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_iff
% 5.12/5.36 thf(fact_3687_divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_add_eq_iff
% 5.12/5.36 thf(fact_3688_divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_add_eq_iff
% 5.12/5.36 thf(fact_3689_divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_add_eq_iff
% 5.12/5.36 thf(fact_3690_less__add__iff2,axiom,
% 5.12/5.36 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.36 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff2
% 5.12/5.36 thf(fact_3691_less__add__iff2,axiom,
% 5.12/5.36 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff2
% 5.12/5.36 thf(fact_3692_less__add__iff2,axiom,
% 5.12/5.36 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.36 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff2
% 5.12/5.36 thf(fact_3693_less__add__iff1,axiom,
% 5.12/5.36 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.12/5.36 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff1
% 5.12/5.36 thf(fact_3694_less__add__iff1,axiom,
% 5.12/5.36 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff1
% 5.12/5.36 thf(fact_3695_less__add__iff1,axiom,
% 5.12/5.36 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.12/5.36 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.12/5.36 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_add_iff1
% 5.12/5.36 thf(fact_3696_divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_diff_eq_iff
% 5.12/5.36 thf(fact_3697_divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_diff_eq_iff
% 5.12/5.36 thf(fact_3698_divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z2 ) @ Y )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_diff_eq_iff
% 5.12/5.36 thf(fact_3699_diff__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_divide_eq_iff
% 5.12/5.36 thf(fact_3700_diff__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_divide_eq_iff
% 5.12/5.36 thf(fact_3701_diff__divide__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_divide_eq_iff
% 5.12/5.36 thf(fact_3702_diff__frac__eq,axiom,
% 5.12/5.36 ! [Y: complex,Z2: complex,X: complex,W: complex] :
% 5.12/5.36 ( ( Y != zero_zero_complex )
% 5.12/5.36 => ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z2 ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_frac_eq
% 5.12/5.36 thf(fact_3703_diff__frac__eq,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real,W: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_frac_eq
% 5.12/5.36 thf(fact_3704_diff__frac__eq,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat,W: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % diff_frac_eq
% 5.12/5.36 thf(fact_3705_add__divide__eq__if__simps_I4_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z2 ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(4)
% 5.12/5.36 thf(fact_3706_add__divide__eq__if__simps_I4_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z2 ) )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(4)
% 5.12/5.36 thf(fact_3707_add__divide__eq__if__simps_I4_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.12/5.36 = A ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z2 ) )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z2 ) @ B ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(4)
% 5.12/5.36 thf(fact_3708_real__of__int__div4,axiom,
% 5.12/5.36 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % real_of_int_div4
% 5.12/5.36 thf(fact_3709_ex__less__of__nat__mult,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ? [N2: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ex_less_of_nat_mult
% 5.12/5.36 thf(fact_3710_ex__less__of__nat__mult,axiom,
% 5.12/5.36 ! [X: rat,Y: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.36 => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ex_less_of_nat_mult
% 5.12/5.36 thf(fact_3711_eq__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ( ( C != zero_zero_real )
% 5.12/5.36 => ( ( times_times_real @ A @ C )
% 5.12/5.36 = ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ( C = zero_zero_real )
% 5.12/5.36 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % eq_minus_divide_eq
% 5.12/5.36 thf(fact_3712_eq__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: complex,B: complex,C: complex] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.12/5.36 = ( ( ( C != zero_zero_complex )
% 5.12/5.36 => ( ( times_times_complex @ A @ C )
% 5.12/5.36 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.12/5.36 & ( ( C = zero_zero_complex )
% 5.12/5.36 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % eq_minus_divide_eq
% 5.12/5.36 thf(fact_3713_eq__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ( ( C != zero_zero_rat )
% 5.12/5.36 => ( ( times_times_rat @ A @ C )
% 5.12/5.36 = ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ( C = zero_zero_rat )
% 5.12/5.36 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % eq_minus_divide_eq
% 5.12/5.36 thf(fact_3714_minus__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = A )
% 5.12/5.36 = ( ( ( C != zero_zero_real )
% 5.12/5.36 => ( ( uminus_uminus_real @ B )
% 5.12/5.36 = ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ( C = zero_zero_real )
% 5.12/5.36 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_eq_eq
% 5.12/5.36 thf(fact_3715_minus__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: complex,C: complex,A: complex] :
% 5.12/5.36 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.36 = A )
% 5.12/5.36 = ( ( ( C != zero_zero_complex )
% 5.12/5.36 => ( ( uminus1482373934393186551omplex @ B )
% 5.12/5.36 = ( times_times_complex @ A @ C ) ) )
% 5.12/5.36 & ( ( C = zero_zero_complex )
% 5.12/5.36 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_eq_eq
% 5.12/5.36 thf(fact_3716_minus__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = A )
% 5.12/5.36 = ( ( ( C != zero_zero_rat )
% 5.12/5.36 => ( ( uminus_uminus_rat @ B )
% 5.12/5.36 = ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ( C = zero_zero_rat )
% 5.12/5.36 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_eq_eq
% 5.12/5.36 thf(fact_3717_nonzero__neg__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: real,A: real,C: real] :
% 5.12/5.36 ( ( B != zero_zero_real )
% 5.12/5.36 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.36 = C )
% 5.12/5.36 = ( ( uminus_uminus_real @ A )
% 5.12/5.36 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq
% 5.12/5.36 thf(fact_3718_nonzero__neg__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: complex,A: complex,C: complex] :
% 5.12/5.36 ( ( B != zero_zero_complex )
% 5.12/5.36 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.36 = C )
% 5.12/5.36 = ( ( uminus1482373934393186551omplex @ A )
% 5.12/5.36 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq
% 5.12/5.36 thf(fact_3719_nonzero__neg__divide__eq__eq,axiom,
% 5.12/5.36 ! [B: rat,A: rat,C: rat] :
% 5.12/5.36 ( ( B != zero_zero_rat )
% 5.12/5.36 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.12/5.36 = C )
% 5.12/5.36 = ( ( uminus_uminus_rat @ A )
% 5.12/5.36 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq
% 5.12/5.36 thf(fact_3720_nonzero__neg__divide__eq__eq2,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( B != zero_zero_real )
% 5.12/5.36 => ( ( C
% 5.12/5.36 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.12/5.36 = ( ( times_times_real @ C @ B )
% 5.12/5.36 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq2
% 5.12/5.36 thf(fact_3721_nonzero__neg__divide__eq__eq2,axiom,
% 5.12/5.36 ! [B: complex,C: complex,A: complex] :
% 5.12/5.36 ( ( B != zero_zero_complex )
% 5.12/5.36 => ( ( C
% 5.12/5.36 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.36 = ( ( times_times_complex @ C @ B )
% 5.12/5.36 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq2
% 5.12/5.36 thf(fact_3722_nonzero__neg__divide__eq__eq2,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( B != zero_zero_rat )
% 5.12/5.36 => ( ( C
% 5.12/5.36 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.12/5.36 = ( ( times_times_rat @ C @ B )
% 5.12/5.36 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % nonzero_neg_divide_eq_eq2
% 5.12/5.36 thf(fact_3723_power__less__power__Suc,axiom,
% 5.12/5.36 ! [A: real,N: nat] :
% 5.12/5.36 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.36 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_less_power_Suc
% 5.12/5.36 thf(fact_3724_power__less__power__Suc,axiom,
% 5.12/5.36 ! [A: rat,N: nat] :
% 5.12/5.36 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.36 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_less_power_Suc
% 5.12/5.36 thf(fact_3725_power__less__power__Suc,axiom,
% 5.12/5.36 ! [A: nat,N: nat] :
% 5.12/5.36 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.36 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_less_power_Suc
% 5.12/5.36 thf(fact_3726_power__less__power__Suc,axiom,
% 5.12/5.36 ! [A: int,N: nat] :
% 5.12/5.36 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.36 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_less_power_Suc
% 5.12/5.36 thf(fact_3727_power__gt1__lemma,axiom,
% 5.12/5.36 ! [A: real,N: nat] :
% 5.12/5.36 ( ( ord_less_real @ one_one_real @ A )
% 5.12/5.36 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_gt1_lemma
% 5.12/5.36 thf(fact_3728_power__gt1__lemma,axiom,
% 5.12/5.36 ! [A: rat,N: nat] :
% 5.12/5.36 ( ( ord_less_rat @ one_one_rat @ A )
% 5.12/5.36 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_gt1_lemma
% 5.12/5.36 thf(fact_3729_power__gt1__lemma,axiom,
% 5.12/5.36 ! [A: nat,N: nat] :
% 5.12/5.36 ( ( ord_less_nat @ one_one_nat @ A )
% 5.12/5.36 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_gt1_lemma
% 5.12/5.36 thf(fact_3730_power__gt1__lemma,axiom,
% 5.12/5.36 ! [A: int,N: nat] :
% 5.12/5.36 ( ( ord_less_int @ one_one_int @ A )
% 5.12/5.36 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_gt1_lemma
% 5.12/5.36 thf(fact_3731_square__diff__one__factored,axiom,
% 5.12/5.36 ! [X: complex] :
% 5.12/5.36 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.12/5.36 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % square_diff_one_factored
% 5.12/5.36 thf(fact_3732_square__diff__one__factored,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.12/5.36 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % square_diff_one_factored
% 5.12/5.36 thf(fact_3733_square__diff__one__factored,axiom,
% 5.12/5.36 ! [X: rat] :
% 5.12/5.36 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.12/5.36 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % square_diff_one_factored
% 5.12/5.36 thf(fact_3734_square__diff__one__factored,axiom,
% 5.12/5.36 ! [X: int] :
% 5.12/5.36 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.12/5.36 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % square_diff_one_factored
% 5.12/5.36 thf(fact_3735_abs__mult__pos,axiom,
% 5.12/5.36 ! [X: code_integer,Y: code_integer] :
% 5.12/5.36 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.12/5.36 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.12/5.36 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_mult_pos
% 5.12/5.36 thf(fact_3736_abs__mult__pos,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.12/5.36 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_mult_pos
% 5.12/5.36 thf(fact_3737_abs__mult__pos,axiom,
% 5.12/5.36 ! [X: rat,Y: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.36 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.12/5.36 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_mult_pos
% 5.12/5.36 thf(fact_3738_abs__mult__pos,axiom,
% 5.12/5.36 ! [X: int,Y: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.36 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.12/5.36 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_mult_pos
% 5.12/5.36 thf(fact_3739_abs__eq__mult,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.36 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.12/5.36 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.36 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.12/5.36 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.12/5.36 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_eq_mult
% 5.12/5.36 thf(fact_3740_abs__eq__mult,axiom,
% 5.12/5.36 ! [A: real,B: real] :
% 5.12/5.36 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.36 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.12/5.36 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.36 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.12/5.36 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.12/5.36 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_eq_mult
% 5.12/5.36 thf(fact_3741_abs__eq__mult,axiom,
% 5.12/5.36 ! [A: rat,B: rat] :
% 5.12/5.36 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.36 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.12/5.36 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.36 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.12/5.36 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.36 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_eq_mult
% 5.12/5.36 thf(fact_3742_abs__eq__mult,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.36 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.12/5.36 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.36 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.12/5.36 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.12/5.36 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % abs_eq_mult
% 5.12/5.36 thf(fact_3743_power__minus,axiom,
% 5.12/5.36 ! [A: int,N: nat] :
% 5.12/5.36 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.12/5.36 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus
% 5.12/5.36 thf(fact_3744_power__minus,axiom,
% 5.12/5.36 ! [A: real,N: nat] :
% 5.12/5.36 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.12/5.36 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus
% 5.12/5.36 thf(fact_3745_power__minus,axiom,
% 5.12/5.36 ! [A: complex,N: nat] :
% 5.12/5.36 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.12/5.36 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus
% 5.12/5.36 thf(fact_3746_power__minus,axiom,
% 5.12/5.36 ! [A: code_integer,N: nat] :
% 5.12/5.36 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.12/5.36 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus
% 5.12/5.36 thf(fact_3747_power__minus,axiom,
% 5.12/5.36 ! [A: rat,N: nat] :
% 5.12/5.36 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.12/5.36 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus
% 5.12/5.36 thf(fact_3748_div__mult1__eq,axiom,
% 5.12/5.36 ! [A: int,B: int,C: int] :
% 5.12/5.36 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.36 = ( 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 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult1_eq
% 5.12/5.36 thf(fact_3749_div__mult1__eq,axiom,
% 5.12/5.36 ! [A: nat,B: nat,C: nat] :
% 5.12/5.36 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.36 = ( 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 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult1_eq
% 5.12/5.36 thf(fact_3750_div__mult1__eq,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.36 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult1_eq
% 5.12/5.36 thf(fact_3751_div__mult1__eq,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.12/5.36 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 5.12/5.36 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult1_eq
% 5.12/5.36 thf(fact_3752_cancel__div__mod__rules_I2_J,axiom,
% 5.12/5.36 ! [B: int,A: int,C: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_plus_int @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(2)
% 5.12/5.36 thf(fact_3753_cancel__div__mod__rules_I2_J,axiom,
% 5.12/5.36 ! [B: nat,A: nat,C: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_plus_nat @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(2)
% 5.12/5.36 thf(fact_3754_cancel__div__mod__rules_I2_J,axiom,
% 5.12/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(2)
% 5.12/5.36 thf(fact_3755_cancel__div__mod__rules_I2_J,axiom,
% 5.12/5.36 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(2)
% 5.12/5.36 thf(fact_3756_cancel__div__mod__rules_I1_J,axiom,
% 5.12/5.36 ! [A: int,B: int,C: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_plus_int @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(1)
% 5.12/5.36 thf(fact_3757_cancel__div__mod__rules_I1_J,axiom,
% 5.12/5.36 ! [A: nat,B: nat,C: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_plus_nat @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(1)
% 5.12/5.36 thf(fact_3758_cancel__div__mod__rules_I1_J,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(1)
% 5.12/5.36 thf(fact_3759_cancel__div__mod__rules_I1_J,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 5.12/5.36 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 5.12/5.36
% 5.12/5.36 % cancel_div_mod_rules(1)
% 5.12/5.36 thf(fact_3760_mod__div__decomp,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( A
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_decomp
% 5.12/5.36 thf(fact_3761_mod__div__decomp,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( A
% 5.12/5.36 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_decomp
% 5.12/5.36 thf(fact_3762_mod__div__decomp,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( A
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_decomp
% 5.12/5.36 thf(fact_3763_mod__div__decomp,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( A
% 5.12/5.36 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_decomp
% 5.12/5.36 thf(fact_3764_div__mult__mod__eq,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult_mod_eq
% 5.12/5.36 thf(fact_3765_div__mult__mod__eq,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult_mod_eq
% 5.12/5.36 thf(fact_3766_div__mult__mod__eq,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult_mod_eq
% 5.12/5.36 thf(fact_3767_div__mult__mod__eq,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % div_mult_mod_eq
% 5.12/5.36 thf(fact_3768_mod__div__mult__eq,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_mult_eq
% 5.12/5.36 thf(fact_3769_mod__div__mult__eq,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_mult_eq
% 5.12/5.36 thf(fact_3770_mod__div__mult__eq,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_mult_eq
% 5.12/5.36 thf(fact_3771_mod__div__mult__eq,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_div_mult_eq
% 5.12/5.36 thf(fact_3772_mod__mult__div__eq,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult_div_eq
% 5.12/5.36 thf(fact_3773_mod__mult__div__eq,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult_div_eq
% 5.12/5.36 thf(fact_3774_mod__mult__div__eq,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult_div_eq
% 5.12/5.36 thf(fact_3775_mod__mult__div__eq,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult_div_eq
% 5.12/5.36 thf(fact_3776_mult__div__mod__eq,axiom,
% 5.12/5.36 ! [B: int,A: int] :
% 5.12/5.36 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mult_div_mod_eq
% 5.12/5.36 thf(fact_3777_mult__div__mod__eq,axiom,
% 5.12/5.36 ! [B: nat,A: nat] :
% 5.12/5.36 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mult_div_mod_eq
% 5.12/5.36 thf(fact_3778_mult__div__mod__eq,axiom,
% 5.12/5.36 ! [B: code_integer,A: code_integer] :
% 5.12/5.36 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mult_div_mod_eq
% 5.12/5.36 thf(fact_3779_mult__div__mod__eq,axiom,
% 5.12/5.36 ! [B: code_natural,A: code_natural] :
% 5.12/5.36 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.36 = A ) ).
% 5.12/5.36
% 5.12/5.36 % mult_div_mod_eq
% 5.12/5.36 thf(fact_3780_minus__div__mult__eq__mod,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.12/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_div_mult_eq_mod
% 5.12/5.36 thf(fact_3781_minus__div__mult__eq__mod,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.12/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_div_mult_eq_mod
% 5.12/5.36 thf(fact_3782_minus__div__mult__eq__mod,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.12/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_div_mult_eq_mod
% 5.12/5.36 thf(fact_3783_minus__div__mult__eq__mod,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.12/5.36 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_div_mult_eq_mod
% 5.12/5.36 thf(fact_3784_minus__mod__eq__div__mult,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.36 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_div_mult
% 5.12/5.36 thf(fact_3785_minus__mod__eq__div__mult,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.36 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_div_mult
% 5.12/5.36 thf(fact_3786_minus__mod__eq__div__mult,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.36 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_div_mult
% 5.12/5.36 thf(fact_3787_minus__mod__eq__div__mult,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.36 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_div_mult
% 5.12/5.36 thf(fact_3788_minus__mod__eq__mult__div,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.36 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_mult_div
% 5.12/5.36 thf(fact_3789_minus__mod__eq__mult__div,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.36 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_mult_div
% 5.12/5.36 thf(fact_3790_minus__mod__eq__mult__div,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.36 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_mult_div
% 5.12/5.36 thf(fact_3791_minus__mod__eq__mult__div,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.36 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mod_eq_mult_div
% 5.12/5.36 thf(fact_3792_minus__mult__div__eq__mod,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.12/5.36 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mult_div_eq_mod
% 5.12/5.36 thf(fact_3793_minus__mult__div__eq__mod,axiom,
% 5.12/5.36 ! [A: nat,B: nat] :
% 5.12/5.36 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.12/5.36 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mult_div_eq_mod
% 5.12/5.36 thf(fact_3794_minus__mult__div__eq__mod,axiom,
% 5.12/5.36 ! [A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.12/5.36 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mult_div_eq_mod
% 5.12/5.36 thf(fact_3795_minus__mult__div__eq__mod,axiom,
% 5.12/5.36 ! [A: code_natural,B: code_natural] :
% 5.12/5.36 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.12/5.36 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_mult_div_eq_mod
% 5.12/5.36 thf(fact_3796_exp__minus__inverse,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.12/5.36 = one_one_real ) ).
% 5.12/5.36
% 5.12/5.36 % exp_minus_inverse
% 5.12/5.36 thf(fact_3797_exp__minus__inverse,axiom,
% 5.12/5.36 ! [X: complex] :
% 5.12/5.36 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.12/5.36 = one_one_complex ) ).
% 5.12/5.36
% 5.12/5.36 % exp_minus_inverse
% 5.12/5.36 thf(fact_3798_exp__of__nat2__mult,axiom,
% 5.12/5.36 ! [X: complex,N: nat] :
% 5.12/5.36 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.12/5.36 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.12/5.36
% 5.12/5.36 % exp_of_nat2_mult
% 5.12/5.36 thf(fact_3799_exp__of__nat2__mult,axiom,
% 5.12/5.36 ! [X: real,N: nat] :
% 5.12/5.36 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.36 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.12/5.36
% 5.12/5.36 % exp_of_nat2_mult
% 5.12/5.36 thf(fact_3800_exp__of__nat__mult,axiom,
% 5.12/5.36 ! [N: nat,X: complex] :
% 5.12/5.36 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 5.12/5.36 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.12/5.36
% 5.12/5.36 % exp_of_nat_mult
% 5.12/5.36 thf(fact_3801_exp__of__nat__mult,axiom,
% 5.12/5.36 ! [N: nat,X: real] :
% 5.12/5.36 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 5.12/5.36 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.12/5.36
% 5.12/5.36 % exp_of_nat_mult
% 5.12/5.36 thf(fact_3802_reals__Archimedean3,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ! [Y5: real] :
% 5.12/5.36 ? [N2: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % reals_Archimedean3
% 5.12/5.36 thf(fact_3803_pos__zmult__eq__1__iff,axiom,
% 5.12/5.36 ! [M2: int,N: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ M2 )
% 5.12/5.36 => ( ( ( times_times_int @ M2 @ N )
% 5.12/5.36 = one_one_int )
% 5.12/5.36 = ( ( M2 = one_one_int )
% 5.12/5.36 & ( N = one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_zmult_eq_1_iff
% 5.12/5.36 thf(fact_3804_powr__mult,axiom,
% 5.12/5.36 ! [X: real,Y: real,A: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.12/5.36 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % powr_mult
% 5.12/5.36 thf(fact_3805_minusinfinity,axiom,
% 5.12/5.36 ! [D: int,P1: int > $o,P: int > $o] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ! [X3: int,K2: int] :
% 5.12/5.36 ( ( P1 @ X3 )
% 5.12/5.36 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.12/5.36 => ( ? [Z5: int] :
% 5.12/5.36 ! [X3: int] :
% 5.12/5.36 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.36 => ( ( P @ X3 )
% 5.12/5.36 = ( P1 @ X3 ) ) )
% 5.12/5.36 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.12/5.36 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minusinfinity
% 5.12/5.36 thf(fact_3806_plusinfinity,axiom,
% 5.12/5.36 ! [D: int,P5: int > $o,P: int > $o] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ! [X3: int,K2: int] :
% 5.12/5.36 ( ( P5 @ X3 )
% 5.12/5.36 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.12/5.36 => ( ? [Z5: int] :
% 5.12/5.36 ! [X3: int] :
% 5.12/5.36 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.36 => ( ( P @ X3 )
% 5.12/5.36 = ( P5 @ X3 ) ) )
% 5.12/5.36 => ( ? [X_12: int] : ( P5 @ X_12 )
% 5.12/5.36 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % plusinfinity
% 5.12/5.36 thf(fact_3807_zdiv__zmult2__eq,axiom,
% 5.12/5.36 ! [C: int,A: int,B: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.36 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % zdiv_zmult2_eq
% 5.12/5.36 thf(fact_3808_divide__powr__uminus,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.12/5.36 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_powr_uminus
% 5.12/5.36 thf(fact_3809_ln__powr,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( X != zero_zero_real )
% 5.12/5.36 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.12/5.36 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ln_powr
% 5.12/5.36 thf(fact_3810_log__powr,axiom,
% 5.12/5.36 ! [X: real,B: real,Y: real] :
% 5.12/5.36 ( ( X != zero_zero_real )
% 5.12/5.36 => ( ( log2 @ B @ ( powr_real @ X @ Y ) )
% 5.12/5.36 = ( times_times_real @ Y @ ( log2 @ B @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % log_powr
% 5.12/5.36 thf(fact_3811_div__mod__decomp__int,axiom,
% 5.12/5.36 ! [A2: int,N: int] :
% 5.12/5.36 ( A2
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % div_mod_decomp_int
% 5.12/5.36 thf(fact_3812_tanh__real__gt__neg1,axiom,
% 5.12/5.36 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % tanh_real_gt_neg1
% 5.12/5.36 thf(fact_3813_of__int__nonneg,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_nonneg
% 5.12/5.36 thf(fact_3814_of__int__nonneg,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_nonneg
% 5.12/5.36 thf(fact_3815_of__int__nonneg,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_nonneg
% 5.12/5.36 thf(fact_3816_of__int__leD,axiom,
% 5.12/5.36 ! [N: int,X: code_integer] :
% 5.12/5.36 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_leD
% 5.12/5.36 thf(fact_3817_of__int__leD,axiom,
% 5.12/5.36 ! [N: int,X: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_leD
% 5.12/5.36 thf(fact_3818_of__int__leD,axiom,
% 5.12/5.36 ! [N: int,X: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_leD
% 5.12/5.36 thf(fact_3819_of__int__leD,axiom,
% 5.12/5.36 ! [N: int,X: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_leD
% 5.12/5.36 thf(fact_3820_of__int__pos,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_pos
% 5.12/5.36 thf(fact_3821_of__int__pos,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_pos
% 5.12/5.36 thf(fact_3822_of__int__pos,axiom,
% 5.12/5.36 ! [Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_pos
% 5.12/5.36 thf(fact_3823_of__int__lessD,axiom,
% 5.12/5.36 ! [N: int,X: code_integer] :
% 5.12/5.36 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_lessD
% 5.12/5.36 thf(fact_3824_of__int__lessD,axiom,
% 5.12/5.36 ! [N: int,X: real] :
% 5.12/5.36 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_lessD
% 5.12/5.36 thf(fact_3825_of__int__lessD,axiom,
% 5.12/5.36 ! [N: int,X: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_lessD
% 5.12/5.36 thf(fact_3826_of__int__lessD,axiom,
% 5.12/5.36 ! [N: int,X: int] :
% 5.12/5.36 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.12/5.36 => ( ( N = zero_zero_int )
% 5.12/5.36 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_lessD
% 5.12/5.36 thf(fact_3827_floor__exists1,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ? [X3: int] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 5.12/5.36 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.12/5.36 & ! [Y5: int] :
% 5.12/5.36 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X )
% 5.12/5.36 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.12/5.36 => ( Y5 = X3 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % floor_exists1
% 5.12/5.36 thf(fact_3828_floor__exists1,axiom,
% 5.12/5.36 ! [X: rat] :
% 5.12/5.36 ? [X3: int] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 5.12/5.36 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.12/5.36 & ! [Y5: int] :
% 5.12/5.36 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X )
% 5.12/5.36 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.12/5.36 => ( Y5 = X3 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % floor_exists1
% 5.12/5.36 thf(fact_3829_floor__exists,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ? [Z4: int] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X )
% 5.12/5.36 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % floor_exists
% 5.12/5.36 thf(fact_3830_floor__exists,axiom,
% 5.12/5.36 ! [X: rat] :
% 5.12/5.36 ? [Z4: int] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X )
% 5.12/5.36 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % floor_exists
% 5.12/5.36 thf(fact_3831_of__int__ceiling__le__add__one,axiom,
% 5.12/5.36 ! [R4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R4 ) ) @ ( plus_plus_real @ R4 @ one_one_real ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_ceiling_le_add_one
% 5.12/5.36 thf(fact_3832_of__int__ceiling__le__add__one,axiom,
% 5.12/5.36 ! [R4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R4 ) ) @ ( plus_plus_rat @ R4 @ one_one_rat ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_ceiling_le_add_one
% 5.12/5.36 thf(fact_3833_of__int__ceiling__diff__one__le,axiom,
% 5.12/5.36 ! [R4: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R4 ) ) @ one_one_real ) @ R4 ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_ceiling_diff_one_le
% 5.12/5.36 thf(fact_3834_of__int__ceiling__diff__one__le,axiom,
% 5.12/5.36 ! [R4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R4 ) ) @ one_one_rat ) @ R4 ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_ceiling_diff_one_le
% 5.12/5.36 thf(fact_3835_of__nat__less__of__int__iff,axiom,
% 5.12/5.36 ! [N: nat,X: int] :
% 5.12/5.36 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 5.12/5.36 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_nat_less_of_int_iff
% 5.12/5.36 thf(fact_3836_of__nat__less__of__int__iff,axiom,
% 5.12/5.36 ! [N: nat,X: int] :
% 5.12/5.36 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 5.12/5.36 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_nat_less_of_int_iff
% 5.12/5.36 thf(fact_3837_of__nat__less__of__int__iff,axiom,
% 5.12/5.36 ! [N: nat,X: int] :
% 5.12/5.36 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 5.12/5.36 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_nat_less_of_int_iff
% 5.12/5.36 thf(fact_3838_field__le__mult__one__interval,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ! [Z4: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Z4 )
% 5.12/5.36 => ( ( ord_less_real @ Z4 @ one_one_real )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ Z4 @ X ) @ Y ) ) )
% 5.12/5.36 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.36
% 5.12/5.36 % field_le_mult_one_interval
% 5.12/5.36 thf(fact_3839_field__le__mult__one__interval,axiom,
% 5.12/5.36 ! [X: rat,Y: rat] :
% 5.12/5.36 ( ! [Z4: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 5.12/5.36 => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X ) @ Y ) ) )
% 5.12/5.36 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.12/5.36
% 5.12/5.36 % field_le_mult_one_interval
% 5.12/5.36 thf(fact_3840_mult__less__cancel__right2,axiom,
% 5.12/5.36 ! [A: real,C: real] :
% 5.12/5.36 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ A @ one_one_real ) )
% 5.12/5.36 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right2
% 5.12/5.36 thf(fact_3841_mult__less__cancel__right2,axiom,
% 5.12/5.36 ! [A: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.12/5.36 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right2
% 5.12/5.36 thf(fact_3842_mult__less__cancel__right2,axiom,
% 5.12/5.36 ! [A: int,C: int] :
% 5.12/5.36 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_int @ A @ one_one_int ) )
% 5.12/5.36 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right2
% 5.12/5.36 thf(fact_3843_mult__less__cancel__right1,axiom,
% 5.12/5.36 ! [C: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ one_one_real @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right1
% 5.12/5.36 thf(fact_3844_mult__less__cancel__right1,axiom,
% 5.12/5.36 ! [C: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right1
% 5.12/5.36 thf(fact_3845_mult__less__cancel__right1,axiom,
% 5.12/5.36 ! [C: int,B: int] :
% 5.12/5.36 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_int @ one_one_int @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_right1
% 5.12/5.36 thf(fact_3846_mult__less__cancel__left2,axiom,
% 5.12/5.36 ! [C: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ A @ one_one_real ) )
% 5.12/5.36 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left2
% 5.12/5.36 thf(fact_3847_mult__less__cancel__left2,axiom,
% 5.12/5.36 ! [C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.12/5.36 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left2
% 5.12/5.36 thf(fact_3848_mult__less__cancel__left2,axiom,
% 5.12/5.36 ! [C: int,A: int] :
% 5.12/5.36 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_int @ A @ one_one_int ) )
% 5.12/5.36 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left2
% 5.12/5.36 thf(fact_3849_mult__less__cancel__left1,axiom,
% 5.12/5.36 ! [C: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ one_one_real @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left1
% 5.12/5.36 thf(fact_3850_mult__less__cancel__left1,axiom,
% 5.12/5.36 ! [C: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left1
% 5.12/5.36 thf(fact_3851_mult__less__cancel__left1,axiom,
% 5.12/5.36 ! [C: int,B: int] :
% 5.12/5.36 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_int @ one_one_int @ B ) )
% 5.12/5.36 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_cancel_left1
% 5.12/5.36 thf(fact_3852_mult__le__cancel__right2,axiom,
% 5.12/5.36 ! [A: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.12/5.36 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right2
% 5.12/5.36 thf(fact_3853_mult__le__cancel__right2,axiom,
% 5.12/5.36 ! [A: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.12/5.36 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right2
% 5.12/5.36 thf(fact_3854_mult__le__cancel__right2,axiom,
% 5.12/5.36 ! [A: int,C: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.12/5.36 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.12/5.36 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right2
% 5.12/5.36 thf(fact_3855_mult__le__cancel__right1,axiom,
% 5.12/5.36 ! [C: real,B: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.12/5.36 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right1
% 5.12/5.36 thf(fact_3856_mult__le__cancel__right1,axiom,
% 5.12/5.36 ! [C: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.12/5.36 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right1
% 5.12/5.36 thf(fact_3857_mult__le__cancel__right1,axiom,
% 5.12/5.36 ! [C: int,B: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.12/5.36 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_right1
% 5.12/5.36 thf(fact_3858_mult__le__cancel__left2,axiom,
% 5.12/5.36 ! [C: real,A: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.12/5.36 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left2
% 5.12/5.36 thf(fact_3859_mult__le__cancel__left2,axiom,
% 5.12/5.36 ! [C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.12/5.36 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left2
% 5.12/5.36 thf(fact_3860_mult__le__cancel__left2,axiom,
% 5.12/5.36 ! [C: int,A: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.12/5.36 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.12/5.36 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left2
% 5.12/5.36 thf(fact_3861_mult__le__cancel__left1,axiom,
% 5.12/5.36 ! [C: real,B: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.12/5.36 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left1
% 5.12/5.36 thf(fact_3862_mult__le__cancel__left1,axiom,
% 5.12/5.36 ! [C: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.12/5.36 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left1
% 5.12/5.36 thf(fact_3863_mult__le__cancel__left1,axiom,
% 5.12/5.36 ! [C: int,B: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.12/5.36 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.12/5.36 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.12/5.36 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_left1
% 5.12/5.36 thf(fact_3864_divide__le__eq,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_le_eq
% 5.12/5.36 thf(fact_3865_divide__le__eq,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_le_eq
% 5.12/5.36 thf(fact_3866_le__divide__eq,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_divide_eq
% 5.12/5.36 thf(fact_3867_le__divide__eq,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_divide_eq
% 5.12/5.36 thf(fact_3868_divide__left__mono,axiom,
% 5.12/5.36 ! [B: real,A: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ B @ A )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_left_mono
% 5.12/5.36 thf(fact_3869_divide__left__mono,axiom,
% 5.12/5.36 ! [B: rat,A: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ B @ A )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.36 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_left_mono
% 5.12/5.36 thf(fact_3870_neg__divide__le__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_divide_le_eq
% 5.12/5.36 thf(fact_3871_neg__divide__le__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_divide_le_eq
% 5.12/5.36 thf(fact_3872_neg__le__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_le_divide_eq
% 5.12/5.36 thf(fact_3873_neg__le__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_le_divide_eq
% 5.12/5.36 thf(fact_3874_pos__divide__le__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_divide_le_eq
% 5.12/5.36 thf(fact_3875_pos__divide__le__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.12/5.36 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_divide_le_eq
% 5.12/5.36 thf(fact_3876_pos__le__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.12/5.36 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_le_divide_eq
% 5.12/5.36 thf(fact_3877_pos__le__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.36 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_le_divide_eq
% 5.12/5.36 thf(fact_3878_mult__imp__div__pos__le,axiom,
% 5.12/5.36 ! [Y: real,X: real,Z2: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z2 @ Y ) )
% 5.12/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_div_pos_le
% 5.12/5.36 thf(fact_3879_mult__imp__div__pos__le,axiom,
% 5.12/5.36 ! [Y: rat,X: rat,Z2: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.36 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z2 @ Y ) )
% 5.12/5.36 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_div_pos_le
% 5.12/5.36 thf(fact_3880_mult__imp__le__div__pos,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ Y ) @ X )
% 5.12/5.36 => ( ord_less_eq_real @ Z2 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_le_div_pos
% 5.12/5.36 thf(fact_3881_mult__imp__le__div__pos,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ Y ) @ X )
% 5.12/5.36 => ( ord_less_eq_rat @ Z2 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_imp_le_div_pos
% 5.12/5.36 thf(fact_3882_divide__left__mono__neg,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.36 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_left_mono_neg
% 5.12/5.36 thf(fact_3883_divide__left__mono__neg,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.36 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.36 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % divide_left_mono_neg
% 5.12/5.36 thf(fact_3884_convex__bound__le,axiom,
% 5.12/5.36 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ X @ A )
% 5.12/5.36 => ( ( ord_less_eq_real @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.12/5.36 => ( ( ( plus_plus_real @ U @ V )
% 5.12/5.36 = one_one_real )
% 5.12/5.36 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_le
% 5.12/5.36 thf(fact_3885_convex__bound__le,axiom,
% 5.12/5.36 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ X @ A )
% 5.12/5.36 => ( ( ord_less_eq_rat @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.12/5.36 => ( ( ( plus_plus_rat @ U @ V )
% 5.12/5.36 = one_one_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_le
% 5.12/5.36 thf(fact_3886_convex__bound__le,axiom,
% 5.12/5.36 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ X @ A )
% 5.12/5.36 => ( ( ord_less_eq_int @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.12/5.36 => ( ( ( plus_plus_int @ U @ V )
% 5.12/5.36 = one_one_int )
% 5.12/5.36 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_le
% 5.12/5.36 thf(fact_3887_int__le__real__less,axiom,
% 5.12/5.36 ( ord_less_eq_int
% 5.12/5.36 = ( ^ [N4: int,M5: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_le_real_less
% 5.12/5.36 thf(fact_3888_int__less__real__le,axiom,
% 5.12/5.36 ( ord_less_int
% 5.12/5.36 = ( ^ [N4: int,M5: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M5 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_less_real_le
% 5.12/5.36 thf(fact_3889_frac__le__eq,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real,W: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z2 ) )
% 5.12/5.36 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % frac_le_eq
% 5.12/5.36 thf(fact_3890_frac__le__eq,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat,W: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z2 ) )
% 5.12/5.36 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % frac_le_eq
% 5.12/5.36 thf(fact_3891_frac__less__eq,axiom,
% 5.12/5.36 ! [Y: real,Z2: real,X: real,W: real] :
% 5.12/5.36 ( ( Y != zero_zero_real )
% 5.12/5.36 => ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z2 ) )
% 5.12/5.36 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z2 ) ) @ zero_zero_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % frac_less_eq
% 5.12/5.36 thf(fact_3892_frac__less__eq,axiom,
% 5.12/5.36 ! [Y: rat,Z2: rat,X: rat,W: rat] :
% 5.12/5.36 ( ( Y != zero_zero_rat )
% 5.12/5.36 => ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z2 ) )
% 5.12/5.36 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z2 ) ) @ zero_zero_rat ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % frac_less_eq
% 5.12/5.36 thf(fact_3893_power__Suc__less,axiom,
% 5.12/5.36 ! [A: real,N: nat] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.36 => ( ( ord_less_real @ A @ one_one_real )
% 5.12/5.36 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_Suc_less
% 5.12/5.36 thf(fact_3894_power__Suc__less,axiom,
% 5.12/5.36 ! [A: rat,N: nat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.36 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.12/5.36 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_Suc_less
% 5.12/5.36 thf(fact_3895_power__Suc__less,axiom,
% 5.12/5.36 ! [A: nat,N: nat] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.12/5.36 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.12/5.36 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_Suc_less
% 5.12/5.36 thf(fact_3896_power__Suc__less,axiom,
% 5.12/5.36 ! [A: int,N: nat] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.36 => ( ( ord_less_int @ A @ one_one_int )
% 5.12/5.36 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_Suc_less
% 5.12/5.36 thf(fact_3897_pos__minus__divide__less__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_minus_divide_less_eq
% 5.12/5.36 thf(fact_3898_pos__minus__divide__less__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_minus_divide_less_eq
% 5.12/5.36 thf(fact_3899_pos__less__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_less_minus_divide_eq
% 5.12/5.36 thf(fact_3900_pos__less__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_less_minus_divide_eq
% 5.12/5.36 thf(fact_3901_neg__minus__divide__less__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_minus_divide_less_eq
% 5.12/5.36 thf(fact_3902_neg__minus__divide__less__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_minus_divide_less_eq
% 5.12/5.36 thf(fact_3903_neg__less__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_less_minus_divide_eq
% 5.12/5.36 thf(fact_3904_neg__less__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_less_minus_divide_eq
% 5.12/5.36 thf(fact_3905_minus__divide__less__eq,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_less_eq
% 5.12/5.36 thf(fact_3906_minus__divide__less__eq,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_less_eq
% 5.12/5.36 thf(fact_3907_less__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_minus_divide_eq
% 5.12/5.36 thf(fact_3908_less__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % less_minus_divide_eq
% 5.12/5.36 thf(fact_3909_add__divide__eq__if__simps_I3_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(3)
% 5.12/5.36 thf(fact_3910_add__divide__eq__if__simps_I3_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(3)
% 5.12/5.36 thf(fact_3911_add__divide__eq__if__simps_I3_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.12/5.36 = B ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(3)
% 5.12/5.36 thf(fact_3912_minus__divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_add_eq_iff
% 5.12/5.36 thf(fact_3913_minus__divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_add_eq_iff
% 5.12/5.36 thf(fact_3914_minus__divide__add__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_add_eq_iff
% 5.12/5.36 thf(fact_3915_add__divide__eq__if__simps_I6_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(6)
% 5.12/5.36 thf(fact_3916_add__divide__eq__if__simps_I6_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(6)
% 5.12/5.36 thf(fact_3917_add__divide__eq__if__simps_I6_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z2 ) ) @ B )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(6)
% 5.12/5.36 thf(fact_3918_add__divide__eq__if__simps_I5_J,axiom,
% 5.12/5.36 ! [Z2: real,A: real,B: real] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.12/5.36 = ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(5)
% 5.12/5.36 thf(fact_3919_add__divide__eq__if__simps_I5_J,axiom,
% 5.12/5.36 ! [Z2: complex,A: complex,B: complex] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.12/5.36 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(5)
% 5.12/5.36 thf(fact_3920_add__divide__eq__if__simps_I5_J,axiom,
% 5.12/5.36 ! [Z2: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ( Z2 = zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.12/5.36 = ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z2 ) @ B )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z2 ) ) @ Z2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_divide_eq_if_simps(5)
% 5.12/5.36 thf(fact_3921_minus__divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( Z2 != zero_zero_real )
% 5.12/5.36 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_diff_eq_iff
% 5.12/5.36 thf(fact_3922_minus__divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: complex,X: complex,Y: complex] :
% 5.12/5.36 ( ( Z2 != zero_zero_complex )
% 5.12/5.36 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_diff_eq_iff
% 5.12/5.36 thf(fact_3923_minus__divide__diff__eq__iff,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( Z2 != zero_zero_rat )
% 5.12/5.36 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z2 ) ) @ Y )
% 5.12/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z2 ) ) @ Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_diff_eq_iff
% 5.12/5.36 thf(fact_3924_ceiling__divide__eq__div,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.12/5.36 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_divide_eq_div
% 5.12/5.36 thf(fact_3925_ceiling__divide__eq__div,axiom,
% 5.12/5.36 ! [A: int,B: int] :
% 5.12/5.36 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.12/5.36 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_divide_eq_div
% 5.12/5.36 thf(fact_3926_mod__mult2__eq_H,axiom,
% 5.12/5.36 ! [A: code_integer,M2: nat,N: nat] :
% 5.12/5.36 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M2 ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult2_eq'
% 5.12/5.36 thf(fact_3927_mod__mult2__eq_H,axiom,
% 5.12/5.36 ! [A: code_natural,M2: nat,N: nat] :
% 5.12/5.36 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N ) ) )
% 5.12/5.36 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult2_eq'
% 5.12/5.36 thf(fact_3928_mod__mult2__eq_H,axiom,
% 5.12/5.36 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.36 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.12/5.36 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult2_eq'
% 5.12/5.36 thf(fact_3929_mod__mult2__eq_H,axiom,
% 5.12/5.36 ! [A: int,M2: nat,N: nat] :
% 5.12/5.36 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mod_mult2_eq'
% 5.12/5.36 thf(fact_3930_real__of__int__div__aux,axiom,
% 5.12/5.36 ! [X: int,D: int] :
% 5.12/5.36 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.12/5.36 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % real_of_int_div_aux
% 5.12/5.36 thf(fact_3931_zmult__zless__mono2__lemma,axiom,
% 5.12/5.36 ! [I: int,J2: int,K: nat] :
% 5.12/5.36 ( ( ord_less_int @ I @ J2 )
% 5.12/5.36 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.36 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % zmult_zless_mono2_lemma
% 5.12/5.36 thf(fact_3932_incr__mult__lemma,axiom,
% 5.12/5.36 ! [D: int,P: int > $o,K: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ! [X3: int] :
% 5.12/5.36 ( ( P @ X3 )
% 5.12/5.36 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.36 => ! [X4: int] :
% 5.12/5.36 ( ( P @ X4 )
% 5.12/5.36 => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % incr_mult_lemma
% 5.12/5.36 thf(fact_3933_unique__quotient__lemma__neg,axiom,
% 5.12/5.36 ! [B: int,Q6: int,R5: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ R4 @ zero_zero_int )
% 5.12/5.36 => ( ( ord_less_int @ B @ R4 )
% 5.12/5.36 => ( ( ord_less_int @ B @ R5 )
% 5.12/5.36 => ( ord_less_eq_int @ Q5 @ Q6 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % unique_quotient_lemma_neg
% 5.12/5.36 thf(fact_3934_unique__quotient__lemma,axiom,
% 5.12/5.36 ! [B: int,Q6: int,R5: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 5.12/5.36 => ( ( ord_less_int @ R5 @ B )
% 5.12/5.36 => ( ( ord_less_int @ R4 @ B )
% 5.12/5.36 => ( ord_less_eq_int @ Q6 @ Q5 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % unique_quotient_lemma
% 5.12/5.36 thf(fact_3935_zdiv__mono2__neg__lemma,axiom,
% 5.12/5.36 ! [B: int,Q5: int,R4: int,B4: int,Q6: int,R5: int] :
% 5.12/5.36 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 )
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R5 ) )
% 5.12/5.36 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R5 ) @ zero_zero_int )
% 5.12/5.36 => ( ( ord_less_int @ R4 @ B )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 5.12/5.36 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.12/5.36 => ( ( ord_less_eq_int @ B4 @ B )
% 5.12/5.36 => ( ord_less_eq_int @ Q6 @ Q5 ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % zdiv_mono2_neg_lemma
% 5.12/5.36 thf(fact_3936_zdiv__mono2__lemma,axiom,
% 5.12/5.36 ! [B: int,Q5: int,R4: int,B4: int,Q6: int,R5: int] :
% 5.12/5.36 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 )
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R5 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R5 ) )
% 5.12/5.36 => ( ( ord_less_int @ R5 @ B4 )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.12/5.36 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.12/5.36 => ( ( ord_less_eq_int @ B4 @ B )
% 5.12/5.36 => ( ord_less_eq_int @ Q5 @ Q6 ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % zdiv_mono2_lemma
% 5.12/5.36 thf(fact_3937_q__pos__lemma,axiom,
% 5.12/5.36 ! [B4: int,Q6: int,R5: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q6 ) @ R5 ) )
% 5.12/5.36 => ( ( ord_less_int @ R5 @ B4 )
% 5.12/5.36 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.12/5.36 => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % q_pos_lemma
% 5.12/5.36 thf(fact_3938_decr__mult__lemma,axiom,
% 5.12/5.36 ! [D: int,P: int > $o,K: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ! [X3: int] :
% 5.12/5.36 ( ( P @ X3 )
% 5.12/5.36 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.36 => ! [X4: int] :
% 5.12/5.36 ( ( P @ X4 )
% 5.12/5.36 => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % decr_mult_lemma
% 5.12/5.36 thf(fact_3939_ln__mult,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.12/5.36 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ln_mult
% 5.12/5.36 thf(fact_3940_powr__def,axiom,
% 5.12/5.36 ( powr_real
% 5.12/5.36 = ( ^ [X2: real,A3: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % powr_def
% 5.12/5.36 thf(fact_3941_ceiling__split,axiom,
% 5.12/5.36 ! [P: int > $o,T: real] :
% 5.12/5.36 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.12/5.36 = ( ! [I2: int] :
% 5.12/5.36 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) @ T )
% 5.12/5.36 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I2 ) ) )
% 5.12/5.36 => ( P @ I2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_split
% 5.12/5.36 thf(fact_3942_ceiling__split,axiom,
% 5.12/5.36 ! [P: int > $o,T: rat] :
% 5.12/5.36 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.12/5.36 = ( ! [I2: int] :
% 5.12/5.36 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 5.12/5.36 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 5.12/5.36 => ( P @ I2 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_split
% 5.12/5.36 thf(fact_3943_ceiling__eq__iff,axiom,
% 5.12/5.36 ! [X: real,A: int] :
% 5.12/5.36 ( ( ( archim7802044766580827645g_real @ X )
% 5.12/5.36 = A )
% 5.12/5.36 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 5.12/5.36 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_eq_iff
% 5.12/5.36 thf(fact_3944_ceiling__eq__iff,axiom,
% 5.12/5.36 ! [X: rat,A: int] :
% 5.12/5.36 ( ( ( archim2889992004027027881ng_rat @ X )
% 5.12/5.36 = A )
% 5.12/5.36 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 5.12/5.36 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_eq_iff
% 5.12/5.36 thf(fact_3945_ceiling__unique,axiom,
% 5.12/5.36 ! [Z2: int,X: real] :
% 5.12/5.36 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) @ X )
% 5.12/5.36 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.36 => ( ( archim7802044766580827645g_real @ X )
% 5.12/5.36 = Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_unique
% 5.12/5.36 thf(fact_3946_ceiling__unique,axiom,
% 5.12/5.36 ! [Z2: int,X: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X )
% 5.12/5.36 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.36 => ( ( archim2889992004027027881ng_rat @ X )
% 5.12/5.36 = Z2 ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_unique
% 5.12/5.36 thf(fact_3947_ceiling__correct,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 5.12/5.36 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_correct
% 5.12/5.36 thf(fact_3948_ceiling__correct,axiom,
% 5.12/5.36 ! [X: rat] :
% 5.12/5.36 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 5.12/5.36 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_correct
% 5.12/5.36 thf(fact_3949_ceiling__less__iff,axiom,
% 5.12/5.36 ! [X: real,Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z2 )
% 5.12/5.36 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_less_iff
% 5.12/5.36 thf(fact_3950_ceiling__less__iff,axiom,
% 5.12/5.36 ! [X: rat,Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z2 )
% 5.12/5.36 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ceiling_less_iff
% 5.12/5.36 thf(fact_3951_le__ceiling__iff,axiom,
% 5.12/5.36 ! [Z2: int,X: rat] :
% 5.12/5.36 ( ( ord_less_eq_int @ Z2 @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.36 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_ceiling_iff
% 5.12/5.36 thf(fact_3952_le__ceiling__iff,axiom,
% 5.12/5.36 ! [Z2: int,X: real] :
% 5.12/5.36 ( ( ord_less_eq_int @ Z2 @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.36 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_ceiling_iff
% 5.12/5.36 thf(fact_3953_convex__bound__lt,axiom,
% 5.12/5.36 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.12/5.36 ( ( ord_less_real @ X @ A )
% 5.12/5.36 => ( ( ord_less_real @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.12/5.36 => ( ( ( plus_plus_real @ U @ V )
% 5.12/5.36 = one_one_real )
% 5.12/5.36 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_lt
% 5.12/5.36 thf(fact_3954_convex__bound__lt,axiom,
% 5.12/5.36 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.12/5.36 ( ( ord_less_rat @ X @ A )
% 5.12/5.36 => ( ( ord_less_rat @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.12/5.36 => ( ( ( plus_plus_rat @ U @ V )
% 5.12/5.36 = one_one_rat )
% 5.12/5.36 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_lt
% 5.12/5.36 thf(fact_3955_convex__bound__lt,axiom,
% 5.12/5.36 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.12/5.36 ( ( ord_less_int @ X @ A )
% 5.12/5.36 => ( ( ord_less_int @ Y @ A )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.12/5.36 => ( ( ( plus_plus_int @ U @ V )
% 5.12/5.36 = one_one_int )
% 5.12/5.36 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % convex_bound_lt
% 5.12/5.36 thf(fact_3956_le__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: real,B: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_minus_divide_eq
% 5.12/5.36 thf(fact_3957_le__minus__divide__eq,axiom,
% 5.12/5.36 ! [A: rat,B: rat,C: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % le_minus_divide_eq
% 5.12/5.36 thf(fact_3958_minus__divide__le__eq,axiom,
% 5.12/5.36 ! [B: real,C: real,A: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_le_eq
% 5.12/5.36 thf(fact_3959_minus__divide__le__eq,axiom,
% 5.12/5.36 ! [B: rat,C: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.12/5.36 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % minus_divide_le_eq
% 5.12/5.36 thf(fact_3960_neg__le__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_le_minus_divide_eq
% 5.12/5.36 thf(fact_3961_neg__le__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_le_minus_divide_eq
% 5.12/5.36 thf(fact_3962_neg__minus__divide__le__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_minus_divide_le_eq
% 5.12/5.36 thf(fact_3963_neg__minus__divide__le__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % neg_minus_divide_le_eq
% 5.12/5.36 thf(fact_3964_pos__le__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: real,A: real,B: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_le_minus_divide_eq
% 5.12/5.36 thf(fact_3965_pos__le__minus__divide__eq,axiom,
% 5.12/5.36 ! [C: rat,A: rat,B: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.12/5.36 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_le_minus_divide_eq
% 5.12/5.36 thf(fact_3966_pos__minus__divide__le__eq,axiom,
% 5.12/5.36 ! [C: real,B: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_minus_divide_le_eq
% 5.12/5.36 thf(fact_3967_pos__minus__divide__le__eq,axiom,
% 5.12/5.36 ! [C: rat,B: rat,A: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.12/5.36 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % pos_minus_divide_le_eq
% 5.12/5.36 thf(fact_3968_scaling__mono,axiom,
% 5.12/5.36 ! [U: real,V: real,R4: real,S: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ U @ V )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ R4 )
% 5.12/5.36 => ( ( ord_less_eq_real @ R4 @ S )
% 5.12/5.36 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R4 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % scaling_mono
% 5.12/5.36 thf(fact_3969_scaling__mono,axiom,
% 5.12/5.36 ! [U: rat,V: rat,R4: rat,S: rat] :
% 5.12/5.36 ( ( ord_less_eq_rat @ U @ V )
% 5.12/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ R4 )
% 5.12/5.36 => ( ( ord_less_eq_rat @ R4 @ S )
% 5.12/5.36 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R4 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % scaling_mono
% 5.12/5.36 thf(fact_3970_real__of__int__div2,axiom,
% 5.12/5.36 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % real_of_int_div2
% 5.12/5.36 thf(fact_3971_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.12/5.36 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.36 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.12/5.36 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.36 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.12/5.36 thf(fact_3972_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.12/5.36 ! [C: nat,A: nat,B: nat] :
% 5.12/5.36 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.12/5.36 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.36 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.12/5.36 thf(fact_3973_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.12/5.36 ! [C: int,A: int,B: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.12/5.36 thf(fact_3974_real__of__int__div3,axiom,
% 5.12/5.36 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 5.12/5.36
% 5.12/5.36 % real_of_int_div3
% 5.12/5.36 thf(fact_3975_power__eq__if,axiom,
% 5.12/5.36 ( power_power_complex
% 5.12/5.36 = ( ^ [P6: complex,M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_eq_if
% 5.12/5.36 thf(fact_3976_power__eq__if,axiom,
% 5.12/5.36 ( power_power_real
% 5.12/5.36 = ( ^ [P6: real,M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_eq_if
% 5.12/5.36 thf(fact_3977_power__eq__if,axiom,
% 5.12/5.36 ( power_power_rat
% 5.12/5.36 = ( ^ [P6: rat,M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_eq_if
% 5.12/5.36 thf(fact_3978_power__eq__if,axiom,
% 5.12/5.36 ( power_power_nat
% 5.12/5.36 = ( ^ [P6: nat,M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_eq_if
% 5.12/5.36 thf(fact_3979_power__eq__if,axiom,
% 5.12/5.36 ( power_power_int
% 5.12/5.36 = ( ^ [P6: int,M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_eq_if
% 5.12/5.36 thf(fact_3980_power__minus__mult,axiom,
% 5.12/5.36 ! [N: nat,A: complex] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.12/5.36 = ( power_power_complex @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus_mult
% 5.12/5.36 thf(fact_3981_power__minus__mult,axiom,
% 5.12/5.36 ! [N: nat,A: real] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.12/5.36 = ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus_mult
% 5.12/5.36 thf(fact_3982_power__minus__mult,axiom,
% 5.12/5.36 ! [N: nat,A: rat] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.12/5.36 = ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus_mult
% 5.12/5.36 thf(fact_3983_power__minus__mult,axiom,
% 5.12/5.36 ! [N: nat,A: nat] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.12/5.36 = ( power_power_nat @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus_mult
% 5.12/5.36 thf(fact_3984_power__minus__mult,axiom,
% 5.12/5.36 ! [N: nat,A: int] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.12/5.36 = ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % power_minus_mult
% 5.12/5.36 thf(fact_3985_real__archimedian__rdiv__eq__0,axiom,
% 5.12/5.36 ! [X: real,C: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.12/5.36 => ( ! [M3: nat] :
% 5.12/5.36 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 5.12/5.36 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X ) @ C ) )
% 5.12/5.36 => ( X = zero_zero_real ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % real_archimedian_rdiv_eq_0
% 5.12/5.36 thf(fact_3986_powr__mult__base,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.12/5.36 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % powr_mult_base
% 5.12/5.36 thf(fact_3987_log__mult,axiom,
% 5.12/5.36 ! [A: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.36 => ( ( A != one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.36 => ( ( log2 @ A @ ( times_times_real @ X @ Y ) )
% 5.12/5.36 = ( plus_plus_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % log_mult
% 5.12/5.36 thf(fact_3988_split__zdiv,axiom,
% 5.12/5.36 ! [P: int > $o,N: int,K: int] :
% 5.12/5.36 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.12/5.36 = ( ( ( K = zero_zero_int )
% 5.12/5.36 => ( P @ zero_zero_int ) )
% 5.12/5.36 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.36 => ! [I2: int,J3: int] :
% 5.12/5.36 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.12/5.36 & ( ord_less_int @ J3 @ K )
% 5.12/5.36 & ( N
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.36 => ( P @ I2 ) ) )
% 5.12/5.36 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.36 => ! [I2: int,J3: int] :
% 5.12/5.36 ( ( ( ord_less_int @ K @ J3 )
% 5.12/5.36 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.12/5.36 & ( N
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.36 => ( P @ I2 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % split_zdiv
% 5.12/5.36 thf(fact_3989_int__div__neg__eq,axiom,
% 5.12/5.36 ! [A: int,B: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ R4 @ zero_zero_int )
% 5.12/5.36 => ( ( ord_less_int @ B @ R4 )
% 5.12/5.36 => ( ( divide_divide_int @ A @ B )
% 5.12/5.36 = Q5 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_div_neg_eq
% 5.12/5.36 thf(fact_3990_int__div__pos__eq,axiom,
% 5.12/5.36 ! [A: int,B: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.12/5.36 => ( ( ord_less_int @ R4 @ B )
% 5.12/5.36 => ( ( divide_divide_int @ A @ B )
% 5.12/5.36 = Q5 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_div_pos_eq
% 5.12/5.36 thf(fact_3991_ln__realpow,axiom,
% 5.12/5.36 ! [X: real,N: nat] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.12/5.36 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ln_realpow
% 5.12/5.36 thf(fact_3992_log__nat__power,axiom,
% 5.12/5.36 ! [X: real,B: real,N: nat] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( log2 @ B @ ( power_power_real @ X @ N ) )
% 5.12/5.36 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % log_nat_power
% 5.12/5.36 thf(fact_3993_int__mod__pos__eq,axiom,
% 5.12/5.36 ! [A: int,B: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.12/5.36 => ( ( ord_less_int @ R4 @ B )
% 5.12/5.36 => ( ( modulo_modulo_int @ A @ B )
% 5.12/5.36 = R4 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_mod_pos_eq
% 5.12/5.36 thf(fact_3994_int__mod__neg__eq,axiom,
% 5.12/5.36 ! [A: int,B: int,Q5: int,R4: int] :
% 5.12/5.36 ( ( A
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.12/5.36 => ( ( ord_less_eq_int @ R4 @ zero_zero_int )
% 5.12/5.36 => ( ( ord_less_int @ B @ R4 )
% 5.12/5.36 => ( ( modulo_modulo_int @ A @ B )
% 5.12/5.36 = R4 ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % int_mod_neg_eq
% 5.12/5.36 thf(fact_3995_split__zmod,axiom,
% 5.12/5.36 ! [P: int > $o,N: int,K: int] :
% 5.12/5.36 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.12/5.36 = ( ( ( K = zero_zero_int )
% 5.12/5.36 => ( P @ N ) )
% 5.12/5.36 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.36 => ! [I2: int,J3: int] :
% 5.12/5.36 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.12/5.36 & ( ord_less_int @ J3 @ K )
% 5.12/5.36 & ( N
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.36 => ( P @ J3 ) ) )
% 5.12/5.36 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.36 => ! [I2: int,J3: int] :
% 5.12/5.36 ( ( ( ord_less_int @ K @ J3 )
% 5.12/5.36 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.12/5.36 & ( N
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.36 => ( P @ J3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % split_zmod
% 5.12/5.36 thf(fact_3996_zmod__zmult2__eq,axiom,
% 5.12/5.36 ! [C: int,A: int,B: int] :
% 5.12/5.36 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.12/5.36 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % zmod_zmult2_eq
% 5.12/5.36 thf(fact_3997_of__int__of__nat,axiom,
% 5.12/5.36 ( ring_18347121197199848620nteger
% 5.12/5.36 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_of_nat
% 5.12/5.36 thf(fact_3998_of__int__of__nat,axiom,
% 5.12/5.36 ( ring_17405671764205052669omplex
% 5.12/5.36 = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_of_nat
% 5.12/5.36 thf(fact_3999_of__int__of__nat,axiom,
% 5.12/5.36 ( ring_1_of_int_real
% 5.12/5.36 = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_of_nat
% 5.12/5.36 thf(fact_4000_of__int__of__nat,axiom,
% 5.12/5.36 ( ring_1_of_int_rat
% 5.12/5.36 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_of_nat
% 5.12/5.36 thf(fact_4001_of__int__of__nat,axiom,
% 5.12/5.36 ( ring_1_of_int_int
% 5.12/5.36 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % of_int_of_nat
% 5.12/5.36 thf(fact_4002_linear__plus__1__le__power,axiom,
% 5.12/5.36 ! [X: real,N: nat] :
% 5.12/5.36 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % linear_plus_1_le_power
% 5.12/5.36 thf(fact_4003_ln__powr__bound2,axiom,
% 5.12/5.36 ! [X: real,A: real] :
% 5.12/5.36 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.36 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % ln_powr_bound2
% 5.12/5.36 thf(fact_4004_Bernoulli__inequality,axiom,
% 5.12/5.36 ! [X: real,N: nat] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.36 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % Bernoulli_inequality
% 5.12/5.36 thf(fact_4005_log__eq__div__ln__mult__log,axiom,
% 5.12/5.36 ! [A: real,B: real,X: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.36 => ( ( A != one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.36 => ( ( B != one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( log2 @ A @ X )
% 5.12/5.36 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log2 @ B @ X ) ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % log_eq_div_ln_mult_log
% 5.12/5.36 thf(fact_4006_incr__lemma,axiom,
% 5.12/5.36 ! [D: int,Z2: int,X: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ord_less_int @ Z2 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % incr_lemma
% 5.12/5.36 thf(fact_4007_decr__lemma,axiom,
% 5.12/5.36 ! [D: int,X: int,Z2: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.36 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z2 ) ) @ one_one_int ) @ D ) ) @ Z2 ) ) ).
% 5.12/5.36
% 5.12/5.36 % decr_lemma
% 5.12/5.36 thf(fact_4008_log__add__eq__powr,axiom,
% 5.12/5.36 ! [B: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.36 => ( ( B != one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( plus_plus_real @ ( log2 @ B @ X ) @ Y )
% 5.12/5.36 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % log_add_eq_powr
% 5.12/5.36 thf(fact_4009_add__log__eq__powr,axiom,
% 5.12/5.36 ! [B: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.36 => ( ( B != one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( plus_plus_real @ Y @ ( log2 @ B @ X ) )
% 5.12/5.36 = ( log2 @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % add_log_eq_powr
% 5.12/5.36 thf(fact_4010_split__pos__lemma,axiom,
% 5.12/5.36 ! [K: int,P: int > int > $o,N: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.36 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.12/5.36 = ( ! [I2: int,J3: int] :
% 5.12/5.36 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.12/5.36 & ( ord_less_int @ J3 @ K )
% 5.12/5.36 & ( N
% 5.12/5.36 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.12/5.36 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % split_pos_lemma
% 5.12/5.36 thf(fact_4011_mult__le__cancel__iff2,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( times_times_real @ Z2 @ X ) @ ( times_times_real @ Z2 @ Y ) )
% 5.12/5.36 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff2
% 5.12/5.36 thf(fact_4012_mult__le__cancel__iff2,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ ( times_times_rat @ Z2 @ Y ) )
% 5.12/5.36 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff2
% 5.12/5.36 thf(fact_4013_mult__le__cancel__iff2,axiom,
% 5.12/5.36 ! [Z2: int,X: int,Y: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_int @ ( times_times_int @ Z2 @ X ) @ ( times_times_int @ Z2 @ Y ) )
% 5.12/5.36 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff2
% 5.12/5.36 thf(fact_4014_mult__le__cancel__iff1,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff1
% 5.12/5.36 thf(fact_4015_mult__le__cancel__iff1,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff1
% 5.12/5.36 thf(fact_4016_mult__le__cancel__iff1,axiom,
% 5.12/5.36 ! [Z2: int,X: int,Y: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_le_cancel_iff1
% 5.12/5.36 thf(fact_4017_mult__less__iff1,axiom,
% 5.12/5.36 ! [Z2: real,X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.12/5.36 => ( ( ord_less_real @ ( times_times_real @ X @ Z2 ) @ ( times_times_real @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_iff1
% 5.12/5.36 thf(fact_4018_mult__less__iff1,axiom,
% 5.12/5.36 ! [Z2: rat,X: rat,Y: rat] :
% 5.12/5.36 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.12/5.36 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z2 ) @ ( times_times_rat @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_iff1
% 5.12/5.36 thf(fact_4019_mult__less__iff1,axiom,
% 5.12/5.36 ! [Z2: int,X: int,Y: int] :
% 5.12/5.36 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 5.12/5.36 => ( ( ord_less_int @ ( times_times_int @ X @ Z2 ) @ ( times_times_int @ Y @ Z2 ) )
% 5.12/5.36 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_less_iff1
% 5.12/5.36 thf(fact_4020_powr__real__of__int,axiom,
% 5.12/5.36 ! [X: real,N: int] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.12/5.36 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.12/5.36 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 5.12/5.36 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.12/5.36 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.12/5.36 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % powr_real_of_int
% 5.12/5.36 thf(fact_4021_floor__log__eq__powr__iff,axiom,
% 5.12/5.36 ! [X: real,B: real,K: int] :
% 5.12/5.36 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.36 => ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.36 => ( ( ( archim6058952711729229775r_real @ ( log2 @ B @ X ) )
% 5.12/5.36 = K )
% 5.12/5.36 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.12/5.36 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % floor_log_eq_powr_iff
% 5.12/5.36 thf(fact_4022_arctan__add,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.36 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.36 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.12/5.36 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % arctan_add
% 5.12/5.36 thf(fact_4023_split__root,axiom,
% 5.12/5.36 ! [P: real > $o,N: nat,X: real] :
% 5.12/5.36 ( ( P @ ( root @ N @ X ) )
% 5.12/5.36 = ( ( ( N = zero_zero_nat )
% 5.12/5.36 => ( P @ zero_zero_real ) )
% 5.12/5.36 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.36 => ! [Y6: real] :
% 5.12/5.36 ( ( ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.12/5.36 = X )
% 5.12/5.36 => ( P @ Y6 ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % split_root
% 5.12/5.36 thf(fact_4024_tanh__add,axiom,
% 5.12/5.36 ! [X: complex,Y: complex] :
% 5.12/5.36 ( ( ( cosh_complex @ X )
% 5.12/5.36 != zero_zero_complex )
% 5.12/5.36 => ( ( ( cosh_complex @ Y )
% 5.12/5.36 != zero_zero_complex )
% 5.12/5.36 => ( ( tanh_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.12/5.36 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % tanh_add
% 5.12/5.36 thf(fact_4025_tanh__add,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ( cosh_real @ X )
% 5.12/5.36 != zero_zero_real )
% 5.12/5.36 => ( ( ( cosh_real @ Y )
% 5.12/5.36 != zero_zero_real )
% 5.12/5.36 => ( ( tanh_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.36 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % tanh_add
% 5.12/5.36 thf(fact_4026_sgn__sgn,axiom,
% 5.12/5.36 ! [A: real] :
% 5.12/5.36 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.36 = ( sgn_sgn_real @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % sgn_sgn
% 5.12/5.36 thf(fact_4027_sgn__sgn,axiom,
% 5.12/5.36 ! [A: int] :
% 5.12/5.36 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.36 = ( sgn_sgn_int @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % sgn_sgn
% 5.12/5.36 thf(fact_4028_sgn__sgn,axiom,
% 5.12/5.36 ! [A: complex] :
% 5.12/5.36 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 5.12/5.36 = ( sgn_sgn_complex @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % sgn_sgn
% 5.12/5.36 thf(fact_4029_sgn__sgn,axiom,
% 5.12/5.36 ! [A: code_integer] :
% 5.12/5.36 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.36 = ( sgn_sgn_Code_integer @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % sgn_sgn
% 5.12/5.36 thf(fact_4030_sgn__sgn,axiom,
% 5.12/5.36 ! [A: rat] :
% 5.12/5.36 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.36 = ( sgn_sgn_rat @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % sgn_sgn
% 5.12/5.36 thf(fact_4031_cosh__real__eq__iff,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ( cosh_real @ X )
% 5.12/5.36 = ( cosh_real @ Y ) )
% 5.12/5.36 = ( ( abs_abs_real @ X )
% 5.12/5.36 = ( abs_abs_real @ Y ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % cosh_real_eq_iff
% 5.12/5.36 thf(fact_4032_cosh__real__abs,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( cosh_real @ ( abs_abs_real @ X ) )
% 5.12/5.36 = ( cosh_real @ X ) ) ).
% 5.12/5.36
% 5.12/5.36 % cosh_real_abs
% 5.12/5.36 thf(fact_4033_tanh__real__eq__iff,axiom,
% 5.12/5.36 ! [X: real,Y: real] :
% 5.12/5.36 ( ( ( tanh_real @ X )
% 5.12/5.36 = ( tanh_real @ Y ) )
% 5.12/5.36 = ( X = Y ) ) ).
% 5.12/5.36
% 5.12/5.36 % tanh_real_eq_iff
% 5.12/5.36 thf(fact_4034_inverse__zero,axiom,
% 5.12/5.36 ( ( inverse_inverse_real @ zero_zero_real )
% 5.12/5.36 = zero_zero_real ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_zero
% 5.12/5.36 thf(fact_4035_inverse__zero,axiom,
% 5.12/5.36 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.12/5.36 = zero_zero_complex ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_zero
% 5.12/5.36 thf(fact_4036_inverse__zero,axiom,
% 5.12/5.36 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.12/5.36 = zero_zero_rat ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_zero
% 5.12/5.36 thf(fact_4037_inverse__nonzero__iff__nonzero,axiom,
% 5.12/5.36 ! [A: real] :
% 5.12/5.36 ( ( ( inverse_inverse_real @ A )
% 5.12/5.36 = zero_zero_real )
% 5.12/5.36 = ( A = zero_zero_real ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_nonzero_iff_nonzero
% 5.12/5.36 thf(fact_4038_inverse__nonzero__iff__nonzero,axiom,
% 5.12/5.36 ! [A: complex] :
% 5.12/5.36 ( ( ( invers8013647133539491842omplex @ A )
% 5.12/5.36 = zero_zero_complex )
% 5.12/5.36 = ( A = zero_zero_complex ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_nonzero_iff_nonzero
% 5.12/5.36 thf(fact_4039_inverse__nonzero__iff__nonzero,axiom,
% 5.12/5.36 ! [A: rat] :
% 5.12/5.36 ( ( ( inverse_inverse_rat @ A )
% 5.12/5.36 = zero_zero_rat )
% 5.12/5.36 = ( A = zero_zero_rat ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_nonzero_iff_nonzero
% 5.12/5.36 thf(fact_4040_inverse__eq__1__iff,axiom,
% 5.12/5.36 ! [X: real] :
% 5.12/5.36 ( ( ( inverse_inverse_real @ X )
% 5.12/5.36 = one_one_real )
% 5.12/5.36 = ( X = one_one_real ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_eq_1_iff
% 5.12/5.36 thf(fact_4041_inverse__eq__1__iff,axiom,
% 5.12/5.36 ! [X: complex] :
% 5.12/5.36 ( ( ( invers8013647133539491842omplex @ X )
% 5.12/5.36 = one_one_complex )
% 5.12/5.36 = ( X = one_one_complex ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_eq_1_iff
% 5.12/5.36 thf(fact_4042_inverse__eq__1__iff,axiom,
% 5.12/5.36 ! [X: rat] :
% 5.12/5.36 ( ( ( inverse_inverse_rat @ X )
% 5.12/5.36 = one_one_rat )
% 5.12/5.36 = ( X = one_one_rat ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_eq_1_iff
% 5.12/5.36 thf(fact_4043_inverse__1,axiom,
% 5.12/5.36 ( ( inverse_inverse_real @ one_one_real )
% 5.12/5.36 = one_one_real ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_1
% 5.12/5.36 thf(fact_4044_inverse__1,axiom,
% 5.12/5.36 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.12/5.36 = one_one_complex ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_1
% 5.12/5.36 thf(fact_4045_inverse__1,axiom,
% 5.12/5.36 ( ( inverse_inverse_rat @ one_one_rat )
% 5.12/5.36 = one_one_rat ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_1
% 5.12/5.36 thf(fact_4046_mult__is__0,axiom,
% 5.12/5.36 ! [M2: nat,N: nat] :
% 5.12/5.36 ( ( ( times_times_nat @ M2 @ N )
% 5.12/5.36 = zero_zero_nat )
% 5.12/5.36 = ( ( M2 = zero_zero_nat )
% 5.12/5.36 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_is_0
% 5.12/5.36 thf(fact_4047_mult__0__right,axiom,
% 5.12/5.36 ! [M2: nat] :
% 5.12/5.36 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 5.12/5.36 = zero_zero_nat ) ).
% 5.12/5.36
% 5.12/5.36 % mult_0_right
% 5.12/5.36 thf(fact_4048_mult__cancel1,axiom,
% 5.12/5.36 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.36 ( ( ( times_times_nat @ K @ M2 )
% 5.12/5.36 = ( times_times_nat @ K @ N ) )
% 5.12/5.36 = ( ( M2 = N )
% 5.12/5.36 | ( K = zero_zero_nat ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_cancel1
% 5.12/5.36 thf(fact_4049_mult__cancel2,axiom,
% 5.12/5.36 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.36 ( ( ( times_times_nat @ M2 @ K )
% 5.12/5.36 = ( times_times_nat @ N @ K ) )
% 5.12/5.36 = ( ( M2 = N )
% 5.12/5.36 | ( K = zero_zero_nat ) ) ) ).
% 5.12/5.36
% 5.12/5.36 % mult_cancel2
% 5.12/5.36 thf(fact_4050_inverse__divide,axiom,
% 5.12/5.36 ! [A: real,B: real] :
% 5.12/5.36 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.36 = ( divide_divide_real @ B @ A ) ) ).
% 5.12/5.36
% 5.12/5.36 % inverse_divide
% 5.12/5.36 thf(fact_4051_inverse__divide,axiom,
% 5.12/5.36 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.37 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_divide
% 5.12/5.37 thf(fact_4052_inverse__divide,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.12/5.37 = ( divide_divide_rat @ B @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_divide
% 5.12/5.37 thf(fact_4053_inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_minus_eq
% 5.12/5.37 thf(fact_4054_inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_minus_eq
% 5.12/5.37 thf(fact_4055_inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.12/5.37 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_minus_eq
% 5.12/5.37 thf(fact_4056_sgn__0,axiom,
% 5.12/5.37 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.12/5.37 = zero_zero_complex ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0
% 5.12/5.37 thf(fact_4057_sgn__0,axiom,
% 5.12/5.37 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.12/5.37 = zero_z3403309356797280102nteger ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0
% 5.12/5.37 thf(fact_4058_sgn__0,axiom,
% 5.12/5.37 ( ( sgn_sgn_real @ zero_zero_real )
% 5.12/5.37 = zero_zero_real ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0
% 5.12/5.37 thf(fact_4059_sgn__0,axiom,
% 5.12/5.37 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.12/5.37 = zero_zero_rat ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0
% 5.12/5.37 thf(fact_4060_sgn__0,axiom,
% 5.12/5.37 ( ( sgn_sgn_int @ zero_zero_int )
% 5.12/5.37 = zero_zero_int ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0
% 5.12/5.37 thf(fact_4061_sgn__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_real @ one_one_real )
% 5.12/5.37 = one_one_real ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1
% 5.12/5.37 thf(fact_4062_sgn__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_int @ one_one_int )
% 5.12/5.37 = one_one_int ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1
% 5.12/5.37 thf(fact_4063_sgn__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_complex @ one_one_complex )
% 5.12/5.37 = one_one_complex ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1
% 5.12/5.37 thf(fact_4064_sgn__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 5.12/5.37 = one_one_Code_integer ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1
% 5.12/5.37 thf(fact_4065_sgn__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_rat @ one_one_rat )
% 5.12/5.37 = one_one_rat ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1
% 5.12/5.37 thf(fact_4066_sgn__divide,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.37 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_divide
% 5.12/5.37 thf(fact_4067_sgn__divide,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.37 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_divide
% 5.12/5.37 thf(fact_4068_sgn__divide,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 5.12/5.37 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_divide
% 5.12/5.37 thf(fact_4069_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 5.12/5.37 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % idom_abs_sgn_class.sgn_minus
% 5.12/5.37 thf(fact_4070_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % idom_abs_sgn_class.sgn_minus
% 5.12/5.37 thf(fact_4071_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % idom_abs_sgn_class.sgn_minus
% 5.12/5.37 thf(fact_4072_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.37 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % idom_abs_sgn_class.sgn_minus
% 5.12/5.37 thf(fact_4073_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 5.12/5.37 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % idom_abs_sgn_class.sgn_minus
% 5.12/5.37 thf(fact_4074_nat__mult__eq__1__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ( times_times_nat @ M2 @ N )
% 5.12/5.37 = one_one_nat )
% 5.12/5.37 = ( ( M2 = one_one_nat )
% 5.12/5.37 & ( N = one_one_nat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_eq_1_iff
% 5.12/5.37 thf(fact_4075_nat__1__eq__mult__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( one_one_nat
% 5.12/5.37 = ( times_times_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( M2 = one_one_nat )
% 5.12/5.37 & ( N = one_one_nat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_1_eq_mult_iff
% 5.12/5.37 thf(fact_4076_cosh__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( cosh_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( cosh_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_minus
% 5.12/5.37 thf(fact_4077_cosh__minus,axiom,
% 5.12/5.37 ! [X: complex] :
% 5.12/5.37 ( ( cosh_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.37 = ( cosh_complex @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_minus
% 5.12/5.37 thf(fact_4078_floor__of__int,axiom,
% 5.12/5.37 ! [Z2: int] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.37 = Z2 ) ).
% 5.12/5.37
% 5.12/5.37 % floor_of_int
% 5.12/5.37 thf(fact_4079_floor__of__int,axiom,
% 5.12/5.37 ! [Z2: int] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.37 = Z2 ) ).
% 5.12/5.37
% 5.12/5.37 % floor_of_int
% 5.12/5.37 thf(fact_4080_of__int__floor__cancel,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = X )
% 5.12/5.37 = ( ? [N4: int] :
% 5.12/5.37 ( X
% 5.12/5.37 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % of_int_floor_cancel
% 5.12/5.37 thf(fact_4081_of__int__floor__cancel,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = X )
% 5.12/5.37 = ( ? [N4: int] :
% 5.12/5.37 ( X
% 5.12/5.37 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % of_int_floor_cancel
% 5.12/5.37 thf(fact_4082_arctan__eq__zero__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ( arctan @ X )
% 5.12/5.37 = zero_zero_real )
% 5.12/5.37 = ( X = zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_eq_zero_iff
% 5.12/5.37 thf(fact_4083_arctan__zero__zero,axiom,
% 5.12/5.37 ( ( arctan @ zero_zero_real )
% 5.12/5.37 = zero_zero_real ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_zero_zero
% 5.12/5.37 thf(fact_4084_inverse__nonpositive__iff__nonpositive,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.12/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_nonpositive_iff_nonpositive
% 5.12/5.37 thf(fact_4085_inverse__nonpositive__iff__nonpositive,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.12/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_nonpositive_iff_nonpositive
% 5.12/5.37 thf(fact_4086_inverse__nonnegative__iff__nonnegative,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_nonnegative_iff_nonnegative
% 5.12/5.37 thf(fact_4087_inverse__nonnegative__iff__nonnegative,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_nonnegative_iff_nonnegative
% 5.12/5.37 thf(fact_4088_inverse__less__iff__less,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.37 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff_less
% 5.12/5.37 thf(fact_4089_inverse__less__iff__less,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.37 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff_less
% 5.12/5.37 thf(fact_4090_inverse__less__iff__less__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff_less_neg
% 5.12/5.37 thf(fact_4091_inverse__less__iff__less__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff_less_neg
% 5.12/5.37 thf(fact_4092_inverse__negative__iff__negative,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.12/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_negative_iff_negative
% 5.12/5.37 thf(fact_4093_inverse__negative__iff__negative,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.12/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_negative_iff_negative
% 5.12/5.37 thf(fact_4094_inverse__positive__iff__positive,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_positive_iff_positive
% 5.12/5.37 thf(fact_4095_inverse__positive__iff__positive,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_positive_iff_positive
% 5.12/5.37 thf(fact_4096_sgn__less,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.12/5.37 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_less
% 5.12/5.37 thf(fact_4097_sgn__less,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 5.12/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_less
% 5.12/5.37 thf(fact_4098_sgn__less,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.12/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_less
% 5.12/5.37 thf(fact_4099_sgn__less,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.12/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_less
% 5.12/5.37 thf(fact_4100_sgn__greater,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_greater
% 5.12/5.37 thf(fact_4101_sgn__greater,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_greater
% 5.12/5.37 thf(fact_4102_sgn__greater,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_greater
% 5.12/5.37 thf(fact_4103_sgn__greater,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.37 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_greater
% 5.12/5.37 thf(fact_4104_one__eq__mult__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ( suc @ zero_zero_nat )
% 5.12/5.37 = ( times_times_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( M2
% 5.12/5.37 = ( suc @ zero_zero_nat ) )
% 5.12/5.37 & ( N
% 5.12/5.37 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_eq_mult_iff
% 5.12/5.37 thf(fact_4105_mult__eq__1__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ( times_times_nat @ M2 @ N )
% 5.12/5.37 = ( suc @ zero_zero_nat ) )
% 5.12/5.37 = ( ( M2
% 5.12/5.37 = ( suc @ zero_zero_nat ) )
% 5.12/5.37 & ( N
% 5.12/5.37 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_eq_1_iff
% 5.12/5.37 thf(fact_4106_mult__less__cancel2,axiom,
% 5.12/5.37 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) )
% 5.12/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_less_cancel2
% 5.12/5.37 thf(fact_4107_nat__0__less__mult__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.37 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_0_less_mult_iff
% 5.12/5.37 thf(fact_4108_divide__sgn,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 5.12/5.37 = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_sgn
% 5.12/5.37 thf(fact_4109_divide__sgn,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 5.12/5.37 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_sgn
% 5.12/5.37 thf(fact_4110_mult__Suc__right,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_nat @ M2 @ ( suc @ N ) )
% 5.12/5.37 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_Suc_right
% 5.12/5.37 thf(fact_4111_floor__zero,axiom,
% 5.12/5.37 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 5.12/5.37 = zero_zero_int ) ).
% 5.12/5.37
% 5.12/5.37 % floor_zero
% 5.12/5.37 thf(fact_4112_floor__zero,axiom,
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 5.12/5.37 = zero_zero_int ) ).
% 5.12/5.37
% 5.12/5.37 % floor_zero
% 5.12/5.37 thf(fact_4113_cosh__0,axiom,
% 5.12/5.37 ( ( cosh_complex @ zero_zero_complex )
% 5.12/5.37 = one_one_complex ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_0
% 5.12/5.37 thf(fact_4114_cosh__0,axiom,
% 5.12/5.37 ( ( cosh_real @ zero_zero_real )
% 5.12/5.37 = one_one_real ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_0
% 5.12/5.37 thf(fact_4115_floor__one,axiom,
% 5.12/5.37 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.12/5.37 = one_one_int ) ).
% 5.12/5.37
% 5.12/5.37 % floor_one
% 5.12/5.37 thf(fact_4116_floor__one,axiom,
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.12/5.37 = one_one_int ) ).
% 5.12/5.37
% 5.12/5.37 % floor_one
% 5.12/5.37 thf(fact_4117_floor__of__nat,axiom,
% 5.12/5.37 ! [N: nat] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.37 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_of_nat
% 5.12/5.37 thf(fact_4118_floor__of__nat,axiom,
% 5.12/5.37 ! [N: nat] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.12/5.37 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_of_nat
% 5.12/5.37 thf(fact_4119_zero__less__arctan__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 5.12/5.37 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_less_arctan_iff
% 5.12/5.37 thf(fact_4120_arctan__less__zero__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 5.12/5.37 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_less_zero_iff
% 5.12/5.37 thf(fact_4121_arctan__le__zero__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.12/5.37 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_le_zero_iff
% 5.12/5.37 thf(fact_4122_zero__le__arctan__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_le_arctan_iff
% 5.12/5.37 thf(fact_4123_inverse__le__iff__le,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.12/5.37 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff_le
% 5.12/5.37 thf(fact_4124_inverse__le__iff__le,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.12/5.37 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff_le
% 5.12/5.37 thf(fact_4125_inverse__le__iff__le__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff_le_neg
% 5.12/5.37 thf(fact_4126_inverse__le__iff__le__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff_le_neg
% 5.12/5.37 thf(fact_4127_left__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.12/5.37 = one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % left_inverse
% 5.12/5.37 thf(fact_4128_left__inverse,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.12/5.37 = one_one_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % left_inverse
% 5.12/5.37 thf(fact_4129_left__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.12/5.37 = one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % left_inverse
% 5.12/5.37 thf(fact_4130_right__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 = one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % right_inverse
% 5.12/5.37 thf(fact_4131_right__inverse,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.12/5.37 = one_one_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % right_inverse
% 5.12/5.37 thf(fact_4132_right__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 = one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % right_inverse
% 5.12/5.37 thf(fact_4133_sgn__pos,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.37 => ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = one_one_Code_integer ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_pos
% 5.12/5.37 thf(fact_4134_sgn__pos,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( sgn_sgn_real @ A )
% 5.12/5.37 = one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_pos
% 5.12/5.37 thf(fact_4135_sgn__pos,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_pos
% 5.12/5.37 thf(fact_4136_sgn__pos,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.37 => ( ( sgn_sgn_int @ A )
% 5.12/5.37 = one_one_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_pos
% 5.12/5.37 thf(fact_4137_one__le__mult__iff,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.12/5.37 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_mult_iff
% 5.12/5.37 thf(fact_4138_abs__sgn__eq__1,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 = one_one_Code_integer ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq_1
% 5.12/5.37 thf(fact_4139_abs__sgn__eq__1,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.37 = one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq_1
% 5.12/5.37 thf(fact_4140_abs__sgn__eq__1,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.37 = one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq_1
% 5.12/5.37 thf(fact_4141_abs__sgn__eq__1,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( A != zero_zero_int )
% 5.12/5.37 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.37 = one_one_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq_1
% 5.12/5.37 thf(fact_4142_mult__le__cancel2,axiom,
% 5.12/5.37 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) )
% 5.12/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_le_cancel2
% 5.12/5.37 thf(fact_4143_div__mult__self__is__m,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 5.12/5.37 = M2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_mult_self_is_m
% 5.12/5.37 thf(fact_4144_div__mult__self1__is__m,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 5.12/5.37 = M2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_mult_self1_is_m
% 5.12/5.37 thf(fact_4145_Suc__mod__mult__self4,axiom,
% 5.12/5.37 ! [N: nat,K: nat,M2: nat] :
% 5.12/5.37 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M2 ) ) @ N )
% 5.12/5.37 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mod_mult_self4
% 5.12/5.37 thf(fact_4146_Suc__mod__mult__self3,axiom,
% 5.12/5.37 ! [K: nat,N: nat,M2: nat] :
% 5.12/5.37 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M2 ) ) @ N )
% 5.12/5.37 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mod_mult_self3
% 5.12/5.37 thf(fact_4147_Suc__mod__mult__self2,axiom,
% 5.12/5.37 ! [M2: nat,N: nat,K: nat] :
% 5.12/5.37 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.12/5.37 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mod_mult_self2
% 5.12/5.37 thf(fact_4148_Suc__mod__mult__self1,axiom,
% 5.12/5.37 ! [M2: nat,K: nat,N: nat] :
% 5.12/5.37 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.12/5.37 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mod_mult_self1
% 5.12/5.37 thf(fact_4149_floor__uminus__of__int,axiom,
% 5.12/5.37 ! [Z2: int] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( ring_1_of_int_real @ Z2 ) ) )
% 5.12/5.37 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_uminus_of_int
% 5.12/5.37 thf(fact_4150_floor__uminus__of__int,axiom,
% 5.12/5.37 ! [Z2: int] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z2 ) ) )
% 5.12/5.37 = ( uminus_uminus_int @ Z2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_uminus_of_int
% 5.12/5.37 thf(fact_4151_floor__diff__of__int,axiom,
% 5.12/5.37 ! [X: real,Z2: int] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
% 5.12/5.37 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ Z2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_diff_of_int
% 5.12/5.37 thf(fact_4152_floor__diff__of__int,axiom,
% 5.12/5.37 ! [X: rat,Z2: int] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) )
% 5.12/5.37 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ Z2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_diff_of_int
% 5.12/5.37 thf(fact_4153_sgn__neg,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.37 => ( ( sgn_sgn_int @ A )
% 5.12/5.37 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_neg
% 5.12/5.37 thf(fact_4154_sgn__neg,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.37 => ( ( sgn_sgn_real @ A )
% 5.12/5.37 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_neg
% 5.12/5.37 thf(fact_4155_sgn__neg,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_neg
% 5.12/5.37 thf(fact_4156_sgn__neg,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.37 => ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_neg
% 5.12/5.37 thf(fact_4157_zero__le__floor,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_le_floor
% 5.12/5.37 thf(fact_4158_zero__le__floor,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_le_floor
% 5.12/5.37 thf(fact_4159_floor__less__zero,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.12/5.37 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_zero
% 5.12/5.37 thf(fact_4160_floor__less__zero,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.12/5.37 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_zero
% 5.12/5.37 thf(fact_4161_zero__less__floor,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_less_floor
% 5.12/5.37 thf(fact_4162_zero__less__floor,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % zero_less_floor
% 5.12/5.37 thf(fact_4163_floor__le__zero,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.12/5.37 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_zero
% 5.12/5.37 thf(fact_4164_floor__le__zero,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.12/5.37 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_zero
% 5.12/5.37 thf(fact_4165_one__le__floor,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_floor
% 5.12/5.37 thf(fact_4166_one__le__floor,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_floor
% 5.12/5.37 thf(fact_4167_floor__less__one,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.12/5.37 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_one
% 5.12/5.37 thf(fact_4168_floor__less__one,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.12/5.37 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_one
% 5.12/5.37 thf(fact_4169_floor__diff__one,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.12/5.37 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_diff_one
% 5.12/5.37 thf(fact_4170_floor__diff__one,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.12/5.37 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_diff_one
% 5.12/5.37 thf(fact_4171_arctan__eq__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ( arctan @ X )
% 5.12/5.37 = ( arctan @ Y ) )
% 5.12/5.37 = ( X = Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_eq_iff
% 5.12/5.37 thf(fact_4172_field__class_Ofield__inverse__zero,axiom,
% 5.12/5.37 ( ( inverse_inverse_real @ zero_zero_real )
% 5.12/5.37 = zero_zero_real ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse_zero
% 5.12/5.37 thf(fact_4173_field__class_Ofield__inverse__zero,axiom,
% 5.12/5.37 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.12/5.37 = zero_zero_complex ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse_zero
% 5.12/5.37 thf(fact_4174_field__class_Ofield__inverse__zero,axiom,
% 5.12/5.37 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.12/5.37 = zero_zero_rat ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse_zero
% 5.12/5.37 thf(fact_4175_inverse__zero__imp__zero,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( inverse_inverse_real @ A )
% 5.12/5.37 = zero_zero_real )
% 5.12/5.37 => ( A = zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_zero_imp_zero
% 5.12/5.37 thf(fact_4176_inverse__zero__imp__zero,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( ( invers8013647133539491842omplex @ A )
% 5.12/5.37 = zero_zero_complex )
% 5.12/5.37 => ( A = zero_zero_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_zero_imp_zero
% 5.12/5.37 thf(fact_4177_inverse__zero__imp__zero,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( inverse_inverse_rat @ A )
% 5.12/5.37 = zero_zero_rat )
% 5.12/5.37 => ( A = zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_zero_imp_zero
% 5.12/5.37 thf(fact_4178_nonzero__inverse__eq__imp__eq,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ( inverse_inverse_real @ A )
% 5.12/5.37 = ( inverse_inverse_real @ B ) )
% 5.12/5.37 => ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( A = B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_imp_eq
% 5.12/5.37 thf(fact_4179_nonzero__inverse__eq__imp__eq,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( ( invers8013647133539491842omplex @ A )
% 5.12/5.37 = ( invers8013647133539491842omplex @ B ) )
% 5.12/5.37 => ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( A = B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_imp_eq
% 5.12/5.37 thf(fact_4180_nonzero__inverse__eq__imp__eq,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ( inverse_inverse_rat @ A )
% 5.12/5.37 = ( inverse_inverse_rat @ B ) )
% 5.12/5.37 => ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( A = B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_imp_eq
% 5.12/5.37 thf(fact_4181_nonzero__inverse__inverse__eq,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 = A ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_inverse_eq
% 5.12/5.37 thf(fact_4182_nonzero__inverse__inverse__eq,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.12/5.37 = A ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_inverse_eq
% 5.12/5.37 thf(fact_4183_nonzero__inverse__inverse__eq,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 = A ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_inverse_eq
% 5.12/5.37 thf(fact_4184_nonzero__imp__inverse__nonzero,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ A )
% 5.12/5.37 != zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_imp_inverse_nonzero
% 5.12/5.37 thf(fact_4185_nonzero__imp__inverse__nonzero,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ A )
% 5.12/5.37 != zero_zero_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_imp_inverse_nonzero
% 5.12/5.37 thf(fact_4186_nonzero__imp__inverse__nonzero,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ A )
% 5.12/5.37 != zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_imp_inverse_nonzero
% 5.12/5.37 thf(fact_4187_sgn__0__0,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = zero_z3403309356797280102nteger )
% 5.12/5.37 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0_0
% 5.12/5.37 thf(fact_4188_sgn__0__0,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ A )
% 5.12/5.37 = zero_zero_real )
% 5.12/5.37 = ( A = zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0_0
% 5.12/5.37 thf(fact_4189_sgn__0__0,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = zero_zero_rat )
% 5.12/5.37 = ( A = zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0_0
% 5.12/5.37 thf(fact_4190_sgn__0__0,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ A )
% 5.12/5.37 = zero_zero_int )
% 5.12/5.37 = ( A = zero_zero_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_0_0
% 5.12/5.37 thf(fact_4191_sgn__eq__0__iff,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( ( sgn_sgn_complex @ A )
% 5.12/5.37 = zero_zero_complex )
% 5.12/5.37 = ( A = zero_zero_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_eq_0_iff
% 5.12/5.37 thf(fact_4192_sgn__eq__0__iff,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = zero_z3403309356797280102nteger )
% 5.12/5.37 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_eq_0_iff
% 5.12/5.37 thf(fact_4193_sgn__eq__0__iff,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ A )
% 5.12/5.37 = zero_zero_real )
% 5.12/5.37 = ( A = zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_eq_0_iff
% 5.12/5.37 thf(fact_4194_sgn__eq__0__iff,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = zero_zero_rat )
% 5.12/5.37 = ( A = zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_eq_0_iff
% 5.12/5.37 thf(fact_4195_sgn__eq__0__iff,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ A )
% 5.12/5.37 = zero_zero_int )
% 5.12/5.37 = ( A = zero_zero_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_eq_0_iff
% 5.12/5.37 thf(fact_4196_sgn__mult,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 5.12/5.37 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult
% 5.12/5.37 thf(fact_4197_sgn__mult,axiom,
% 5.12/5.37 ! [A: code_integer,B: code_integer] :
% 5.12/5.37 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.12/5.37 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult
% 5.12/5.37 thf(fact_4198_sgn__mult,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 5.12/5.37 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult
% 5.12/5.37 thf(fact_4199_sgn__mult,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.37 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult
% 5.12/5.37 thf(fact_4200_sgn__mult,axiom,
% 5.12/5.37 ! [A: int,B: int] :
% 5.12/5.37 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 5.12/5.37 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult
% 5.12/5.37 thf(fact_4201_same__sgn__sgn__add,axiom,
% 5.12/5.37 ! [B: code_integer,A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ B )
% 5.12/5.37 = ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.37 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_sgn_add
% 5.12/5.37 thf(fact_4202_same__sgn__sgn__add,axiom,
% 5.12/5.37 ! [B: real,A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ B )
% 5.12/5.37 = ( sgn_sgn_real @ A ) )
% 5.12/5.37 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 5.12/5.37 = ( sgn_sgn_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_sgn_add
% 5.12/5.37 thf(fact_4203_same__sgn__sgn__add,axiom,
% 5.12/5.37 ! [B: rat,A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ B )
% 5.12/5.37 = ( sgn_sgn_rat @ A ) )
% 5.12/5.37 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.37 = ( sgn_sgn_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_sgn_add
% 5.12/5.37 thf(fact_4204_same__sgn__sgn__add,axiom,
% 5.12/5.37 ! [B: int,A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ B )
% 5.12/5.37 = ( sgn_sgn_int @ A ) )
% 5.12/5.37 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.37 = ( sgn_sgn_int @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_sgn_add
% 5.12/5.37 thf(fact_4205_cosh__real__nonzero,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( cosh_real @ X )
% 5.12/5.37 != zero_zero_real ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonzero
% 5.12/5.37 thf(fact_4206_Suc__mult__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ( times_times_nat @ ( suc @ K ) @ M2 )
% 5.12/5.37 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.12/5.37 = ( M2 = N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mult_cancel1
% 5.12/5.37 thf(fact_4207_mult__0,axiom,
% 5.12/5.37 ! [N: nat] :
% 5.12/5.37 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.12/5.37 = zero_zero_nat ) ).
% 5.12/5.37
% 5.12/5.37 % mult_0
% 5.12/5.37 thf(fact_4208_arctan__monotone,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_real @ X @ Y )
% 5.12/5.37 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_monotone
% 5.12/5.37 thf(fact_4209_arctan__less__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.12/5.37 = ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_less_iff
% 5.12/5.37 thf(fact_4210_mult__le__mono2,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.37 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_le_mono2
% 5.12/5.37 thf(fact_4211_mult__le__mono1,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.37 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J2 @ K ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_le_mono1
% 5.12/5.37 thf(fact_4212_mult__le__mono,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,K: nat,L: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.37 => ( ( ord_less_eq_nat @ K @ L )
% 5.12/5.37 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J2 @ L ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_le_mono
% 5.12/5.37 thf(fact_4213_le__square,axiom,
% 5.12/5.37 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_square
% 5.12/5.37 thf(fact_4214_le__cube,axiom,
% 5.12/5.37 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_cube
% 5.12/5.37 thf(fact_4215_arctan__le__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.12/5.37 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_le_iff
% 5.12/5.37 thf(fact_4216_arctan__monotone_H,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.37 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_monotone'
% 5.12/5.37 thf(fact_4217_add__mult__distrib2,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_nat @ K @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % add_mult_distrib2
% 5.12/5.37 thf(fact_4218_add__mult__distrib,axiom,
% 5.12/5.37 ! [M2: nat,N: nat,K: nat] :
% 5.12/5.37 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N ) @ K )
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % add_mult_distrib
% 5.12/5.37 thf(fact_4219_diff__mult__distrib2,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.37 = ( minus_minus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % diff_mult_distrib2
% 5.12/5.37 thf(fact_4220_diff__mult__distrib,axiom,
% 5.12/5.37 ! [M2: nat,N: nat,K: nat] :
% 5.12/5.37 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N ) @ K )
% 5.12/5.37 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % diff_mult_distrib
% 5.12/5.37 thf(fact_4221_nat__mult__1__right,axiom,
% 5.12/5.37 ! [N: nat] :
% 5.12/5.37 ( ( times_times_nat @ N @ one_one_nat )
% 5.12/5.37 = N ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_1_right
% 5.12/5.37 thf(fact_4222_nat__mult__1,axiom,
% 5.12/5.37 ! [N: nat] :
% 5.12/5.37 ( ( times_times_nat @ one_one_nat @ N )
% 5.12/5.37 = N ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_1
% 5.12/5.37 thf(fact_4223_div__mult2__eq,axiom,
% 5.12/5.37 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.37 ( ( divide_divide_nat @ M2 @ ( times_times_nat @ N @ Q5 ) )
% 5.12/5.37 = ( divide_divide_nat @ ( divide_divide_nat @ M2 @ N ) @ Q5 ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_mult2_eq
% 5.12/5.37 thf(fact_4224_arctan__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( arctan @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( arctan @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % arctan_minus
% 5.12/5.37 thf(fact_4225_floor__mono,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.37 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_mono
% 5.12/5.37 thf(fact_4226_floor__mono,axiom,
% 5.12/5.37 ! [X: rat,Y: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.37 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_mono
% 5.12/5.37 thf(fact_4227_of__int__floor__le,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 5.12/5.37
% 5.12/5.37 % of_int_floor_le
% 5.12/5.37 thf(fact_4228_of__int__floor__le,axiom,
% 5.12/5.37 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 5.12/5.37
% 5.12/5.37 % of_int_floor_le
% 5.12/5.37 thf(fact_4229_inverse__less__imp__less,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ord_less_real @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_imp_less
% 5.12/5.37 thf(fact_4230_inverse__less__imp__less,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_imp_less
% 5.12/5.37 thf(fact_4231_less__imp__inverse__less,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ B )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_imp_inverse_less
% 5.12/5.37 thf(fact_4232_less__imp__inverse__less,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ B )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_imp_inverse_less
% 5.12/5.37 thf(fact_4233_inverse__less__imp__less__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_imp_less_neg
% 5.12/5.37 thf(fact_4234_inverse__less__imp__less__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_imp_less_neg
% 5.12/5.37 thf(fact_4235_less__imp__inverse__less__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ B )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_imp_inverse_less_neg
% 5.12/5.37 thf(fact_4236_less__imp__inverse__less__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ B )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_imp_inverse_less_neg
% 5.12/5.37 thf(fact_4237_inverse__negative__imp__negative,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.12/5.37 => ( ( A != zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_negative_imp_negative
% 5.12/5.37 thf(fact_4238_inverse__negative__imp__negative,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.12/5.37 => ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_negative_imp_negative
% 5.12/5.37 thf(fact_4239_inverse__positive__imp__positive,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 => ( ( A != zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_positive_imp_positive
% 5.12/5.37 thf(fact_4240_inverse__positive__imp__positive,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 => ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_positive_imp_positive
% 5.12/5.37 thf(fact_4241_negative__imp__inverse__negative,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % negative_imp_inverse_negative
% 5.12/5.37 thf(fact_4242_negative__imp__inverse__negative,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % negative_imp_inverse_negative
% 5.12/5.37 thf(fact_4243_positive__imp__inverse__positive,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % positive_imp_inverse_positive
% 5.12/5.37 thf(fact_4244_positive__imp__inverse__positive,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % positive_imp_inverse_positive
% 5.12/5.37 thf(fact_4245_floor__less__cancel,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 5.12/5.37 => ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_cancel
% 5.12/5.37 thf(fact_4246_floor__less__cancel,axiom,
% 5.12/5.37 ! [X: rat,Y: rat] :
% 5.12/5.37 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 5.12/5.37 => ( ord_less_rat @ X @ Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_cancel
% 5.12/5.37 thf(fact_4247_nonzero__inverse__mult__distrib,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.12/5.37 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_mult_distrib
% 5.12/5.37 thf(fact_4248_nonzero__inverse__mult__distrib,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.12/5.37 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_mult_distrib
% 5.12/5.37 thf(fact_4249_nonzero__inverse__mult__distrib,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.37 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_mult_distrib
% 5.12/5.37 thf(fact_4250_nonzero__inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_minus_eq
% 5.12/5.37 thf(fact_4251_nonzero__inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_minus_eq
% 5.12/5.37 thf(fact_4252_nonzero__inverse__minus__eq,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.12/5.37 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_minus_eq
% 5.12/5.37 thf(fact_4253_inverse__unique,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ( times_times_real @ A @ B )
% 5.12/5.37 = one_one_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ A )
% 5.12/5.37 = B ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_unique
% 5.12/5.37 thf(fact_4254_inverse__unique,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( ( times_times_complex @ A @ B )
% 5.12/5.37 = one_one_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ A )
% 5.12/5.37 = B ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_unique
% 5.12/5.37 thf(fact_4255_inverse__unique,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ( times_times_rat @ A @ B )
% 5.12/5.37 = one_one_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ A )
% 5.12/5.37 = B ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_unique
% 5.12/5.37 thf(fact_4256_field__class_Ofield__divide__inverse,axiom,
% 5.12/5.37 ( divide_divide_real
% 5.12/5.37 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_divide_inverse
% 5.12/5.37 thf(fact_4257_field__class_Ofield__divide__inverse,axiom,
% 5.12/5.37 ( divide1717551699836669952omplex
% 5.12/5.37 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_divide_inverse
% 5.12/5.37 thf(fact_4258_field__class_Ofield__divide__inverse,axiom,
% 5.12/5.37 ( divide_divide_rat
% 5.12/5.37 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_divide_inverse
% 5.12/5.37 thf(fact_4259_divide__inverse,axiom,
% 5.12/5.37 ( divide_divide_real
% 5.12/5.37 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse
% 5.12/5.37 thf(fact_4260_divide__inverse,axiom,
% 5.12/5.37 ( divide1717551699836669952omplex
% 5.12/5.37 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse
% 5.12/5.37 thf(fact_4261_divide__inverse,axiom,
% 5.12/5.37 ( divide_divide_rat
% 5.12/5.37 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse
% 5.12/5.37 thf(fact_4262_divide__inverse__commute,axiom,
% 5.12/5.37 ( divide_divide_real
% 5.12/5.37 = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse_commute
% 5.12/5.37 thf(fact_4263_divide__inverse__commute,axiom,
% 5.12/5.37 ( divide1717551699836669952omplex
% 5.12/5.37 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse_commute
% 5.12/5.37 thf(fact_4264_divide__inverse__commute,axiom,
% 5.12/5.37 ( divide_divide_rat
% 5.12/5.37 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B2 ) @ A3 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_inverse_commute
% 5.12/5.37 thf(fact_4265_inverse__eq__divide,axiom,
% 5.12/5.37 ( inverse_inverse_real
% 5.12/5.37 = ( divide_divide_real @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_eq_divide
% 5.12/5.37 thf(fact_4266_inverse__eq__divide,axiom,
% 5.12/5.37 ( invers8013647133539491842omplex
% 5.12/5.37 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_eq_divide
% 5.12/5.37 thf(fact_4267_inverse__eq__divide,axiom,
% 5.12/5.37 ( inverse_inverse_rat
% 5.12/5.37 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_eq_divide
% 5.12/5.37 thf(fact_4268_power__mult__power__inverse__commute,axiom,
% 5.12/5.37 ! [X: real,M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) )
% 5.12/5.37 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) @ ( power_power_real @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_power_inverse_commute
% 5.12/5.37 thf(fact_4269_power__mult__power__inverse__commute,axiom,
% 5.12/5.37 ! [X: complex,M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) )
% 5.12/5.37 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) @ ( power_power_complex @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_power_inverse_commute
% 5.12/5.37 thf(fact_4270_power__mult__power__inverse__commute,axiom,
% 5.12/5.37 ! [X: rat,M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) )
% 5.12/5.37 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) @ ( power_power_rat @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_power_inverse_commute
% 5.12/5.37 thf(fact_4271_power__mult__inverse__distrib,axiom,
% 5.12/5.37 ! [X: real,M2: nat] :
% 5.12/5.37 ( ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( inverse_inverse_real @ X ) )
% 5.12/5.37 = ( times_times_real @ ( inverse_inverse_real @ X ) @ ( power_power_real @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_inverse_distrib
% 5.12/5.37 thf(fact_4272_power__mult__inverse__distrib,axiom,
% 5.12/5.37 ! [X: complex,M2: nat] :
% 5.12/5.37 ( ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( invers8013647133539491842omplex @ X ) )
% 5.12/5.37 = ( times_times_complex @ ( invers8013647133539491842omplex @ X ) @ ( power_power_complex @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_inverse_distrib
% 5.12/5.37 thf(fact_4273_power__mult__inverse__distrib,axiom,
% 5.12/5.37 ! [X: rat,M2: nat] :
% 5.12/5.37 ( ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( inverse_inverse_rat @ X ) )
% 5.12/5.37 = ( times_times_rat @ ( inverse_inverse_rat @ X ) @ ( power_power_rat @ X @ M2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_mult_inverse_distrib
% 5.12/5.37 thf(fact_4274_mult__inverse__of__nat__commute,axiom,
% 5.12/5.37 ! [Xa: nat,X: real] :
% 5.12/5.37 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_real @ X @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_nat_commute
% 5.12/5.37 thf(fact_4275_mult__inverse__of__nat__commute,axiom,
% 5.12/5.37 ! [Xa: nat,X: complex] :
% 5.12/5.37 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_nat_commute
% 5.12/5.37 thf(fact_4276_mult__inverse__of__nat__commute,axiom,
% 5.12/5.37 ! [Xa: nat,X: rat] :
% 5.12/5.37 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_nat_commute
% 5.12/5.37 thf(fact_4277_nonzero__abs__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.37 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_abs_inverse
% 5.12/5.37 thf(fact_4278_nonzero__abs__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.12/5.37 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_abs_inverse
% 5.12/5.37 thf(fact_4279_sgn__not__eq__imp,axiom,
% 5.12/5.37 ! [B: int,A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ B )
% 5.12/5.37 != ( sgn_sgn_int @ A ) )
% 5.12/5.37 => ( ( ( sgn_sgn_int @ A )
% 5.12/5.37 != zero_zero_int )
% 5.12/5.37 => ( ( ( sgn_sgn_int @ B )
% 5.12/5.37 != zero_zero_int )
% 5.12/5.37 => ( ( sgn_sgn_int @ A )
% 5.12/5.37 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_not_eq_imp
% 5.12/5.37 thf(fact_4280_sgn__not__eq__imp,axiom,
% 5.12/5.37 ! [B: real,A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ B )
% 5.12/5.37 != ( sgn_sgn_real @ A ) )
% 5.12/5.37 => ( ( ( sgn_sgn_real @ A )
% 5.12/5.37 != zero_zero_real )
% 5.12/5.37 => ( ( ( sgn_sgn_real @ B )
% 5.12/5.37 != zero_zero_real )
% 5.12/5.37 => ( ( sgn_sgn_real @ A )
% 5.12/5.37 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_not_eq_imp
% 5.12/5.37 thf(fact_4281_sgn__not__eq__imp,axiom,
% 5.12/5.37 ! [B: code_integer,A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ B )
% 5.12/5.37 != ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 => ( ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 != zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( ( sgn_sgn_Code_integer @ B )
% 5.12/5.37 != zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_not_eq_imp
% 5.12/5.37 thf(fact_4282_sgn__not__eq__imp,axiom,
% 5.12/5.37 ! [B: rat,A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ B )
% 5.12/5.37 != ( sgn_sgn_rat @ A ) )
% 5.12/5.37 => ( ( ( sgn_sgn_rat @ A )
% 5.12/5.37 != zero_zero_rat )
% 5.12/5.37 => ( ( ( sgn_sgn_rat @ B )
% 5.12/5.37 != zero_zero_rat )
% 5.12/5.37 => ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_not_eq_imp
% 5.12/5.37 thf(fact_4283_mult__inverse__of__int__commute,axiom,
% 5.12/5.37 ! [Xa: int,X: real] :
% 5.12/5.37 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_real @ X @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_int_commute
% 5.12/5.37 thf(fact_4284_mult__inverse__of__int__commute,axiom,
% 5.12/5.37 ! [Xa: int,X: complex] :
% 5.12/5.37 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_int_commute
% 5.12/5.37 thf(fact_4285_mult__inverse__of__int__commute,axiom,
% 5.12/5.37 ! [Xa: int,X: rat] :
% 5.12/5.37 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) @ X )
% 5.12/5.37 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_inverse_of_int_commute
% 5.12/5.37 thf(fact_4286_sgn__minus__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.37 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_minus_1
% 5.12/5.37 thf(fact_4287_sgn__minus__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.37 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_minus_1
% 5.12/5.37 thf(fact_4288_sgn__minus__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_minus_1
% 5.12/5.37 thf(fact_4289_sgn__minus__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_minus_1
% 5.12/5.37 thf(fact_4290_sgn__minus__1,axiom,
% 5.12/5.37 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.37 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_minus_1
% 5.12/5.37 thf(fact_4291_linordered__idom__class_Oabs__sgn,axiom,
% 5.12/5.37 ( abs_abs_Code_integer
% 5.12/5.37 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % linordered_idom_class.abs_sgn
% 5.12/5.37 thf(fact_4292_linordered__idom__class_Oabs__sgn,axiom,
% 5.12/5.37 ( abs_abs_real
% 5.12/5.37 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % linordered_idom_class.abs_sgn
% 5.12/5.37 thf(fact_4293_linordered__idom__class_Oabs__sgn,axiom,
% 5.12/5.37 ( abs_abs_rat
% 5.12/5.37 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % linordered_idom_class.abs_sgn
% 5.12/5.37 thf(fact_4294_linordered__idom__class_Oabs__sgn,axiom,
% 5.12/5.37 ( abs_abs_int
% 5.12/5.37 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % linordered_idom_class.abs_sgn
% 5.12/5.37 thf(fact_4295_abs__mult__sgn,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % abs_mult_sgn
% 5.12/5.37 thf(fact_4296_abs__mult__sgn,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % abs_mult_sgn
% 5.12/5.37 thf(fact_4297_abs__mult__sgn,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % abs_mult_sgn
% 5.12/5.37 thf(fact_4298_abs__mult__sgn,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % abs_mult_sgn
% 5.12/5.37 thf(fact_4299_abs__mult__sgn,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % abs_mult_sgn
% 5.12/5.37 thf(fact_4300_sgn__mult__abs,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult_abs
% 5.12/5.37 thf(fact_4301_sgn__mult__abs,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult_abs
% 5.12/5.37 thf(fact_4302_sgn__mult__abs,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult_abs
% 5.12/5.37 thf(fact_4303_sgn__mult__abs,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult_abs
% 5.12/5.37 thf(fact_4304_sgn__mult__abs,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.12/5.37 = A ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_mult_abs
% 5.12/5.37 thf(fact_4305_mult__sgn__abs,axiom,
% 5.12/5.37 ! [X: code_integer] :
% 5.12/5.37 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 5.12/5.37 = X ) ).
% 5.12/5.37
% 5.12/5.37 % mult_sgn_abs
% 5.12/5.37 thf(fact_4306_mult__sgn__abs,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( times_times_real @ ( sgn_sgn_real @ X ) @ ( abs_abs_real @ X ) )
% 5.12/5.37 = X ) ).
% 5.12/5.37
% 5.12/5.37 % mult_sgn_abs
% 5.12/5.37 thf(fact_4307_mult__sgn__abs,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 5.12/5.37 = X ) ).
% 5.12/5.37
% 5.12/5.37 % mult_sgn_abs
% 5.12/5.37 thf(fact_4308_mult__sgn__abs,axiom,
% 5.12/5.37 ! [X: int] :
% 5.12/5.37 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 5.12/5.37 = X ) ).
% 5.12/5.37
% 5.12/5.37 % mult_sgn_abs
% 5.12/5.37 thf(fact_4309_same__sgn__abs__add,axiom,
% 5.12/5.37 ! [B: code_integer,A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ B )
% 5.12/5.37 = ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.37 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_abs_add
% 5.12/5.37 thf(fact_4310_same__sgn__abs__add,axiom,
% 5.12/5.37 ! [B: real,A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ B )
% 5.12/5.37 = ( sgn_sgn_real @ A ) )
% 5.12/5.37 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 5.12/5.37 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_abs_add
% 5.12/5.37 thf(fact_4311_same__sgn__abs__add,axiom,
% 5.12/5.37 ! [B: rat,A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ B )
% 5.12/5.37 = ( sgn_sgn_rat @ A ) )
% 5.12/5.37 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.37 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_abs_add
% 5.12/5.37 thf(fact_4312_same__sgn__abs__add,axiom,
% 5.12/5.37 ! [B: int,A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ B )
% 5.12/5.37 = ( sgn_sgn_int @ A ) )
% 5.12/5.37 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.37 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % same_sgn_abs_add
% 5.12/5.37 thf(fact_4313_floor__le__ceiling,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_ceiling
% 5.12/5.37 thf(fact_4314_floor__le__ceiling,axiom,
% 5.12/5.37 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim2889992004027027881ng_rat @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_ceiling
% 5.12/5.37 thf(fact_4315_exp__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( exp_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( inverse_inverse_real @ ( exp_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % exp_minus
% 5.12/5.37 thf(fact_4316_exp__minus,axiom,
% 5.12/5.37 ! [X: complex] :
% 5.12/5.37 ( ( exp_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.37 = ( invers8013647133539491842omplex @ ( exp_complex @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % exp_minus
% 5.12/5.37 thf(fact_4317_powr__minus,axiom,
% 5.12/5.37 ! [X: real,A: real] :
% 5.12/5.37 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 5.12/5.37 = ( inverse_inverse_real @ ( powr_real @ X @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % powr_minus
% 5.12/5.37 thf(fact_4318_cosh__real__pos,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_pos
% 5.12/5.37 thf(fact_4319_arcosh__cosh__real,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.12/5.37 = X ) ) ).
% 5.12/5.37
% 5.12/5.37 % arcosh_cosh_real
% 5.12/5.37 thf(fact_4320_cosh__real__nonneg,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonneg
% 5.12/5.37 thf(fact_4321_cosh__real__nonneg__le__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.37 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.12/5.37 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonneg_le_iff
% 5.12/5.37 thf(fact_4322_cosh__real__nonpos__le__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.12/5.37 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonpos_le_iff
% 5.12/5.37 thf(fact_4323_divide__real__def,axiom,
% 5.12/5.37 ( divide_divide_real
% 5.12/5.37 = ( ^ [X2: real,Y6: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y6 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % divide_real_def
% 5.12/5.37 thf(fact_4324_cosh__real__ge__1,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_ge_1
% 5.12/5.37 thf(fact_4325_Suc__mult__less__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.12/5.37 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mult_less_cancel1
% 5.12/5.37 thf(fact_4326_mult__less__mono1,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.37 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.37 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J2 @ K ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_less_mono1
% 5.12/5.37 thf(fact_4327_mult__less__mono2,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,K: nat] :
% 5.12/5.37 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.37 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_less_mono2
% 5.12/5.37 thf(fact_4328_Suc__mult__le__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.12/5.37 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_mult_le_cancel1
% 5.12/5.37 thf(fact_4329_mult__Suc,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( times_times_nat @ ( suc @ M2 ) @ N )
% 5.12/5.37 = ( plus_plus_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_Suc
% 5.12/5.37 thf(fact_4330_mult__eq__self__implies__10,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( M2
% 5.12/5.37 = ( times_times_nat @ M2 @ N ) )
% 5.12/5.37 => ( ( N = one_one_nat )
% 5.12/5.37 | ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_eq_self_implies_10
% 5.12/5.37 thf(fact_4331_less__mult__imp__div__less,axiom,
% 5.12/5.37 ! [M2: nat,I: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I @ N ) )
% 5.12/5.37 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_mult_imp_div_less
% 5.12/5.37 thf(fact_4332_div__times__less__eq__dividend,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) @ M2 ) ).
% 5.12/5.37
% 5.12/5.37 % div_times_less_eq_dividend
% 5.12/5.37 thf(fact_4333_times__div__less__eq__dividend,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) @ M2 ) ).
% 5.12/5.37
% 5.12/5.37 % times_div_less_eq_dividend
% 5.12/5.37 thf(fact_4334_mod__eq__0D,axiom,
% 5.12/5.37 ! [M2: nat,D: nat] :
% 5.12/5.37 ( ( ( modulo_modulo_nat @ M2 @ D )
% 5.12/5.37 = zero_zero_nat )
% 5.12/5.37 => ? [Q3: nat] :
% 5.12/5.37 ( M2
% 5.12/5.37 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mod_eq_0D
% 5.12/5.37 thf(fact_4335_int__ops_I7_J,axiom,
% 5.12/5.37 ! [A: nat,B: nat] :
% 5.12/5.37 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.12/5.37 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % int_ops(7)
% 5.12/5.37 thf(fact_4336_inverse__le__imp__le,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_imp_le
% 5.12/5.37 thf(fact_4337_inverse__le__imp__le,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_imp_le
% 5.12/5.37 thf(fact_4338_le__imp__inverse__le,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_imp_inverse_le
% 5.12/5.37 thf(fact_4339_le__imp__inverse__le,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_imp_inverse_le
% 5.12/5.37 thf(fact_4340_inverse__le__imp__le__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_imp_le_neg
% 5.12/5.37 thf(fact_4341_inverse__le__imp__le__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_imp_le_neg
% 5.12/5.37 thf(fact_4342_le__imp__inverse__le__neg,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.12/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.12/5.37 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_imp_inverse_le_neg
% 5.12/5.37 thf(fact_4343_le__imp__inverse__le__neg,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ A @ B )
% 5.12/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_imp_inverse_le_neg
% 5.12/5.37 thf(fact_4344_inverse__le__1__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.12/5.37 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.37 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_1_iff
% 5.12/5.37 thf(fact_4345_inverse__le__1__iff,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.12/5.37 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.37 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_1_iff
% 5.12/5.37 thf(fact_4346_one__less__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( ord_less_real @ A @ one_one_real )
% 5.12/5.37 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_less_inverse
% 5.12/5.37 thf(fact_4347_one__less__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.12/5.37 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_less_inverse
% 5.12/5.37 thf(fact_4348_one__less__inverse__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.12/5.37 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_less_inverse_iff
% 5.12/5.37 thf(fact_4349_one__less__inverse__iff,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.12/5.37 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.37 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_less_inverse_iff
% 5.12/5.37 thf(fact_4350_field__class_Ofield__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.12/5.37 = one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse
% 5.12/5.37 thf(fact_4351_field__class_Ofield__inverse,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.12/5.37 = one_one_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse
% 5.12/5.37 thf(fact_4352_field__class_Ofield__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.12/5.37 = one_one_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % field_class.field_inverse
% 5.12/5.37 thf(fact_4353_division__ring__inverse__add,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_add
% 5.12/5.37 thf(fact_4354_division__ring__inverse__add,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.12/5.37 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_add
% 5.12/5.37 thf(fact_4355_division__ring__inverse__add,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_add
% 5.12/5.37 thf(fact_4356_inverse__add,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_add
% 5.12/5.37 thf(fact_4357_inverse__add,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.12/5.37 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_add
% 5.12/5.37 thf(fact_4358_inverse__add,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_add
% 5.12/5.37 thf(fact_4359_division__ring__inverse__diff,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_diff
% 5.12/5.37 thf(fact_4360_division__ring__inverse__diff,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.12/5.37 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_diff
% 5.12/5.37 thf(fact_4361_division__ring__inverse__diff,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % division_ring_inverse_diff
% 5.12/5.37 thf(fact_4362_nonzero__inverse__eq__divide,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( inverse_inverse_real @ A )
% 5.12/5.37 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_divide
% 5.12/5.37 thf(fact_4363_nonzero__inverse__eq__divide,axiom,
% 5.12/5.37 ! [A: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( invers8013647133539491842omplex @ A )
% 5.12/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_divide
% 5.12/5.37 thf(fact_4364_nonzero__inverse__eq__divide,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( inverse_inverse_rat @ A )
% 5.12/5.37 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nonzero_inverse_eq_divide
% 5.12/5.37 thf(fact_4365_le__floor__iff,axiom,
% 5.12/5.37 ! [Z2: int,X: real] :
% 5.12/5.37 ( ( ord_less_eq_int @ Z2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_floor_iff
% 5.12/5.37 thf(fact_4366_le__floor__iff,axiom,
% 5.12/5.37 ! [Z2: int,X: rat] :
% 5.12/5.37 ( ( ord_less_eq_int @ Z2 @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_floor_iff
% 5.12/5.37 thf(fact_4367_floor__less__iff,axiom,
% 5.12/5.37 ! [X: real,Z2: int] :
% 5.12/5.37 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z2 )
% 5.12/5.37 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_iff
% 5.12/5.37 thf(fact_4368_floor__less__iff,axiom,
% 5.12/5.37 ! [X: rat,Z2: int] :
% 5.12/5.37 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z2 )
% 5.12/5.37 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_less_iff
% 5.12/5.37 thf(fact_4369_le__mult__nat__floor,axiom,
% 5.12/5.37 ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_mult_nat_floor
% 5.12/5.37 thf(fact_4370_le__mult__nat__floor,axiom,
% 5.12/5.37 ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_mult_nat_floor
% 5.12/5.37 thf(fact_4371_le__floor__add,axiom,
% 5.12/5.37 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_floor_add
% 5.12/5.37 thf(fact_4372_le__floor__add,axiom,
% 5.12/5.37 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_floor_add
% 5.12/5.37 thf(fact_4373_int__add__floor,axiom,
% 5.12/5.37 ! [Z2: int,X: real] :
% 5.12/5.37 ( ( plus_plus_int @ Z2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z2 ) @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % int_add_floor
% 5.12/5.37 thf(fact_4374_int__add__floor,axiom,
% 5.12/5.37 ! [Z2: int,X: rat] :
% 5.12/5.37 ( ( plus_plus_int @ Z2 @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % int_add_floor
% 5.12/5.37 thf(fact_4375_floor__add__int,axiom,
% 5.12/5.37 ! [X: real,Z2: int] :
% 5.12/5.37 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z2 )
% 5.12/5.37 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_add_int
% 5.12/5.37 thf(fact_4376_floor__add__int,axiom,
% 5.12/5.37 ! [X: rat,Z2: int] :
% 5.12/5.37 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z2 )
% 5.12/5.37 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_add_int
% 5.12/5.37 thf(fact_4377_sgn__1__pos,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = one_one_Code_integer )
% 5.12/5.37 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_pos
% 5.12/5.37 thf(fact_4378_sgn__1__pos,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ A )
% 5.12/5.37 = one_one_real )
% 5.12/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_pos
% 5.12/5.37 thf(fact_4379_sgn__1__pos,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = one_one_rat )
% 5.12/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_pos
% 5.12/5.37 thf(fact_4380_sgn__1__pos,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ A )
% 5.12/5.37 = one_one_int )
% 5.12/5.37 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_pos
% 5.12/5.37 thf(fact_4381_floor__divide__of__int__eq,axiom,
% 5.12/5.37 ! [K: int,L: int] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.12/5.37 = ( divide_divide_int @ K @ L ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_of_int_eq
% 5.12/5.37 thf(fact_4382_floor__divide__of__int__eq,axiom,
% 5.12/5.37 ! [K: int,L: int] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.12/5.37 = ( divide_divide_int @ K @ L ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_of_int_eq
% 5.12/5.37 thf(fact_4383_ceiling__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_int @ ( archim6058952711729229775r_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_minus
% 5.12/5.37 thf(fact_4384_ceiling__minus,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X ) )
% 5.12/5.37 = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_minus
% 5.12/5.37 thf(fact_4385_floor__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_int @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_minus
% 5.12/5.37 thf(fact_4386_floor__minus,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) )
% 5.12/5.37 = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_minus
% 5.12/5.37 thf(fact_4387_ceiling__def,axiom,
% 5.12/5.37 ( archim7802044766580827645g_real
% 5.12/5.37 = ( ^ [X2: real] : ( uminus_uminus_int @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_def
% 5.12/5.37 thf(fact_4388_ceiling__def,axiom,
% 5.12/5.37 ( archim2889992004027027881ng_rat
% 5.12/5.37 = ( ^ [X2: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X2 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_def
% 5.12/5.37 thf(fact_4389_sgn__root,axiom,
% 5.12/5.37 ! [N: nat,X: real] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.12/5.37 = ( sgn_sgn_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_root
% 5.12/5.37 thf(fact_4390_floor__power,axiom,
% 5.12/5.37 ! [X: real,N: nat] :
% 5.12/5.37 ( ( X
% 5.12/5.37 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 5.12/5.37 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 5.12/5.37 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_power
% 5.12/5.37 thf(fact_4391_floor__power,axiom,
% 5.12/5.37 ! [X: rat,N: nat] :
% 5.12/5.37 ( ( X
% 5.12/5.37 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 5.12/5.37 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N ) )
% 5.12/5.37 = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_power
% 5.12/5.37 thf(fact_4392_abs__sgn__eq,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ( A = zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 = zero_z3403309356797280102nteger ) )
% 5.12/5.37 & ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.37 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.37 = one_one_Code_integer ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq
% 5.12/5.37 thf(fact_4393_abs__sgn__eq,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( A = zero_zero_real )
% 5.12/5.37 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.37 = zero_zero_real ) )
% 5.12/5.37 & ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.37 = one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq
% 5.12/5.37 thf(fact_4394_abs__sgn__eq,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( A = zero_zero_rat )
% 5.12/5.37 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.37 = zero_zero_rat ) )
% 5.12/5.37 & ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.37 = one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq
% 5.12/5.37 thf(fact_4395_abs__sgn__eq,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ( A = zero_zero_int )
% 5.12/5.37 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.37 = zero_zero_int ) )
% 5.12/5.37 & ( ( A != zero_zero_int )
% 5.12/5.37 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.37 = one_one_int ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % abs_sgn_eq
% 5.12/5.37 thf(fact_4396_cosh__real__strict__mono,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ Y )
% 5.12/5.37 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_strict_mono
% 5.12/5.37 thf(fact_4397_cosh__real__nonneg__less__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.37 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.12/5.37 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonneg_less_iff
% 5.12/5.37 thf(fact_4398_cosh__real__nonpos__less__iff,axiom,
% 5.12/5.37 ! [X: real,Y: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.12/5.37 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.12/5.37 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % cosh_real_nonpos_less_iff
% 5.12/5.37 thf(fact_4399_inverse__powr,axiom,
% 5.12/5.37 ! [Y: real,A: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.37 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.12/5.37 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_powr
% 5.12/5.37 thf(fact_4400_one__less__mult,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.37 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.12/5.37 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_less_mult
% 5.12/5.37 thf(fact_4401_n__less__m__mult__n,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.12/5.37 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % n_less_m_mult_n
% 5.12/5.37 thf(fact_4402_n__less__n__mult__m,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.12/5.37 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % n_less_n_mult_m
% 5.12/5.37 thf(fact_4403_div__less__iff__less__mult,axiom,
% 5.12/5.37 ! [Q5: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ Q5 )
% 5.12/5.37 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q5 ) @ N )
% 5.12/5.37 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q5 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_less_iff_less_mult
% 5.12/5.37 thf(fact_4404_mod__mult2__eq,axiom,
% 5.12/5.37 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.37 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N @ Q5 ) )
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N ) @ Q5 ) ) @ ( modulo_modulo_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mod_mult2_eq
% 5.12/5.37 thf(fact_4405_div__mod__decomp,axiom,
% 5.12/5.37 ! [A2: nat,N: nat] :
% 5.12/5.37 ( A2
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_mod_decomp
% 5.12/5.37 thf(fact_4406_modulo__nat__def,axiom,
% 5.12/5.37 ( modulo_modulo_nat
% 5.12/5.37 = ( ^ [M5: nat,N4: nat] : ( minus_minus_nat @ M5 @ ( times_times_nat @ ( divide_divide_nat @ M5 @ N4 ) @ N4 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % modulo_nat_def
% 5.12/5.37 thf(fact_4407_nat__abs__mult__distrib,axiom,
% 5.12/5.37 ! [W: int,Z2: int] :
% 5.12/5.37 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z2 ) ) )
% 5.12/5.37 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_abs_mult_distrib
% 5.12/5.37 thf(fact_4408_of__nat__floor,axiom,
% 5.12/5.37 ! [R4: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ R4 )
% 5.12/5.37 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R4 ) ) ) @ R4 ) ) ).
% 5.12/5.37
% 5.12/5.37 % of_nat_floor
% 5.12/5.37 thf(fact_4409_of__nat__floor,axiom,
% 5.12/5.37 ! [R4: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ R4 )
% 5.12/5.37 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R4 ) ) ) @ R4 ) ) ).
% 5.12/5.37
% 5.12/5.37 % of_nat_floor
% 5.12/5.37 thf(fact_4410_inverse__le__iff,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.37 => ( ord_less_eq_real @ B @ A ) )
% 5.12/5.37 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.12/5.37 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff
% 5.12/5.37 thf(fact_4411_inverse__le__iff,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.37 => ( ord_less_eq_rat @ B @ A ) )
% 5.12/5.37 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_le_iff
% 5.12/5.37 thf(fact_4412_inverse__less__iff,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.12/5.37 => ( ord_less_real @ B @ A ) )
% 5.12/5.37 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.12/5.37 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff
% 5.12/5.37 thf(fact_4413_inverse__less__iff,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.12/5.37 => ( ord_less_rat @ B @ A ) )
% 5.12/5.37 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.12/5.37 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_iff
% 5.12/5.37 thf(fact_4414_one__le__inverse,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.12/5.37 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_inverse
% 5.12/5.37 thf(fact_4415_one__le__inverse,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.12/5.37 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_inverse
% 5.12/5.37 thf(fact_4416_inverse__less__1__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.12/5.37 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.37 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_1_iff
% 5.12/5.37 thf(fact_4417_inverse__less__1__iff,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.12/5.37 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.12/5.37 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_less_1_iff
% 5.12/5.37 thf(fact_4418_one__le__inverse__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.12/5.37 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 & ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_inverse_iff
% 5.12/5.37 thf(fact_4419_one__le__inverse__iff,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.12/5.37 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.37 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_le_inverse_iff
% 5.12/5.37 thf(fact_4420_one__add__floor,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.12/5.37 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_add_floor
% 5.12/5.37 thf(fact_4421_one__add__floor,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.12/5.37 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % one_add_floor
% 5.12/5.37 thf(fact_4422_inverse__diff__inverse,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( A != zero_zero_real )
% 5.12/5.37 => ( ( B != zero_zero_real )
% 5.12/5.37 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_diff_inverse
% 5.12/5.37 thf(fact_4423_inverse__diff__inverse,axiom,
% 5.12/5.37 ! [A: complex,B: complex] :
% 5.12/5.37 ( ( A != zero_zero_complex )
% 5.12/5.37 => ( ( B != zero_zero_complex )
% 5.12/5.37 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_diff_inverse
% 5.12/5.37 thf(fact_4424_inverse__diff__inverse,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( A != zero_zero_rat )
% 5.12/5.37 => ( ( B != zero_zero_rat )
% 5.12/5.37 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.12/5.37 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % inverse_diff_inverse
% 5.12/5.37 thf(fact_4425_reals__Archimedean,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 => ? [N2: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % reals_Archimedean
% 5.12/5.37 thf(fact_4426_reals__Archimedean,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.37 => ? [N2: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % reals_Archimedean
% 5.12/5.37 thf(fact_4427_floor__divide__of__nat__eq,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.37 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_of_nat_eq
% 5.12/5.37 thf(fact_4428_floor__divide__of__nat__eq,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.12/5.37 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_of_nat_eq
% 5.12/5.37 thf(fact_4429_nat__floor__neg,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = zero_zero_nat ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_floor_neg
% 5.12/5.37 thf(fact_4430_sgn__real__def,axiom,
% 5.12/5.37 ( sgn_sgn_real
% 5.12/5.37 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_real_def
% 5.12/5.37 thf(fact_4431_sgn__if,axiom,
% 5.12/5.37 ( sgn_sgn_int
% 5.12/5.37 = ( ^ [X2: int] : ( if_int @ ( X2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_if
% 5.12/5.37 thf(fact_4432_sgn__if,axiom,
% 5.12/5.37 ( sgn_sgn_real
% 5.12/5.37 = ( ^ [X2: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X2 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_if
% 5.12/5.37 thf(fact_4433_sgn__if,axiom,
% 5.12/5.37 ( sgn_sgn_Code_integer
% 5.12/5.37 = ( ^ [X2: code_integer] : ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_if
% 5.12/5.37 thf(fact_4434_sgn__if,axiom,
% 5.12/5.37 ( sgn_sgn_rat
% 5.12/5.37 = ( ^ [X2: rat] : ( if_rat @ ( X2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_if
% 5.12/5.37 thf(fact_4435_sgn__1__neg,axiom,
% 5.12/5.37 ! [A: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ A )
% 5.12/5.37 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_neg
% 5.12/5.37 thf(fact_4436_sgn__1__neg,axiom,
% 5.12/5.37 ! [A: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ A )
% 5.12/5.37 = ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_neg
% 5.12/5.37 thf(fact_4437_sgn__1__neg,axiom,
% 5.12/5.37 ! [A: code_integer] :
% 5.12/5.37 ( ( ( sgn_sgn_Code_integer @ A )
% 5.12/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.37 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_neg
% 5.12/5.37 thf(fact_4438_sgn__1__neg,axiom,
% 5.12/5.37 ! [A: rat] :
% 5.12/5.37 ( ( ( sgn_sgn_rat @ A )
% 5.12/5.37 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_1_neg
% 5.12/5.37 thf(fact_4439_floor__eq3,axiom,
% 5.12/5.37 ! [N: nat,X: real] :
% 5.12/5.37 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.12/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq3
% 5.12/5.37 thf(fact_4440_le__nat__floor,axiom,
% 5.12/5.37 ! [X: nat,A: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.12/5.37 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_nat_floor
% 5.12/5.37 thf(fact_4441_ceiling__altdef,axiom,
% 5.12/5.37 ( archim7802044766580827645g_real
% 5.12/5.37 = ( ^ [X2: real] :
% 5.12/5.37 ( if_int
% 5.12/5.37 @ ( X2
% 5.12/5.37 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.12/5.37 @ ( archim6058952711729229775r_real @ X2 )
% 5.12/5.37 @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_altdef
% 5.12/5.37 thf(fact_4442_ceiling__altdef,axiom,
% 5.12/5.37 ( archim2889992004027027881ng_rat
% 5.12/5.37 = ( ^ [X2: rat] :
% 5.12/5.37 ( if_int
% 5.12/5.37 @ ( X2
% 5.12/5.37 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.12/5.37 @ ( archim3151403230148437115or_rat @ X2 )
% 5.12/5.37 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_altdef
% 5.12/5.37 thf(fact_4443_ceiling__diff__floor__le__1,axiom,
% 5.12/5.37 ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_diff_floor_le_1
% 5.12/5.37 thf(fact_4444_ceiling__diff__floor__le__1,axiom,
% 5.12/5.37 ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 5.12/5.37
% 5.12/5.37 % ceiling_diff_floor_le_1
% 5.12/5.37 thf(fact_4445_floor__eq,axiom,
% 5.12/5.37 ! [N: int,X: real] :
% 5.12/5.37 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.12/5.37 => ( ( archim6058952711729229775r_real @ X )
% 5.12/5.37 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq
% 5.12/5.37 thf(fact_4446_real__of__int__floor__add__one__gt,axiom,
% 5.12/5.37 ! [R4: real] : ( ord_less_real @ R4 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R4 ) ) @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_of_int_floor_add_one_gt
% 5.12/5.37 thf(fact_4447_real__of__int__floor__add__one__ge,axiom,
% 5.12/5.37 ! [R4: real] : ( ord_less_eq_real @ R4 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R4 ) ) @ one_one_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_of_int_floor_add_one_ge
% 5.12/5.37 thf(fact_4448_real__of__int__floor__gt__diff__one,axiom,
% 5.12/5.37 ! [R4: real] : ( ord_less_real @ ( minus_minus_real @ R4 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R4 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_of_int_floor_gt_diff_one
% 5.12/5.37 thf(fact_4449_real__of__int__floor__ge__diff__one,axiom,
% 5.12/5.37 ! [R4: real] : ( ord_less_eq_real @ ( minus_minus_real @ R4 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R4 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_of_int_floor_ge_diff_one
% 5.12/5.37 thf(fact_4450_forall__pos__mono__1,axiom,
% 5.12/5.37 ! [P: real > $o,E2: real] :
% 5.12/5.37 ( ! [D5: real,E: real] :
% 5.12/5.37 ( ( ord_less_real @ D5 @ E )
% 5.12/5.37 => ( ( P @ D5 )
% 5.12/5.37 => ( P @ E ) ) )
% 5.12/5.37 => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.12/5.37 => ( P @ E2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % forall_pos_mono_1
% 5.12/5.37 thf(fact_4451_forall__pos__mono,axiom,
% 5.12/5.37 ! [P: real > $o,E2: real] :
% 5.12/5.37 ( ! [D5: real,E: real] :
% 5.12/5.37 ( ( ord_less_real @ D5 @ E )
% 5.12/5.37 => ( ( P @ D5 )
% 5.12/5.37 => ( P @ E ) ) )
% 5.12/5.37 => ( ! [N2: nat] :
% 5.12/5.37 ( ( N2 != zero_zero_nat )
% 5.12/5.37 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.12/5.37 => ( P @ E2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % forall_pos_mono
% 5.12/5.37 thf(fact_4452_real__arch__inverse,axiom,
% 5.12/5.37 ! [E2: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.12/5.37 = ( ? [N4: nat] :
% 5.12/5.37 ( ( N4 != zero_zero_nat )
% 5.12/5.37 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.12/5.37 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_arch_inverse
% 5.12/5.37 thf(fact_4453_ln__inverse,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ln_inverse
% 5.12/5.37 thf(fact_4454_div__nat__eqI,axiom,
% 5.12/5.37 ! [N: nat,Q5: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M2 )
% 5.12/5.37 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 5.12/5.37 => ( ( divide_divide_nat @ M2 @ N )
% 5.12/5.37 = Q5 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_nat_eqI
% 5.12/5.37 thf(fact_4455_less__eq__div__iff__mult__less__eq,axiom,
% 5.12/5.37 ! [Q5: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ Q5 )
% 5.12/5.37 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q5 ) )
% 5.12/5.37 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q5 ) @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_eq_div_iff_mult_less_eq
% 5.12/5.37 thf(fact_4456_split__div,axiom,
% 5.12/5.37 ! [P: nat > $o,M2: nat,N: nat] :
% 5.12/5.37 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( ( N = zero_zero_nat )
% 5.12/5.37 => ( P @ zero_zero_nat ) )
% 5.12/5.37 & ( ( N != zero_zero_nat )
% 5.12/5.37 => ! [I2: nat,J3: nat] :
% 5.12/5.37 ( ( ord_less_nat @ J3 @ N )
% 5.12/5.37 => ( ( M2
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.12/5.37 => ( P @ I2 ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % split_div
% 5.12/5.37 thf(fact_4457_dividend__less__div__times,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % dividend_less_div_times
% 5.12/5.37 thf(fact_4458_dividend__less__times__div,axiom,
% 5.12/5.37 ! [N: nat,M2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % dividend_less_times_div
% 5.12/5.37 thf(fact_4459_mult__eq__if,axiom,
% 5.12/5.37 ( times_times_nat
% 5.12/5.37 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % mult_eq_if
% 5.12/5.37 thf(fact_4460_split__mod,axiom,
% 5.12/5.37 ! [P: nat > $o,M2: nat,N: nat] :
% 5.12/5.37 ( ( P @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( ( N = zero_zero_nat )
% 5.12/5.37 => ( P @ M2 ) )
% 5.12/5.37 & ( ( N != zero_zero_nat )
% 5.12/5.37 => ! [I2: nat,J3: nat] :
% 5.12/5.37 ( ( ord_less_nat @ J3 @ N )
% 5.12/5.37 => ( ( M2
% 5.12/5.37 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.12/5.37 => ( P @ J3 ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % split_mod
% 5.12/5.37 thf(fact_4461_nat__mult__distrib,axiom,
% 5.12/5.37 ! [Z2: int,Z3: int] :
% 5.12/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.37 => ( ( nat2 @ ( times_times_int @ Z2 @ Z3 ) )
% 5.12/5.37 = ( times_times_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z3 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_distrib
% 5.12/5.37 thf(fact_4462_floor__unique,axiom,
% 5.12/5.37 ! [Z2: int,X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) )
% 5.12/5.37 => ( ( archim6058952711729229775r_real @ X )
% 5.12/5.37 = Z2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_unique
% 5.12/5.37 thf(fact_4463_floor__unique,axiom,
% 5.12/5.37 ! [Z2: int,X: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.12/5.37 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) )
% 5.12/5.37 => ( ( archim3151403230148437115or_rat @ X )
% 5.12/5.37 = Z2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_unique
% 5.12/5.37 thf(fact_4464_floor__eq__iff,axiom,
% 5.12/5.37 ! [X: real,A: int] :
% 5.12/5.37 ( ( ( archim6058952711729229775r_real @ X )
% 5.12/5.37 = A )
% 5.12/5.37 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 5.12/5.37 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq_iff
% 5.12/5.37 thf(fact_4465_floor__eq__iff,axiom,
% 5.12/5.37 ! [X: rat,A: int] :
% 5.12/5.37 ( ( ( archim3151403230148437115or_rat @ X )
% 5.12/5.37 = A )
% 5.12/5.37 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 5.12/5.37 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq_iff
% 5.12/5.37 thf(fact_4466_floor__split,axiom,
% 5.12/5.37 ! [P: int > $o,T: real] :
% 5.12/5.37 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.12/5.37 = ( ! [I2: int] :
% 5.12/5.37 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I2 ) @ T )
% 5.12/5.37 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) ) )
% 5.12/5.37 => ( P @ I2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_split
% 5.12/5.37 thf(fact_4467_floor__split,axiom,
% 5.12/5.37 ! [P: int > $o,T: rat] :
% 5.12/5.37 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.12/5.37 = ( ! [I2: int] :
% 5.12/5.37 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 5.12/5.37 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 5.12/5.37 => ( P @ I2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_split
% 5.12/5.37 thf(fact_4468_le__mult__floor,axiom,
% 5.12/5.37 ! [A: real,B: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.12/5.37 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_mult_floor
% 5.12/5.37 thf(fact_4469_le__mult__floor,axiom,
% 5.12/5.37 ! [A: rat,B: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.37 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.12/5.37 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % le_mult_floor
% 5.12/5.37 thf(fact_4470_less__floor__iff,axiom,
% 5.12/5.37 ! [Z2: int,X: real] :
% 5.12/5.37 ( ( ord_less_int @ Z2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_floor_iff
% 5.12/5.37 thf(fact_4471_less__floor__iff,axiom,
% 5.12/5.37 ! [Z2: int,X: rat] :
% 5.12/5.37 ( ( ord_less_int @ Z2 @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.37 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.37
% 5.12/5.37 % less_floor_iff
% 5.12/5.37 thf(fact_4472_floor__le__iff,axiom,
% 5.12/5.37 ! [X: real,Z2: int] :
% 5.12/5.37 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z2 )
% 5.12/5.37 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z2 ) @ one_one_real ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_iff
% 5.12/5.37 thf(fact_4473_floor__le__iff,axiom,
% 5.12/5.37 ! [X: rat,Z2: int] :
% 5.12/5.37 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z2 )
% 5.12/5.37 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z2 ) @ one_one_rat ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_le_iff
% 5.12/5.37 thf(fact_4474_floor__correct,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 5.12/5.37 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_correct
% 5.12/5.37 thf(fact_4475_floor__correct,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 5.12/5.37 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_correct
% 5.12/5.37 thf(fact_4476_ex__inverse__of__nat__less,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 => ? [N2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.12/5.37 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ex_inverse_of_nat_less
% 5.12/5.37 thf(fact_4477_ex__inverse__of__nat__less,axiom,
% 5.12/5.37 ! [X: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.37 => ? [N2: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.12/5.37 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % ex_inverse_of_nat_less
% 5.12/5.37 thf(fact_4478_power__diff__conv__inverse,axiom,
% 5.12/5.37 ! [X: real,M2: nat,N: nat] :
% 5.12/5.37 ( ( X != zero_zero_real )
% 5.12/5.37 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.37 => ( ( power_power_real @ X @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.37 = ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ M2 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_diff_conv_inverse
% 5.12/5.37 thf(fact_4479_power__diff__conv__inverse,axiom,
% 5.12/5.37 ! [X: complex,M2: nat,N: nat] :
% 5.12/5.37 ( ( X != zero_zero_complex )
% 5.12/5.37 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.37 => ( ( power_power_complex @ X @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.37 = ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ M2 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_diff_conv_inverse
% 5.12/5.37 thf(fact_4480_power__diff__conv__inverse,axiom,
% 5.12/5.37 ! [X: rat,M2: nat,N: nat] :
% 5.12/5.37 ( ( X != zero_zero_rat )
% 5.12/5.37 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.37 => ( ( power_power_rat @ X @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.37 = ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ M2 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % power_diff_conv_inverse
% 5.12/5.37 thf(fact_4481_floor__eq4,axiom,
% 5.12/5.37 ! [N: nat,X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.12/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.37 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq4
% 5.12/5.37 thf(fact_4482_sgn__power__injE,axiom,
% 5.12/5.37 ! [A: real,N: nat,X: real,B: real] :
% 5.12/5.37 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.12/5.37 = X )
% 5.12/5.37 => ( ( X
% 5.12/5.37 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.12/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( A = B ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_power_injE
% 5.12/5.37 thf(fact_4483_floor__eq2,axiom,
% 5.12/5.37 ! [N: int,X: real] :
% 5.12/5.37 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.12/5.37 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.12/5.37 => ( ( archim6058952711729229775r_real @ X )
% 5.12/5.37 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_eq2
% 5.12/5.37 thf(fact_4484_floor__divide__real__eq__div,axiom,
% 5.12/5.37 ! [B: int,A: real] :
% 5.12/5.37 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.37 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.12/5.37 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_real_eq_div
% 5.12/5.37 thf(fact_4485_log__inverse,axiom,
% 5.12/5.37 ! [A: real,X: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.37 => ( ( A != one_one_real )
% 5.12/5.37 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.37 => ( ( log2 @ A @ ( inverse_inverse_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( log2 @ A @ X ) ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % log_inverse
% 5.12/5.37 thf(fact_4486_split__div_H,axiom,
% 5.12/5.37 ! [P: nat > $o,M2: nat,N: nat] :
% 5.12/5.37 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 5.12/5.37 = ( ( ( N = zero_zero_nat )
% 5.12/5.37 & ( P @ zero_zero_nat ) )
% 5.12/5.37 | ? [Q4: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M2 )
% 5.12/5.37 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.12/5.37 & ( P @ Q4 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % split_div'
% 5.12/5.37 thf(fact_4487_Suc__times__mod__eq,axiom,
% 5.12/5.37 ! [M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 5.12/5.37 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 5.12/5.37 = one_one_nat ) ) ).
% 5.12/5.37
% 5.12/5.37 % Suc_times_mod_eq
% 5.12/5.37 thf(fact_4488_floor__divide__lower,axiom,
% 5.12/5.37 ! [Q5: real,P4: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ Q5 )
% 5.12/5.37 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q5 ) ) ) @ Q5 ) @ P4 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_lower
% 5.12/5.37 thf(fact_4489_floor__divide__lower,axiom,
% 5.12/5.37 ! [Q5: rat,P4: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ Q5 )
% 5.12/5.37 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q5 ) ) ) @ Q5 ) @ P4 ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_lower
% 5.12/5.37 thf(fact_4490_nat__mult__distrib__neg,axiom,
% 5.12/5.37 ! [Z2: int,Z3: int] :
% 5.12/5.37 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 5.12/5.37 => ( ( nat2 @ ( times_times_int @ Z2 @ Z3 ) )
% 5.12/5.37 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z2 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_distrib_neg
% 5.12/5.37 thf(fact_4491_sgn__power__root,axiom,
% 5.12/5.37 ! [N: nat,X: real] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.12/5.37 = X ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_power_root
% 5.12/5.37 thf(fact_4492_root__sgn__power,axiom,
% 5.12/5.37 ! [N: nat,Y: real] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.37 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 5.12/5.37 = Y ) ) ).
% 5.12/5.37
% 5.12/5.37 % root_sgn_power
% 5.12/5.37 thf(fact_4493_floor__divide__upper,axiom,
% 5.12/5.37 ! [Q5: real,P4: real] :
% 5.12/5.37 ( ( ord_less_real @ zero_zero_real @ Q5 )
% 5.12/5.37 => ( ord_less_real @ P4 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q5 ) ) ) @ one_one_real ) @ Q5 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_upper
% 5.12/5.37 thf(fact_4494_floor__divide__upper,axiom,
% 5.12/5.37 ! [Q5: rat,P4: rat] :
% 5.12/5.37 ( ( ord_less_rat @ zero_zero_rat @ Q5 )
% 5.12/5.37 => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q5 ) ) ) @ one_one_rat ) @ Q5 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % floor_divide_upper
% 5.12/5.37 thf(fact_4495_nat__mult__le__cancel__disj,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_le_cancel_disj
% 5.12/5.37 thf(fact_4496_nat__mult__div__cancel__disj,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ( K = zero_zero_nat )
% 5.12/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = zero_zero_nat ) )
% 5.12/5.37 & ( ( K != zero_zero_nat )
% 5.12/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( divide_divide_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_div_cancel_disj
% 5.12/5.37 thf(fact_4497_nat__mult__less__cancel__disj,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_less_cancel_disj
% 5.12/5.37 thf(fact_4498_sgn__one,axiom,
% 5.12/5.37 ( ( sgn_sgn_real @ one_one_real )
% 5.12/5.37 = one_one_real ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_one
% 5.12/5.37 thf(fact_4499_sgn__one,axiom,
% 5.12/5.37 ( ( sgn_sgn_complex @ one_one_complex )
% 5.12/5.37 = one_one_complex ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_one
% 5.12/5.37 thf(fact_4500_nat__less__add__iff2,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.37 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.37 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I ) @ U ) @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_less_add_iff2
% 5.12/5.37 thf(fact_4501_nat__less__add__iff1,axiom,
% 5.12/5.37 ! [J2: nat,I: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ J2 @ I )
% 5.12/5.37 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.37 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_less_add_iff1
% 5.12/5.37 thf(fact_4502_sgn__zero,axiom,
% 5.12/5.37 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.12/5.37 = zero_zero_complex ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_zero
% 5.12/5.37 thf(fact_4503_sgn__zero,axiom,
% 5.12/5.37 ( ( sgn_sgn_real @ zero_zero_real )
% 5.12/5.37 = zero_zero_real ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_zero
% 5.12/5.37 thf(fact_4504_nat__diff__add__eq2,axiom,
% 5.12/5.37 ! [I: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.37 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.37 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I ) @ U ) @ N ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_diff_add_eq2
% 5.12/5.37 thf(fact_4505_int__sgnE,axiom,
% 5.12/5.37 ! [K: int] :
% 5.12/5.37 ~ ! [N2: nat,L3: int] :
% 5.12/5.37 ( K
% 5.12/5.37 != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % int_sgnE
% 5.12/5.37 thf(fact_4506_div__eq__sgn__abs,axiom,
% 5.12/5.37 ! [K: int,L: int] :
% 5.12/5.37 ( ( ( sgn_sgn_int @ K )
% 5.12/5.37 = ( sgn_sgn_int @ L ) )
% 5.12/5.37 => ( ( divide_divide_int @ K @ L )
% 5.12/5.37 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_eq_sgn_abs
% 5.12/5.37 thf(fact_4507_zsgn__def,axiom,
% 5.12/5.37 ( sgn_sgn_int
% 5.12/5.37 = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % zsgn_def
% 5.12/5.37 thf(fact_4508_div__sgn__abs__cancel,axiom,
% 5.12/5.37 ! [V: int,K: int,L: int] :
% 5.12/5.37 ( ( V != zero_zero_int )
% 5.12/5.37 => ( ( 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 ) ) )
% 5.12/5.37 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % div_sgn_abs_cancel
% 5.12/5.37 thf(fact_4509_nat__mult__eq__cancel__disj,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ( times_times_nat @ K @ M2 )
% 5.12/5.37 = ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( ( K = zero_zero_nat )
% 5.12/5.37 | ( M2 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_eq_cancel_disj
% 5.12/5.37 thf(fact_4510_sgn__zero__iff,axiom,
% 5.12/5.37 ! [X: complex] :
% 5.12/5.37 ( ( ( sgn_sgn_complex @ X )
% 5.12/5.37 = zero_zero_complex )
% 5.12/5.37 = ( X = zero_zero_complex ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_zero_iff
% 5.12/5.37 thf(fact_4511_sgn__zero__iff,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( ( sgn_sgn_real @ X )
% 5.12/5.37 = zero_zero_real )
% 5.12/5.37 = ( X = zero_zero_real ) ) ).
% 5.12/5.37
% 5.12/5.37 % sgn_zero_iff
% 5.12/5.37 thf(fact_4512_Real__Vector__Spaces_Osgn__minus,axiom,
% 5.12/5.37 ! [X: real] :
% 5.12/5.37 ( ( sgn_sgn_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.37 = ( uminus_uminus_real @ ( sgn_sgn_real @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % Real_Vector_Spaces.sgn_minus
% 5.12/5.37 thf(fact_4513_Real__Vector__Spaces_Osgn__minus,axiom,
% 5.12/5.37 ! [X: complex] :
% 5.12/5.37 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.37 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ X ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % Real_Vector_Spaces.sgn_minus
% 5.12/5.37 thf(fact_4514_nat__mult__less__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_less_cancel1
% 5.12/5.37 thf(fact_4515_nat__mult__eq__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ( ( times_times_nat @ K @ M2 )
% 5.12/5.37 = ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( M2 = N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_eq_cancel1
% 5.12/5.37 thf(fact_4516_real__sgn__eq,axiom,
% 5.12/5.37 ( sgn_sgn_real
% 5.12/5.37 = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % real_sgn_eq
% 5.12/5.37 thf(fact_4517_nat__mult__le__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_le_cancel1
% 5.12/5.37 thf(fact_4518_nat__mult__div__cancel1,axiom,
% 5.12/5.37 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.37 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 5.12/5.37
% 5.12/5.37 % nat_mult_div_cancel1
% 5.12/5.37 thf(fact_4519_nat__eq__add__iff1,axiom,
% 5.12/5.37 ! [J2: nat,I: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.37 ( ( ord_less_eq_nat @ J2 @ I )
% 5.12/5.37 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 5.12/5.38 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.38 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J2 ) @ U ) @ M2 )
% 5.12/5.38 = N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_eq_add_iff1
% 5.12/5.38 thf(fact_4520_nat__eq__add__iff2,axiom,
% 5.12/5.38 ! [I: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.38 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 5.12/5.38 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.38 = ( M2
% 5.12/5.38 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I ) @ U ) @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_eq_add_iff2
% 5.12/5.38 thf(fact_4521_nat__le__add__iff1,axiom,
% 5.12/5.38 ! [J2: nat,I: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ J2 @ I )
% 5.12/5.38 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.38 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_le_add_iff1
% 5.12/5.38 thf(fact_4522_nat__le__add__iff2,axiom,
% 5.12/5.38 ! [I: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.38 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.38 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I ) @ U ) @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_le_add_iff2
% 5.12/5.38 thf(fact_4523_nat__diff__add__eq1,axiom,
% 5.12/5.38 ! [J2: nat,I: nat,U: nat,M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ J2 @ I )
% 5.12/5.38 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 5.12/5.38 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_diff_add_eq1
% 5.12/5.38 thf(fact_4524_Cauchy__iff2,axiom,
% 5.12/5.38 ( topolo4055970368930404560y_real
% 5.12/5.38 = ( ^ [X7: nat > real] :
% 5.12/5.38 ! [J3: nat] :
% 5.12/5.38 ? [M7: nat] :
% 5.12/5.38 ! [M5: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.12/5.38 => ! [N4: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.12/5.38 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M5 ) @ ( X7 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Cauchy_iff2
% 5.12/5.38 thf(fact_4525_floor__add,axiom,
% 5.12/5.38 ! [X: real,Y: real] :
% 5.12/5.38 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.12/5.38 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.12/5.38 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_add
% 5.12/5.38 thf(fact_4526_floor__add,axiom,
% 5.12/5.38 ! [X: rat,Y: rat] :
% 5.12/5.38 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.12/5.38 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.12/5.38 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_add
% 5.12/5.38 thf(fact_4527_pochhammer__minus_H,axiom,
% 5.12/5.38 ! [B: code_integer,K: nat] :
% 5.12/5.38 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus'
% 5.12/5.38 thf(fact_4528_pochhammer__minus_H,axiom,
% 5.12/5.38 ! [B: complex,K: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.12/5.38 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus'
% 5.12/5.38 thf(fact_4529_pochhammer__minus_H,axiom,
% 5.12/5.38 ! [B: real,K: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.12/5.38 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus'
% 5.12/5.38 thf(fact_4530_pochhammer__minus_H,axiom,
% 5.12/5.38 ! [B: rat,K: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.12/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus'
% 5.12/5.38 thf(fact_4531_pochhammer__minus_H,axiom,
% 5.12/5.38 ! [B: int,K: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.12/5.38 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus'
% 5.12/5.38 thf(fact_4532_pochhammer__minus,axiom,
% 5.12/5.38 ! [B: code_integer,K: nat] :
% 5.12/5.38 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus
% 5.12/5.38 thf(fact_4533_pochhammer__minus,axiom,
% 5.12/5.38 ! [B: complex,K: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus
% 5.12/5.38 thf(fact_4534_pochhammer__minus,axiom,
% 5.12/5.38 ! [B: real,K: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus
% 5.12/5.38 thf(fact_4535_pochhammer__minus,axiom,
% 5.12/5.38 ! [B: rat,K: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus
% 5.12/5.38 thf(fact_4536_pochhammer__minus,axiom,
% 5.12/5.38 ! [B: int,K: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_minus
% 5.12/5.38 thf(fact_4537_gbinomial__absorption_H,axiom,
% 5.12/5.38 ! [K: nat,A: complex] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_complex @ A @ K )
% 5.12/5.38 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption'
% 5.12/5.38 thf(fact_4538_gbinomial__absorption_H,axiom,
% 5.12/5.38 ! [K: nat,A: real] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_real @ A @ K )
% 5.12/5.38 = ( 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 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption'
% 5.12/5.38 thf(fact_4539_gbinomial__absorption_H,axiom,
% 5.12/5.38 ! [K: nat,A: rat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_rat @ A @ K )
% 5.12/5.38 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption'
% 5.12/5.38 thf(fact_4540_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4541_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4542_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4543_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4544_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4545_mult__ceiling__le__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_ceiling_le_Ints
% 5.12/5.38 thf(fact_4546_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4547_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4548_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4549_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4550_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4551_le__mult__floor__Ints,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_mult_floor_Ints
% 5.12/5.38 thf(fact_4552_frac__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( member_real @ ( archim2898591450579166408c_real @ X ) @ ring_1_Ints_real )
% 5.12/5.38 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_in_Ints_iff
% 5.12/5.38 thf(fact_4553_gbinomial__0_I2_J,axiom,
% 5.12/5.38 ! [K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.12/5.38 = zero_zero_real ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(2)
% 5.12/5.38 thf(fact_4554_gbinomial__0_I2_J,axiom,
% 5.12/5.38 ! [K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.12/5.38 = zero_zero_rat ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(2)
% 5.12/5.38 thf(fact_4555_gbinomial__0_I2_J,axiom,
% 5.12/5.38 ! [K: nat] :
% 5.12/5.38 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.12/5.38 = zero_zero_nat ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(2)
% 5.12/5.38 thf(fact_4556_gbinomial__0_I2_J,axiom,
% 5.12/5.38 ! [K: nat] :
% 5.12/5.38 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.12/5.38 = zero_zero_int ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(2)
% 5.12/5.38 thf(fact_4557_gbinomial__0_I1_J,axiom,
% 5.12/5.38 ! [A: complex] :
% 5.12/5.38 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_complex ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(1)
% 5.12/5.38 thf(fact_4558_gbinomial__0_I1_J,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(1)
% 5.12/5.38 thf(fact_4559_gbinomial__0_I1_J,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(1)
% 5.12/5.38 thf(fact_4560_gbinomial__0_I1_J,axiom,
% 5.12/5.38 ! [A: nat] :
% 5.12/5.38 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_nat ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(1)
% 5.12/5.38 thf(fact_4561_gbinomial__0_I1_J,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_int ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_0(1)
% 5.12/5.38 thf(fact_4562_pochhammer__0,axiom,
% 5.12/5.38 ! [A: complex] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_complex ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0
% 5.12/5.38 thf(fact_4563_pochhammer__0,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0
% 5.12/5.38 thf(fact_4564_pochhammer__0,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0
% 5.12/5.38 thf(fact_4565_pochhammer__0,axiom,
% 5.12/5.38 ! [A: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_nat ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0
% 5.12/5.38 thf(fact_4566_pochhammer__0,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.12/5.38 = one_one_int ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0
% 5.12/5.38 thf(fact_4567_frac__of__int,axiom,
% 5.12/5.38 ! [Z2: int] :
% 5.12/5.38 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.38 = zero_zero_real ) ).
% 5.12/5.38
% 5.12/5.38 % frac_of_int
% 5.12/5.38 thf(fact_4568_frac__of__int,axiom,
% 5.12/5.38 ! [Z2: int] :
% 5.12/5.38 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.38 = zero_zero_rat ) ).
% 5.12/5.38
% 5.12/5.38 % frac_of_int
% 5.12/5.38 thf(fact_4569_frac__eq__0__iff,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( ( archim2898591450579166408c_real @ X )
% 5.12/5.38 = zero_zero_real )
% 5.12/5.38 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_eq_0_iff
% 5.12/5.38 thf(fact_4570_frac__eq__0__iff,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( ( archimedean_frac_rat @ X )
% 5.12/5.38 = zero_zero_rat )
% 5.12/5.38 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_eq_0_iff
% 5.12/5.38 thf(fact_4571_floor__add2,axiom,
% 5.12/5.38 ! [X: real,Y: real] :
% 5.12/5.38 ( ( ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 | ( member_real @ Y @ ring_1_Ints_real ) )
% 5.12/5.38 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_add2
% 5.12/5.38 thf(fact_4572_floor__add2,axiom,
% 5.12/5.38 ! [X: rat,Y: rat] :
% 5.12/5.38 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 5.12/5.38 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_add2
% 5.12/5.38 thf(fact_4573_frac__gt__0__iff,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) )
% 5.12/5.38 = ( ~ ( member_real @ X @ ring_1_Ints_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_gt_0_iff
% 5.12/5.38 thf(fact_4574_frac__gt__0__iff,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 5.12/5.38 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_gt_0_iff
% 5.12/5.38 thf(fact_4575_of__nat__gbinomial,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( semiri8010041392384452111omplex @ ( gbinomial_nat @ N @ K ) )
% 5.12/5.38 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_gbinomial
% 5.12/5.38 thf(fact_4576_of__nat__gbinomial,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( semiri5074537144036343181t_real @ ( gbinomial_nat @ N @ K ) )
% 5.12/5.38 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_gbinomial
% 5.12/5.38 thf(fact_4577_of__nat__gbinomial,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 5.12/5.38 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_gbinomial
% 5.12/5.38 thf(fact_4578_pochhammer__of__nat,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ ( semiri8010041392384452111omplex @ X ) @ N )
% 5.12/5.38 = ( semiri8010041392384452111omplex @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat
% 5.12/5.38 thf(fact_4579_pochhammer__of__nat,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ ( semiri5074537144036343181t_real @ X ) @ N )
% 5.12/5.38 = ( semiri5074537144036343181t_real @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat
% 5.12/5.38 thf(fact_4580_pochhammer__of__nat,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X ) @ N )
% 5.12/5.38 = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat
% 5.12/5.38 thf(fact_4581_pochhammer__of__nat,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X ) @ N )
% 5.12/5.38 = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat
% 5.12/5.38 thf(fact_4582_pochhammer__of__nat,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X ) @ N )
% 5.12/5.38 = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat
% 5.12/5.38 thf(fact_4583_Ints__0,axiom,
% 5.12/5.38 member_complex @ zero_zero_complex @ ring_1_Ints_complex ).
% 5.12/5.38
% 5.12/5.38 % Ints_0
% 5.12/5.38 thf(fact_4584_Ints__0,axiom,
% 5.12/5.38 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 5.12/5.38
% 5.12/5.38 % Ints_0
% 5.12/5.38 thf(fact_4585_Ints__0,axiom,
% 5.12/5.38 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 5.12/5.38
% 5.12/5.38 % Ints_0
% 5.12/5.38 thf(fact_4586_Ints__0,axiom,
% 5.12/5.38 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 5.12/5.38
% 5.12/5.38 % Ints_0
% 5.12/5.38 thf(fact_4587_Ints__mult,axiom,
% 5.12/5.38 ! [A: complex,B: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.12/5.38 => ( member_complex @ ( times_times_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_mult
% 5.12/5.38 thf(fact_4588_Ints__mult,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( times_times_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_mult
% 5.12/5.38 thf(fact_4589_Ints__mult,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.12/5.38 => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_mult
% 5.12/5.38 thf(fact_4590_Ints__mult,axiom,
% 5.12/5.38 ! [A: int,B: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_mult
% 5.12/5.38 thf(fact_4591_Ints__1,axiom,
% 5.12/5.38 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 5.12/5.38
% 5.12/5.38 % Ints_1
% 5.12/5.38 thf(fact_4592_Ints__1,axiom,
% 5.12/5.38 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 5.12/5.38
% 5.12/5.38 % Ints_1
% 5.12/5.38 thf(fact_4593_Ints__1,axiom,
% 5.12/5.38 member_int @ one_one_int @ ring_1_Ints_int ).
% 5.12/5.38
% 5.12/5.38 % Ints_1
% 5.12/5.38 thf(fact_4594_Ints__1,axiom,
% 5.12/5.38 member_real @ one_one_real @ ring_1_Ints_real ).
% 5.12/5.38
% 5.12/5.38 % Ints_1
% 5.12/5.38 thf(fact_4595_Ints__add,axiom,
% 5.12/5.38 ! [A: complex,B: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.12/5.38 => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_add
% 5.12/5.38 thf(fact_4596_Ints__add,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_add
% 5.12/5.38 thf(fact_4597_Ints__add,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.12/5.38 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_add
% 5.12/5.38 thf(fact_4598_Ints__add,axiom,
% 5.12/5.38 ! [A: int,B: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_add
% 5.12/5.38 thf(fact_4599_Ints__diff,axiom,
% 5.12/5.38 ! [A: complex,B: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.12/5.38 => ( member_complex @ ( minus_minus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_diff
% 5.12/5.38 thf(fact_4600_Ints__diff,axiom,
% 5.12/5.38 ! [A: real,B: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( minus_minus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_diff
% 5.12/5.38 thf(fact_4601_Ints__diff,axiom,
% 5.12/5.38 ! [A: rat,B: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.12/5.38 => ( member_rat @ ( minus_minus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_diff
% 5.12/5.38 thf(fact_4602_Ints__diff,axiom,
% 5.12/5.38 ! [A: int,B: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_diff
% 5.12/5.38 thf(fact_4603_minus__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: int] :
% 5.12/5.38 ( ( member_int @ ( uminus_uminus_int @ X ) @ ring_1_Ints_int )
% 5.12/5.38 = ( member_int @ X @ ring_1_Ints_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % minus_in_Ints_iff
% 5.12/5.38 thf(fact_4604_minus__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( member_real @ ( uminus_uminus_real @ X ) @ ring_1_Ints_real )
% 5.12/5.38 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % minus_in_Ints_iff
% 5.12/5.38 thf(fact_4605_minus__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: complex] :
% 5.12/5.38 ( ( member_complex @ ( uminus1482373934393186551omplex @ X ) @ ring_1_Ints_complex )
% 5.12/5.38 = ( member_complex @ X @ ring_1_Ints_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % minus_in_Ints_iff
% 5.12/5.38 thf(fact_4606_minus__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ring_11222124179247155820nteger )
% 5.12/5.38 = ( member_Code_integer @ X @ ring_11222124179247155820nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % minus_in_Ints_iff
% 5.12/5.38 thf(fact_4607_minus__in__Ints__iff,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( member_rat @ ( uminus_uminus_rat @ X ) @ ring_1_Ints_rat )
% 5.12/5.38 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % minus_in_Ints_iff
% 5.12/5.38 thf(fact_4608_Ints__minus,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( uminus_uminus_int @ A ) @ ring_1_Ints_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_minus
% 5.12/5.38 thf(fact_4609_Ints__minus,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( uminus_uminus_real @ A ) @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_minus
% 5.12/5.38 thf(fact_4610_Ints__minus,axiom,
% 5.12/5.38 ! [A: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( member_complex @ ( uminus1482373934393186551omplex @ A ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_minus
% 5.12/5.38 thf(fact_4611_Ints__minus,axiom,
% 5.12/5.38 ! [A: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( member_Code_integer @ ( uminus1351360451143612070nteger @ A ) @ ring_11222124179247155820nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_minus
% 5.12/5.38 thf(fact_4612_Ints__minus,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( member_rat @ ( uminus_uminus_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_minus
% 5.12/5.38 thf(fact_4613_Ints__power,axiom,
% 5.12/5.38 ! [A: int,N: nat] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_power
% 5.12/5.38 thf(fact_4614_Ints__power,axiom,
% 5.12/5.38 ! [A: real,N: nat] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( power_power_real @ A @ N ) @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_power
% 5.12/5.38 thf(fact_4615_Ints__power,axiom,
% 5.12/5.38 ! [A: complex,N: nat] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( member_complex @ ( power_power_complex @ A @ N ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_power
% 5.12/5.38 thf(fact_4616_Ints__of__nat,axiom,
% 5.12/5.38 ! [N: nat] : ( member_complex @ ( semiri8010041392384452111omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_nat
% 5.12/5.38 thf(fact_4617_Ints__of__nat,axiom,
% 5.12/5.38 ! [N: nat] : ( member_real @ ( semiri5074537144036343181t_real @ N ) @ ring_1_Ints_real ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_nat
% 5.12/5.38 thf(fact_4618_Ints__of__nat,axiom,
% 5.12/5.38 ! [N: nat] : ( member_rat @ ( semiri681578069525770553at_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_nat
% 5.12/5.38 thf(fact_4619_Ints__of__nat,axiom,
% 5.12/5.38 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ring_1_Ints_int ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_nat
% 5.12/5.38 thf(fact_4620_Ints__abs,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_abs
% 5.12/5.38 thf(fact_4621_Ints__abs,axiom,
% 5.12/5.38 ! [A: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( member_Code_integer @ ( abs_abs_Code_integer @ A ) @ ring_11222124179247155820nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_abs
% 5.12/5.38 thf(fact_4622_Ints__abs,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( member_rat @ ( abs_abs_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_abs
% 5.12/5.38 thf(fact_4623_Ints__abs,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_abs
% 5.12/5.38 thf(fact_4624_Ints__of__int,axiom,
% 5.12/5.38 ! [Z2: int] : ( member_complex @ ( ring_17405671764205052669omplex @ Z2 ) @ ring_1_Ints_complex ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_int
% 5.12/5.38 thf(fact_4625_Ints__of__int,axiom,
% 5.12/5.38 ! [Z2: int] : ( member_int @ ( ring_1_of_int_int @ Z2 ) @ ring_1_Ints_int ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_int
% 5.12/5.38 thf(fact_4626_Ints__of__int,axiom,
% 5.12/5.38 ! [Z2: int] : ( member_real @ ( ring_1_of_int_real @ Z2 ) @ ring_1_Ints_real ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_int
% 5.12/5.38 thf(fact_4627_Ints__of__int,axiom,
% 5.12/5.38 ! [Z2: int] : ( member_rat @ ( ring_1_of_int_rat @ Z2 ) @ ring_1_Ints_rat ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_of_int
% 5.12/5.38 thf(fact_4628_Ints__induct,axiom,
% 5.12/5.38 ! [Q5: complex,P: complex > $o] :
% 5.12/5.38 ( ( member_complex @ Q5 @ ring_1_Ints_complex )
% 5.12/5.38 => ( ! [Z4: int] : ( P @ ( ring_17405671764205052669omplex @ Z4 ) )
% 5.12/5.38 => ( P @ Q5 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_induct
% 5.12/5.38 thf(fact_4629_Ints__induct,axiom,
% 5.12/5.38 ! [Q5: int,P: int > $o] :
% 5.12/5.38 ( ( member_int @ Q5 @ ring_1_Ints_int )
% 5.12/5.38 => ( ! [Z4: int] : ( P @ ( ring_1_of_int_int @ Z4 ) )
% 5.12/5.38 => ( P @ Q5 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_induct
% 5.12/5.38 thf(fact_4630_Ints__induct,axiom,
% 5.12/5.38 ! [Q5: real,P: real > $o] :
% 5.12/5.38 ( ( member_real @ Q5 @ ring_1_Ints_real )
% 5.12/5.38 => ( ! [Z4: int] : ( P @ ( ring_1_of_int_real @ Z4 ) )
% 5.12/5.38 => ( P @ Q5 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_induct
% 5.12/5.38 thf(fact_4631_Ints__induct,axiom,
% 5.12/5.38 ! [Q5: rat,P: rat > $o] :
% 5.12/5.38 ( ( member_rat @ Q5 @ ring_1_Ints_rat )
% 5.12/5.38 => ( ! [Z4: int] : ( P @ ( ring_1_of_int_rat @ Z4 ) )
% 5.12/5.38 => ( P @ Q5 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_induct
% 5.12/5.38 thf(fact_4632_Ints__cases,axiom,
% 5.12/5.38 ! [Q5: complex] :
% 5.12/5.38 ( ( member_complex @ Q5 @ ring_1_Ints_complex )
% 5.12/5.38 => ~ ! [Z4: int] :
% 5.12/5.38 ( Q5
% 5.12/5.38 != ( ring_17405671764205052669omplex @ Z4 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_cases
% 5.12/5.38 thf(fact_4633_Ints__cases,axiom,
% 5.12/5.38 ! [Q5: int] :
% 5.12/5.38 ( ( member_int @ Q5 @ ring_1_Ints_int )
% 5.12/5.38 => ~ ! [Z4: int] :
% 5.12/5.38 ( Q5
% 5.12/5.38 != ( ring_1_of_int_int @ Z4 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_cases
% 5.12/5.38 thf(fact_4634_Ints__cases,axiom,
% 5.12/5.38 ! [Q5: real] :
% 5.12/5.38 ( ( member_real @ Q5 @ ring_1_Ints_real )
% 5.12/5.38 => ~ ! [Z4: int] :
% 5.12/5.38 ( Q5
% 5.12/5.38 != ( ring_1_of_int_real @ Z4 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_cases
% 5.12/5.38 thf(fact_4635_Ints__cases,axiom,
% 5.12/5.38 ! [Q5: rat] :
% 5.12/5.38 ( ( member_rat @ Q5 @ ring_1_Ints_rat )
% 5.12/5.38 => ~ ! [Z4: int] :
% 5.12/5.38 ( Q5
% 5.12/5.38 != ( ring_1_of_int_rat @ Z4 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_cases
% 5.12/5.38 thf(fact_4636_gbinomial__Suc__Suc,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_Suc_Suc
% 5.12/5.38 thf(fact_4637_gbinomial__Suc__Suc,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_Suc_Suc
% 5.12/5.38 thf(fact_4638_gbinomial__Suc__Suc,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_Suc_Suc
% 5.12/5.38 thf(fact_4639_gbinomial__of__nat__symmetric,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.12/5.38 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_of_nat_symmetric
% 5.12/5.38 thf(fact_4640_gbinomial__of__nat__symmetric,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.12/5.38 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_of_nat_symmetric
% 5.12/5.38 thf(fact_4641_gbinomial__of__nat__symmetric,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.12/5.38 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_of_nat_symmetric
% 5.12/5.38 thf(fact_4642_pochhammer__pos,axiom,
% 5.12/5.38 ! [X: real,N: nat] :
% 5.12/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.38 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_pos
% 5.12/5.38 thf(fact_4643_pochhammer__pos,axiom,
% 5.12/5.38 ! [X: rat,N: nat] :
% 5.12/5.38 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.38 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_pos
% 5.12/5.38 thf(fact_4644_pochhammer__pos,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.38 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_pos
% 5.12/5.38 thf(fact_4645_pochhammer__pos,axiom,
% 5.12/5.38 ! [X: int,N: nat] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ X )
% 5.12/5.38 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_pos
% 5.12/5.38 thf(fact_4646_Ints__double__eq__0__iff,axiom,
% 5.12/5.38 ! [A: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( ( ( plus_plus_complex @ A @ A )
% 5.12/5.38 = zero_zero_complex )
% 5.12/5.38 = ( A = zero_zero_complex ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_double_eq_0_iff
% 5.12/5.38 thf(fact_4647_Ints__double__eq__0__iff,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( ( plus_plus_real @ A @ A )
% 5.12/5.38 = zero_zero_real )
% 5.12/5.38 = ( A = zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_double_eq_0_iff
% 5.12/5.38 thf(fact_4648_Ints__double__eq__0__iff,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( ( plus_plus_rat @ A @ A )
% 5.12/5.38 = zero_zero_rat )
% 5.12/5.38 = ( A = zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_double_eq_0_iff
% 5.12/5.38 thf(fact_4649_Ints__double__eq__0__iff,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( ( plus_plus_int @ A @ A )
% 5.12/5.38 = zero_zero_int )
% 5.12/5.38 = ( A = zero_zero_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_double_eq_0_iff
% 5.12/5.38 thf(fact_4650_pochhammer__neq__0__mono,axiom,
% 5.12/5.38 ! [A: real,M2: nat,N: nat] :
% 5.12/5.38 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 5.12/5.38 != zero_zero_real )
% 5.12/5.38 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.12/5.38 != zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_neq_0_mono
% 5.12/5.38 thf(fact_4651_pochhammer__neq__0__mono,axiom,
% 5.12/5.38 ! [A: rat,M2: nat,N: nat] :
% 5.12/5.38 ( ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 5.12/5.38 != zero_zero_rat )
% 5.12/5.38 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.12/5.38 != zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_neq_0_mono
% 5.12/5.38 thf(fact_4652_pochhammer__eq__0__mono,axiom,
% 5.12/5.38 ! [A: real,N: nat,M2: nat] :
% 5.12/5.38 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.12/5.38 = zero_zero_real )
% 5.12/5.38 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 5.12/5.38 = zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_eq_0_mono
% 5.12/5.38 thf(fact_4653_pochhammer__eq__0__mono,axiom,
% 5.12/5.38 ! [A: rat,N: nat,M2: nat] :
% 5.12/5.38 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.12/5.38 = zero_zero_rat )
% 5.12/5.38 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 5.12/5.38 = zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_eq_0_mono
% 5.12/5.38 thf(fact_4654_frac__neg,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.38 = zero_zero_real ) )
% 5.12/5.38 & ( ~ ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.38 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_neg
% 5.12/5.38 thf(fact_4655_frac__neg,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 5.12/5.38 = zero_zero_rat ) )
% 5.12/5.38 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 5.12/5.38 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_neg
% 5.12/5.38 thf(fact_4656_frac__ge__0,axiom,
% 5.12/5.38 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_ge_0
% 5.12/5.38 thf(fact_4657_frac__ge__0,axiom,
% 5.12/5.38 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_ge_0
% 5.12/5.38 thf(fact_4658_frac__lt__1,axiom,
% 5.12/5.38 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % frac_lt_1
% 5.12/5.38 thf(fact_4659_frac__lt__1,axiom,
% 5.12/5.38 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % frac_lt_1
% 5.12/5.38 thf(fact_4660_frac__1__eq,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 5.12/5.38 = ( archim2898591450579166408c_real @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_1_eq
% 5.12/5.38 thf(fact_4661_frac__1__eq,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 5.12/5.38 = ( archimedean_frac_rat @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_1_eq
% 5.12/5.38 thf(fact_4662_frac__unique__iff,axiom,
% 5.12/5.38 ! [X: real,A: real] :
% 5.12/5.38 ( ( ( archim2898591450579166408c_real @ X )
% 5.12/5.38 = A )
% 5.12/5.38 = ( ( member_real @ ( minus_minus_real @ X @ A ) @ ring_1_Ints_real )
% 5.12/5.38 & ( ord_less_eq_real @ zero_zero_real @ A )
% 5.12/5.38 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_unique_iff
% 5.12/5.38 thf(fact_4663_frac__unique__iff,axiom,
% 5.12/5.38 ! [X: rat,A: rat] :
% 5.12/5.38 ( ( ( archimedean_frac_rat @ X )
% 5.12/5.38 = A )
% 5.12/5.38 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 5.12/5.38 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.12/5.38 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_unique_iff
% 5.12/5.38 thf(fact_4664_gbinomial__addition__formula,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_addition_formula
% 5.12/5.38 thf(fact_4665_gbinomial__addition__formula,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_addition_formula
% 5.12/5.38 thf(fact_4666_gbinomial__addition__formula,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.12/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_addition_formula
% 5.12/5.38 thf(fact_4667_gbinomial__absorb__comp,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.12/5.38 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorb_comp
% 5.12/5.38 thf(fact_4668_gbinomial__absorb__comp,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.12/5.38 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorb_comp
% 5.12/5.38 thf(fact_4669_gbinomial__absorb__comp,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.12/5.38 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorb_comp
% 5.12/5.38 thf(fact_4670_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.12/5.38 ! [K: nat,A: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.12/5.38 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_ge_n_over_k_pow_k
% 5.12/5.38 thf(fact_4671_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.12/5.38 ! [K: nat,A: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.12/5.38 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_ge_n_over_k_pow_k
% 5.12/5.38 thf(fact_4672_gbinomial__mult__1,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.12/5.38 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1
% 5.12/5.38 thf(fact_4673_gbinomial__mult__1,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.12/5.38 = ( 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 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1
% 5.12/5.38 thf(fact_4674_gbinomial__mult__1,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.12/5.38 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1
% 5.12/5.38 thf(fact_4675_gbinomial__mult__1_H,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.12/5.38 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1'
% 5.12/5.38 thf(fact_4676_gbinomial__mult__1_H,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.12/5.38 = ( 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 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1'
% 5.12/5.38 thf(fact_4677_gbinomial__mult__1_H,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.12/5.38 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_mult_1'
% 5.12/5.38 thf(fact_4678_pochhammer__nonneg,axiom,
% 5.12/5.38 ! [X: real,N: nat] :
% 5.12/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_nonneg
% 5.12/5.38 thf(fact_4679_pochhammer__nonneg,axiom,
% 5.12/5.38 ! [X: rat,N: nat] :
% 5.12/5.38 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.12/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_nonneg
% 5.12/5.38 thf(fact_4680_pochhammer__nonneg,axiom,
% 5.12/5.38 ! [X: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.12/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_nonneg
% 5.12/5.38 thf(fact_4681_pochhammer__nonneg,axiom,
% 5.12/5.38 ! [X: int,N: nat] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ X )
% 5.12/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_nonneg
% 5.12/5.38 thf(fact_4682_pochhammer__0__left,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ( N = zero_zero_nat )
% 5.12/5.38 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.12/5.38 = one_one_complex ) )
% 5.12/5.38 & ( ( N != zero_zero_nat )
% 5.12/5.38 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.12/5.38 = zero_zero_complex ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0_left
% 5.12/5.38 thf(fact_4683_pochhammer__0__left,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ( N = zero_zero_nat )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.12/5.38 = one_one_real ) )
% 5.12/5.38 & ( ( N != zero_zero_nat )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.12/5.38 = zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0_left
% 5.12/5.38 thf(fact_4684_pochhammer__0__left,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ( N = zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.12/5.38 = one_one_rat ) )
% 5.12/5.38 & ( ( N != zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.12/5.38 = zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0_left
% 5.12/5.38 thf(fact_4685_pochhammer__0__left,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ( N = zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.12/5.38 = one_one_nat ) )
% 5.12/5.38 & ( ( N != zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.12/5.38 = zero_zero_nat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0_left
% 5.12/5.38 thf(fact_4686_pochhammer__0__left,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ( N = zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.12/5.38 = one_one_int ) )
% 5.12/5.38 & ( ( N != zero_zero_nat )
% 5.12/5.38 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.12/5.38 = zero_zero_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_0_left
% 5.12/5.38 thf(fact_4687_Ints__odd__nonzero,axiom,
% 5.12/5.38 ! [A: complex] :
% 5.12/5.38 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.12/5.38 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 5.12/5.38 != zero_zero_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_nonzero
% 5.12/5.38 thf(fact_4688_Ints__odd__nonzero,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 5.12/5.38 != zero_zero_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_nonzero
% 5.12/5.38 thf(fact_4689_Ints__odd__nonzero,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 5.12/5.38 != zero_zero_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_nonzero
% 5.12/5.38 thf(fact_4690_Ints__odd__nonzero,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 5.12/5.38 != zero_zero_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_nonzero
% 5.12/5.38 thf(fact_4691_Suc__times__gbinomial,axiom,
% 5.12/5.38 ! [K: nat,A: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Suc_times_gbinomial
% 5.12/5.38 thf(fact_4692_Suc__times__gbinomial,axiom,
% 5.12/5.38 ! [K: nat,A: real] :
% 5.12/5.38 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Suc_times_gbinomial
% 5.12/5.38 thf(fact_4693_Suc__times__gbinomial,axiom,
% 5.12/5.38 ! [K: nat,A: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Suc_times_gbinomial
% 5.12/5.38 thf(fact_4694_gbinomial__absorption,axiom,
% 5.12/5.38 ! [K: nat,A: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption
% 5.12/5.38 thf(fact_4695_gbinomial__absorption,axiom,
% 5.12/5.38 ! [K: nat,A: real] :
% 5.12/5.38 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption
% 5.12/5.38 thf(fact_4696_gbinomial__absorption,axiom,
% 5.12/5.38 ! [K: nat,A: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.12/5.38 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_absorption
% 5.12/5.38 thf(fact_4697_gbinomial__trinomial__revision,axiom,
% 5.12/5.38 ! [K: nat,M2: nat,A: complex] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ M2 )
% 5.12/5.38 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M2 ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M2 ) @ K ) )
% 5.12/5.38 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_trinomial_revision
% 5.12/5.38 thf(fact_4698_gbinomial__trinomial__revision,axiom,
% 5.12/5.38 ! [K: nat,M2: nat,A: real] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ M2 )
% 5.12/5.38 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K ) )
% 5.12/5.38 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_trinomial_revision
% 5.12/5.38 thf(fact_4699_gbinomial__trinomial__revision,axiom,
% 5.12/5.38 ! [K: nat,M2: nat,A: rat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ M2 )
% 5.12/5.38 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M2 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M2 ) @ K ) )
% 5.12/5.38 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_trinomial_revision
% 5.12/5.38 thf(fact_4700_Ints__odd__less__0,axiom,
% 5.12/5.38 ! [A: real] :
% 5.12/5.38 ( ( member_real @ A @ ring_1_Ints_real )
% 5.12/5.38 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 5.12/5.38 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_less_0
% 5.12/5.38 thf(fact_4701_Ints__odd__less__0,axiom,
% 5.12/5.38 ! [A: rat] :
% 5.12/5.38 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.12/5.38 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_less_0
% 5.12/5.38 thf(fact_4702_Ints__odd__less__0,axiom,
% 5.12/5.38 ! [A: int] :
% 5.12/5.38 ( ( member_int @ A @ ring_1_Ints_int )
% 5.12/5.38 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.12/5.38 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_odd_less_0
% 5.12/5.38 thf(fact_4703_frac__def,axiom,
% 5.12/5.38 ( archim2898591450579166408c_real
% 5.12/5.38 = ( ^ [X2: real] : ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_def
% 5.12/5.38 thf(fact_4704_frac__def,axiom,
% 5.12/5.38 ( archimedean_frac_rat
% 5.12/5.38 = ( ^ [X2: rat] : ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_def
% 5.12/5.38 thf(fact_4705_pochhammer__rec,axiom,
% 5.12/5.38 ! [A: complex,N: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec
% 5.12/5.38 thf(fact_4706_pochhammer__rec,axiom,
% 5.12/5.38 ! [A: real,N: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec
% 5.12/5.38 thf(fact_4707_pochhammer__rec,axiom,
% 5.12/5.38 ! [A: rat,N: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec
% 5.12/5.38 thf(fact_4708_pochhammer__rec,axiom,
% 5.12/5.38 ! [A: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec
% 5.12/5.38 thf(fact_4709_pochhammer__rec,axiom,
% 5.12/5.38 ! [A: int,N: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec
% 5.12/5.38 thf(fact_4710_pochhammer__Suc,axiom,
% 5.12/5.38 ! [A: complex,N: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_Suc
% 5.12/5.38 thf(fact_4711_pochhammer__Suc,axiom,
% 5.12/5.38 ! [A: real,N: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_Suc
% 5.12/5.38 thf(fact_4712_pochhammer__Suc,axiom,
% 5.12/5.38 ! [A: rat,N: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_Suc
% 5.12/5.38 thf(fact_4713_pochhammer__Suc,axiom,
% 5.12/5.38 ! [A: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_Suc
% 5.12/5.38 thf(fact_4714_pochhammer__Suc,axiom,
% 5.12/5.38 ! [A: int,N: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_Suc
% 5.12/5.38 thf(fact_4715_pochhammer__rec_H,axiom,
% 5.12/5.38 ! [Z2: complex,N: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ Z2 @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_complex @ ( plus_plus_complex @ Z2 @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec'
% 5.12/5.38 thf(fact_4716_pochhammer__rec_H,axiom,
% 5.12/5.38 ! [Z2: real,N: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec'
% 5.12/5.38 thf(fact_4717_pochhammer__rec_H,axiom,
% 5.12/5.38 ! [Z2: rat,N: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec'
% 5.12/5.38 thf(fact_4718_pochhammer__rec_H,axiom,
% 5.12/5.38 ! [Z2: nat,N: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ Z2 @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec'
% 5.12/5.38 thf(fact_4719_pochhammer__rec_H,axiom,
% 5.12/5.38 ! [Z2: int,N: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ Z2 @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_rec'
% 5.12/5.38 thf(fact_4720_pochhammer__eq__0__iff,axiom,
% 5.12/5.38 ! [A: complex,N: nat] :
% 5.12/5.38 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.12/5.38 = zero_zero_complex )
% 5.12/5.38 = ( ? [K3: nat] :
% 5.12/5.38 ( ( ord_less_nat @ K3 @ N )
% 5.12/5.38 & ( A
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_eq_0_iff
% 5.12/5.38 thf(fact_4721_pochhammer__eq__0__iff,axiom,
% 5.12/5.38 ! [A: real,N: nat] :
% 5.12/5.38 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.12/5.38 = zero_zero_real )
% 5.12/5.38 = ( ? [K3: nat] :
% 5.12/5.38 ( ( ord_less_nat @ K3 @ N )
% 5.12/5.38 & ( A
% 5.12/5.38 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_eq_0_iff
% 5.12/5.38 thf(fact_4722_pochhammer__eq__0__iff,axiom,
% 5.12/5.38 ! [A: rat,N: nat] :
% 5.12/5.38 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.12/5.38 = zero_zero_rat )
% 5.12/5.38 = ( ? [K3: nat] :
% 5.12/5.38 ( ( ord_less_nat @ K3 @ N )
% 5.12/5.38 & ( A
% 5.12/5.38 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_eq_0_iff
% 5.12/5.38 thf(fact_4723_pochhammer__of__nat__eq__0__iff,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.12/5.38 = zero_z3403309356797280102nteger )
% 5.12/5.38 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_iff
% 5.12/5.38 thf(fact_4724_pochhammer__of__nat__eq__0__iff,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.12/5.38 = zero_zero_complex )
% 5.12/5.38 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_iff
% 5.12/5.38 thf(fact_4725_pochhammer__of__nat__eq__0__iff,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.12/5.38 = zero_zero_real )
% 5.12/5.38 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_iff
% 5.12/5.38 thf(fact_4726_pochhammer__of__nat__eq__0__iff,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.12/5.38 = zero_zero_rat )
% 5.12/5.38 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_iff
% 5.12/5.38 thf(fact_4727_pochhammer__of__nat__eq__0__iff,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.12/5.38 = zero_zero_int )
% 5.12/5.38 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_iff
% 5.12/5.38 thf(fact_4728_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ K )
% 5.12/5.38 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.12/5.38 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma
% 5.12/5.38 thf(fact_4729_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ K )
% 5.12/5.38 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.12/5.38 = zero_zero_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma
% 5.12/5.38 thf(fact_4730_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ K )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.12/5.38 = zero_zero_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma
% 5.12/5.38 thf(fact_4731_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ K )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.12/5.38 = zero_zero_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma
% 5.12/5.38 thf(fact_4732_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.12/5.38 ! [N: nat,K: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ K )
% 5.12/5.38 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.12/5.38 = zero_zero_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma
% 5.12/5.38 thf(fact_4733_Ints__nonzero__abs__ge1,axiom,
% 5.12/5.38 ! [X: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( ( X != zero_z3403309356797280102nteger )
% 5.12/5.38 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_ge1
% 5.12/5.38 thf(fact_4734_Ints__nonzero__abs__ge1,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 => ( ( X != zero_zero_real )
% 5.12/5.38 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_ge1
% 5.12/5.38 thf(fact_4735_Ints__nonzero__abs__ge1,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( X != zero_zero_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_ge1
% 5.12/5.38 thf(fact_4736_Ints__nonzero__abs__ge1,axiom,
% 5.12/5.38 ! [X: int] :
% 5.12/5.38 ( ( member_int @ X @ ring_1_Ints_int )
% 5.12/5.38 => ( ( X != zero_zero_int )
% 5.12/5.38 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_ge1
% 5.12/5.38 thf(fact_4737_Ints__nonzero__abs__less1,axiom,
% 5.12/5.38 ! [X: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 5.12/5.38 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_less1
% 5.12/5.38 thf(fact_4738_Ints__nonzero__abs__less1,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 => ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.38 => ( X = zero_zero_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_less1
% 5.12/5.38 thf(fact_4739_Ints__nonzero__abs__less1,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 5.12/5.38 => ( X = zero_zero_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_less1
% 5.12/5.38 thf(fact_4740_Ints__nonzero__abs__less1,axiom,
% 5.12/5.38 ! [X: int] :
% 5.12/5.38 ( ( member_int @ X @ ring_1_Ints_int )
% 5.12/5.38 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 5.12/5.38 => ( X = zero_zero_int ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_nonzero_abs_less1
% 5.12/5.38 thf(fact_4741_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.12/5.38 != zero_z3403309356797280102nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma'
% 5.12/5.38 thf(fact_4742_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.12/5.38 != zero_zero_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma'
% 5.12/5.38 thf(fact_4743_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.12/5.38 != zero_zero_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma'
% 5.12/5.38 thf(fact_4744_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.12/5.38 != zero_zero_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma'
% 5.12/5.38 thf(fact_4745_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.38 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.12/5.38 != zero_zero_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_of_nat_eq_0_lemma'
% 5.12/5.38 thf(fact_4746_pochhammer__product_H,axiom,
% 5.12/5.38 ! [Z2: complex,N: nat,M2: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ Z2 @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.38 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( semiri8010041392384452111omplex @ N ) ) @ M2 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product'
% 5.12/5.38 thf(fact_4747_pochhammer__product_H,axiom,
% 5.12/5.38 ! [Z2: real,N: nat,M2: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ Z2 @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.38 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ N ) ) @ M2 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product'
% 5.12/5.38 thf(fact_4748_pochhammer__product_H,axiom,
% 5.12/5.38 ! [Z2: rat,N: nat,M2: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ Z2 @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.38 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ N ) ) @ M2 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product'
% 5.12/5.38 thf(fact_4749_pochhammer__product_H,axiom,
% 5.12/5.38 ! [Z2: nat,N: nat,M2: nat] :
% 5.12/5.38 ( ( comm_s4663373288045622133er_nat @ Z2 @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.38 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ N ) ) @ M2 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product'
% 5.12/5.38 thf(fact_4750_pochhammer__product_H,axiom,
% 5.12/5.38 ! [Z2: int,N: nat,M2: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ Z2 @ ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.38 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ N ) ) @ M2 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product'
% 5.12/5.38 thf(fact_4751_Ints__eq__abs__less1,axiom,
% 5.12/5.38 ! [X: code_integer,Y: code_integer] :
% 5.12/5.38 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 5.12/5.38 => ( ( X = Y )
% 5.12/5.38 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_eq_abs_less1
% 5.12/5.38 thf(fact_4752_Ints__eq__abs__less1,axiom,
% 5.12/5.38 ! [X: real,Y: real] :
% 5.12/5.38 ( ( member_real @ X @ ring_1_Ints_real )
% 5.12/5.38 => ( ( member_real @ Y @ ring_1_Ints_real )
% 5.12/5.38 => ( ( X = Y )
% 5.12/5.38 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_eq_abs_less1
% 5.12/5.38 thf(fact_4753_Ints__eq__abs__less1,axiom,
% 5.12/5.38 ! [X: rat,Y: rat] :
% 5.12/5.38 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 5.12/5.38 => ( ( X = Y )
% 5.12/5.38 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_eq_abs_less1
% 5.12/5.38 thf(fact_4754_Ints__eq__abs__less1,axiom,
% 5.12/5.38 ! [X: int,Y: int] :
% 5.12/5.38 ( ( member_int @ X @ ring_1_Ints_int )
% 5.12/5.38 => ( ( member_int @ Y @ ring_1_Ints_int )
% 5.12/5.38 => ( ( X = Y )
% 5.12/5.38 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % Ints_eq_abs_less1
% 5.12/5.38 thf(fact_4755_gbinomial__rec,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_rec
% 5.12/5.38 thf(fact_4756_gbinomial__rec,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_rec
% 5.12/5.38 thf(fact_4757_gbinomial__rec,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_rec
% 5.12/5.38 thf(fact_4758_gbinomial__factors,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_factors
% 5.12/5.38 thf(fact_4759_gbinomial__factors,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_factors
% 5.12/5.38 thf(fact_4760_gbinomial__factors,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.12/5.38 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_factors
% 5.12/5.38 thf(fact_4761_gbinomial__negated__upper,axiom,
% 5.12/5.38 ( gbinomial_complex
% 5.12/5.38 = ( ^ [A3: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A3 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_negated_upper
% 5.12/5.38 thf(fact_4762_gbinomial__negated__upper,axiom,
% 5.12/5.38 ( gbinomial_real
% 5.12/5.38 = ( ^ [A3: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A3 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_negated_upper
% 5.12/5.38 thf(fact_4763_gbinomial__negated__upper,axiom,
% 5.12/5.38 ( gbinomial_rat
% 5.12/5.38 = ( ^ [A3: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A3 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_negated_upper
% 5.12/5.38 thf(fact_4764_gbinomial__index__swap,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.12/5.38 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_index_swap
% 5.12/5.38 thf(fact_4765_gbinomial__index__swap,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( 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 ) )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_index_swap
% 5.12/5.38 thf(fact_4766_gbinomial__index__swap,axiom,
% 5.12/5.38 ! [K: nat,N: nat] :
% 5.12/5.38 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_index_swap
% 5.12/5.38 thf(fact_4767_gbinomial__minus,axiom,
% 5.12/5.38 ! [A: complex,K: nat] :
% 5.12/5.38 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_minus
% 5.12/5.38 thf(fact_4768_gbinomial__minus,axiom,
% 5.12/5.38 ! [A: real,K: nat] :
% 5.12/5.38 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.12/5.38 = ( 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 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_minus
% 5.12/5.38 thf(fact_4769_gbinomial__minus,axiom,
% 5.12/5.38 ! [A: rat,K: nat] :
% 5.12/5.38 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.12/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_minus
% 5.12/5.38 thf(fact_4770_frac__eq,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( ( archim2898591450579166408c_real @ X )
% 5.12/5.38 = X )
% 5.12/5.38 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.38 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_eq
% 5.12/5.38 thf(fact_4771_frac__eq,axiom,
% 5.12/5.38 ! [X: rat] :
% 5.12/5.38 ( ( ( archimedean_frac_rat @ X )
% 5.12/5.38 = X )
% 5.12/5.38 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.38 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_eq
% 5.12/5.38 thf(fact_4772_gbinomial__reduce__nat,axiom,
% 5.12/5.38 ! [K: nat,A: complex] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_complex @ A @ K )
% 5.12/5.38 = ( 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 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_reduce_nat
% 5.12/5.38 thf(fact_4773_gbinomial__reduce__nat,axiom,
% 5.12/5.38 ! [K: nat,A: real] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_real @ A @ K )
% 5.12/5.38 = ( 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 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_reduce_nat
% 5.12/5.38 thf(fact_4774_gbinomial__reduce__nat,axiom,
% 5.12/5.38 ! [K: nat,A: rat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.38 => ( ( gbinomial_rat @ A @ K )
% 5.12/5.38 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_reduce_nat
% 5.12/5.38 thf(fact_4775_frac__add,axiom,
% 5.12/5.38 ! [X: real,Y: real] :
% 5.12/5.38 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.12/5.38 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.12/5.38 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.38 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_add
% 5.12/5.38 thf(fact_4776_frac__add,axiom,
% 5.12/5.38 ! [X: rat,Y: rat] :
% 5.12/5.38 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.12/5.38 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.12/5.38 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.12/5.38 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.12/5.38 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % frac_add
% 5.12/5.38 thf(fact_4777_pochhammer__product,axiom,
% 5.12/5.38 ! [M2: nat,N: nat,Z2: complex] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( comm_s2602460028002588243omplex @ Z2 @ N )
% 5.12/5.38 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ M2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( semiri8010041392384452111omplex @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product
% 5.12/5.38 thf(fact_4778_pochhammer__product,axiom,
% 5.12/5.38 ! [M2: nat,N: nat,Z2: real] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( comm_s7457072308508201937r_real @ Z2 @ N )
% 5.12/5.38 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product
% 5.12/5.38 thf(fact_4779_pochhammer__product,axiom,
% 5.12/5.38 ! [M2: nat,N: nat,Z2: rat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( comm_s4028243227959126397er_rat @ Z2 @ N )
% 5.12/5.38 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product
% 5.12/5.38 thf(fact_4780_pochhammer__product,axiom,
% 5.12/5.38 ! [M2: nat,N: nat,Z2: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( comm_s4663373288045622133er_nat @ Z2 @ N )
% 5.12/5.38 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z2 @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z2 @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product
% 5.12/5.38 thf(fact_4781_pochhammer__product,axiom,
% 5.12/5.38 ! [M2: nat,N: nat,Z2: int] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( comm_s4660882817536571857er_int @ Z2 @ N )
% 5.12/5.38 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z2 @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z2 @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_product
% 5.12/5.38 thf(fact_4782_pochhammer__absorb__comp,axiom,
% 5.12/5.38 ! [R4: code_integer,K: nat] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R4 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R4 ) @ K ) )
% 5.12/5.38 = ( times_3573771949741848930nteger @ R4 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_absorb_comp
% 5.12/5.38 thf(fact_4783_pochhammer__absorb__comp,axiom,
% 5.12/5.38 ! [R4: complex,K: nat] :
% 5.12/5.38 ( ( times_times_complex @ ( minus_minus_complex @ R4 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R4 ) @ K ) )
% 5.12/5.38 = ( times_times_complex @ R4 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R4 ) @ one_one_complex ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_absorb_comp
% 5.12/5.38 thf(fact_4784_pochhammer__absorb__comp,axiom,
% 5.12/5.38 ! [R4: real,K: nat] :
% 5.12/5.38 ( ( times_times_real @ ( minus_minus_real @ R4 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R4 ) @ K ) )
% 5.12/5.38 = ( times_times_real @ R4 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R4 ) @ one_one_real ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_absorb_comp
% 5.12/5.38 thf(fact_4785_pochhammer__absorb__comp,axiom,
% 5.12/5.38 ! [R4: rat,K: nat] :
% 5.12/5.38 ( ( times_times_rat @ ( minus_minus_rat @ R4 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R4 ) @ K ) )
% 5.12/5.38 = ( times_times_rat @ R4 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R4 ) @ one_one_rat ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_absorb_comp
% 5.12/5.38 thf(fact_4786_pochhammer__absorb__comp,axiom,
% 5.12/5.38 ! [R4: int,K: nat] :
% 5.12/5.38 ( ( times_times_int @ ( minus_minus_int @ R4 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R4 ) @ K ) )
% 5.12/5.38 = ( times_times_int @ R4 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R4 ) @ one_one_int ) @ K ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_absorb_comp
% 5.12/5.38 thf(fact_4787_gbinomial__pochhammer_H,axiom,
% 5.12/5.38 ( gbinomial_complex
% 5.12/5.38 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer'
% 5.12/5.38 thf(fact_4788_gbinomial__pochhammer_H,axiom,
% 5.12/5.38 ( gbinomial_rat
% 5.12/5.38 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer'
% 5.12/5.38 thf(fact_4789_gbinomial__pochhammer_H,axiom,
% 5.12/5.38 ( gbinomial_real
% 5.12/5.38 = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer'
% 5.12/5.38 thf(fact_4790_gbinomial__pochhammer,axiom,
% 5.12/5.38 ( gbinomial_complex
% 5.12/5.38 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer
% 5.12/5.38 thf(fact_4791_gbinomial__pochhammer,axiom,
% 5.12/5.38 ( gbinomial_rat
% 5.12/5.38 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer
% 5.12/5.38 thf(fact_4792_gbinomial__pochhammer,axiom,
% 5.12/5.38 ( gbinomial_real
% 5.12/5.38 = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % gbinomial_pochhammer
% 5.12/5.38 thf(fact_4793_rotate1__length01,axiom,
% 5.12/5.38 ! [Xs: list_VEBT_VEBT] :
% 5.12/5.38 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 5.12/5.38 => ( ( rotate1_VEBT_VEBT @ Xs )
% 5.12/5.38 = Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % rotate1_length01
% 5.12/5.38 thf(fact_4794_rotate1__length01,axiom,
% 5.12/5.38 ! [Xs: list_o] :
% 5.12/5.38 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 5.12/5.38 => ( ( rotate1_o @ Xs )
% 5.12/5.38 = Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % rotate1_length01
% 5.12/5.38 thf(fact_4795_rotate1__length01,axiom,
% 5.12/5.38 ! [Xs: list_nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 5.12/5.38 => ( ( rotate1_nat @ Xs )
% 5.12/5.38 = Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % rotate1_length01
% 5.12/5.38 thf(fact_4796_rotate1__length01,axiom,
% 5.12/5.38 ! [Xs: list_int] :
% 5.12/5.38 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 5.12/5.38 => ( ( rotate1_int @ Xs )
% 5.12/5.38 = Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % rotate1_length01
% 5.12/5.38 thf(fact_4797_pochhammer__same,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_same
% 5.12/5.38 thf(fact_4798_pochhammer__same,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.12/5.38 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_same
% 5.12/5.38 thf(fact_4799_pochhammer__same,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.12/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_same
% 5.12/5.38 thf(fact_4800_pochhammer__same,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.12/5.38 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_same
% 5.12/5.38 thf(fact_4801_pochhammer__same,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.12/5.38 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_same
% 5.12/5.38 thf(fact_4802_fact__reduce,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.38 => ( ( semiri5044797733671781792omplex @ N )
% 5.12/5.38 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_reduce
% 5.12/5.38 thf(fact_4803_fact__reduce,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.38 => ( ( semiri773545260158071498ct_rat @ N )
% 5.12/5.38 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_reduce
% 5.12/5.38 thf(fact_4804_fact__reduce,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.38 => ( ( semiri1406184849735516958ct_int @ N )
% 5.12/5.38 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_reduce
% 5.12/5.38 thf(fact_4805_fact__reduce,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.38 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.12/5.38 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_reduce
% 5.12/5.38 thf(fact_4806_fact__reduce,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.38 => ( ( semiri2265585572941072030t_real @ N )
% 5.12/5.38 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_reduce
% 5.12/5.38 thf(fact_4807_fact__num__eq__if,axiom,
% 5.12/5.38 ( semiri5044797733671781792omplex
% 5.12/5.38 = ( ^ [M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M5 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_num_eq_if
% 5.12/5.38 thf(fact_4808_fact__num__eq__if,axiom,
% 5.12/5.38 ( semiri773545260158071498ct_rat
% 5.12/5.38 = ( ^ [M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M5 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_num_eq_if
% 5.12/5.38 thf(fact_4809_fact__num__eq__if,axiom,
% 5.12/5.38 ( semiri1406184849735516958ct_int
% 5.12/5.38 = ( ^ [M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_num_eq_if
% 5.12/5.38 thf(fact_4810_fact__num__eq__if,axiom,
% 5.12/5.38 ( semiri1408675320244567234ct_nat
% 5.12/5.38 = ( ^ [M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M5 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_num_eq_if
% 5.12/5.38 thf(fact_4811_fact__num__eq__if,axiom,
% 5.12/5.38 ( semiri2265585572941072030t_real
% 5.12/5.38 = ( ^ [M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_num_eq_if
% 5.12/5.38 thf(fact_4812_of__nat__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri8010041392384452111omplex @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.38 = ( semiri5044797733671781792omplex @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_fact
% 5.12/5.38 thf(fact_4813_of__nat__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri681578069525770553at_rat @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.38 = ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_fact
% 5.12/5.38 thf(fact_4814_of__nat__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1314217659103216013at_int @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.38 = ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_fact
% 5.12/5.38 thf(fact_4815_of__nat__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1316708129612266289at_nat @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.38 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_fact
% 5.12/5.38 thf(fact_4816_of__nat__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri5074537144036343181t_real @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.38 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_fact
% 5.12/5.38 thf(fact_4817_length__rotate1,axiom,
% 5.12/5.38 ! [Xs: list_VEBT_VEBT] :
% 5.12/5.38 ( ( size_s6755466524823107622T_VEBT @ ( rotate1_VEBT_VEBT @ Xs ) )
% 5.12/5.38 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % length_rotate1
% 5.12/5.38 thf(fact_4818_length__rotate1,axiom,
% 5.12/5.38 ! [Xs: list_o] :
% 5.12/5.38 ( ( size_size_list_o @ ( rotate1_o @ Xs ) )
% 5.12/5.38 = ( size_size_list_o @ Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % length_rotate1
% 5.12/5.38 thf(fact_4819_length__rotate1,axiom,
% 5.12/5.38 ! [Xs: list_nat] :
% 5.12/5.38 ( ( size_size_list_nat @ ( rotate1_nat @ Xs ) )
% 5.12/5.38 = ( size_size_list_nat @ Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % length_rotate1
% 5.12/5.38 thf(fact_4820_length__rotate1,axiom,
% 5.12/5.38 ! [Xs: list_int] :
% 5.12/5.38 ( ( size_size_list_int @ ( rotate1_int @ Xs ) )
% 5.12/5.38 = ( size_size_list_int @ Xs ) ) ).
% 5.12/5.38
% 5.12/5.38 % length_rotate1
% 5.12/5.38 thf(fact_4821_fact__0,axiom,
% 5.12/5.38 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.12/5.38 = one_one_complex ) ).
% 5.12/5.38
% 5.12/5.38 % fact_0
% 5.12/5.38 thf(fact_4822_fact__0,axiom,
% 5.12/5.38 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.12/5.38 = one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_0
% 5.12/5.38 thf(fact_4823_fact__0,axiom,
% 5.12/5.38 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.12/5.38 = one_one_int ) ).
% 5.12/5.38
% 5.12/5.38 % fact_0
% 5.12/5.38 thf(fact_4824_fact__0,axiom,
% 5.12/5.38 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.12/5.38 = one_one_nat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_0
% 5.12/5.38 thf(fact_4825_fact__0,axiom,
% 5.12/5.38 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.12/5.38 = one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % fact_0
% 5.12/5.38 thf(fact_4826_fact__1,axiom,
% 5.12/5.38 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.12/5.38 = one_one_complex ) ).
% 5.12/5.38
% 5.12/5.38 % fact_1
% 5.12/5.38 thf(fact_4827_fact__1,axiom,
% 5.12/5.38 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.12/5.38 = one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_1
% 5.12/5.38 thf(fact_4828_fact__1,axiom,
% 5.12/5.38 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.12/5.38 = one_one_int ) ).
% 5.12/5.38
% 5.12/5.38 % fact_1
% 5.12/5.38 thf(fact_4829_fact__1,axiom,
% 5.12/5.38 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.12/5.38 = one_one_nat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_1
% 5.12/5.38 thf(fact_4830_fact__1,axiom,
% 5.12/5.38 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.12/5.38 = one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % fact_1
% 5.12/5.38 thf(fact_4831_fact__Suc__0,axiom,
% 5.12/5.38 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.12/5.38 = one_one_complex ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc_0
% 5.12/5.38 thf(fact_4832_fact__Suc__0,axiom,
% 5.12/5.38 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.12/5.38 = one_one_rat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc_0
% 5.12/5.38 thf(fact_4833_fact__Suc__0,axiom,
% 5.12/5.38 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.12/5.38 = one_one_int ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc_0
% 5.12/5.38 thf(fact_4834_fact__Suc__0,axiom,
% 5.12/5.38 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.12/5.38 = one_one_nat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc_0
% 5.12/5.38 thf(fact_4835_fact__Suc__0,axiom,
% 5.12/5.38 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.12/5.38 = one_one_real ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc_0
% 5.12/5.38 thf(fact_4836_fact__Suc,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc
% 5.12/5.38 thf(fact_4837_fact__Suc,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc
% 5.12/5.38 thf(fact_4838_fact__Suc,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc
% 5.12/5.38 thf(fact_4839_fact__Suc,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc
% 5.12/5.38 thf(fact_4840_fact__Suc,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.12/5.38 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_Suc
% 5.12/5.38 thf(fact_4841_fact__nonzero,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri773545260158071498ct_rat @ N )
% 5.12/5.38 != zero_zero_rat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_nonzero
% 5.12/5.38 thf(fact_4842_fact__nonzero,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1406184849735516958ct_int @ N )
% 5.12/5.38 != zero_zero_int ) ).
% 5.12/5.38
% 5.12/5.38 % fact_nonzero
% 5.12/5.38 thf(fact_4843_fact__nonzero,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri1408675320244567234ct_nat @ N )
% 5.12/5.38 != zero_zero_nat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_nonzero
% 5.12/5.38 thf(fact_4844_fact__nonzero,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( semiri2265585572941072030t_real @ N )
% 5.12/5.38 != zero_zero_real ) ).
% 5.12/5.38
% 5.12/5.38 % fact_nonzero
% 5.12/5.38 thf(fact_4845_fact__less__mono__nat,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.38 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.38 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_less_mono_nat
% 5.12/5.38 thf(fact_4846_fact__ge__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_zero
% 5.12/5.38 thf(fact_4847_fact__ge__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_zero
% 5.12/5.38 thf(fact_4848_fact__ge__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_zero
% 5.12/5.38 thf(fact_4849_fact__ge__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_zero
% 5.12/5.38 thf(fact_4850_fact__not__neg,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_not_neg
% 5.12/5.38 thf(fact_4851_fact__not__neg,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.12/5.38
% 5.12/5.38 % fact_not_neg
% 5.12/5.38 thf(fact_4852_fact__not__neg,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.12/5.38
% 5.12/5.38 % fact_not_neg
% 5.12/5.38 thf(fact_4853_fact__not__neg,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.12/5.38
% 5.12/5.38 % fact_not_neg
% 5.12/5.38 thf(fact_4854_fact__gt__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_gt_zero
% 5.12/5.38 thf(fact_4855_fact__gt__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_gt_zero
% 5.12/5.38 thf(fact_4856_fact__gt__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_gt_zero
% 5.12/5.38 thf(fact_4857_fact__gt__zero,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_gt_zero
% 5.12/5.38 thf(fact_4858_fact__ge__1,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_1
% 5.12/5.38 thf(fact_4859_fact__ge__1,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_1
% 5.12/5.38 thf(fact_4860_fact__ge__1,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_1
% 5.12/5.38 thf(fact_4861_fact__ge__1,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_1
% 5.12/5.38 thf(fact_4862_pochhammer__fact,axiom,
% 5.12/5.38 ( semiri5044797733671781792omplex
% 5.12/5.38 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_fact
% 5.12/5.38 thf(fact_4863_pochhammer__fact,axiom,
% 5.12/5.38 ( semiri773545260158071498ct_rat
% 5.12/5.38 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_fact
% 5.12/5.38 thf(fact_4864_pochhammer__fact,axiom,
% 5.12/5.38 ( semiri1406184849735516958ct_int
% 5.12/5.38 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_fact
% 5.12/5.38 thf(fact_4865_pochhammer__fact,axiom,
% 5.12/5.38 ( semiri1408675320244567234ct_nat
% 5.12/5.38 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_fact
% 5.12/5.38 thf(fact_4866_pochhammer__fact,axiom,
% 5.12/5.38 ( semiri2265585572941072030t_real
% 5.12/5.38 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.12/5.38
% 5.12/5.38 % pochhammer_fact
% 5.12/5.38 thf(fact_4867_fact__ge__Suc__0__nat,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_ge_Suc_0_nat
% 5.12/5.38 thf(fact_4868_fact__less__mono,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.38 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.38 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_less_mono
% 5.12/5.38 thf(fact_4869_fact__less__mono,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.38 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.38 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_less_mono
% 5.12/5.38 thf(fact_4870_fact__less__mono,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.38 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.38 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_less_mono
% 5.12/5.38 thf(fact_4871_fact__less__mono,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.38 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.38 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_less_mono
% 5.12/5.38 thf(fact_4872_fact__mod,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 5.12/5.38 = zero_zero_int ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_mod
% 5.12/5.38 thf(fact_4873_fact__mod,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M2 ) )
% 5.12/5.38 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_mod
% 5.12/5.38 thf(fact_4874_fact__mod,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M2 ) )
% 5.12/5.38 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_mod
% 5.12/5.38 thf(fact_4875_fact__mod,axiom,
% 5.12/5.38 ! [M2: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.38 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 5.12/5.38 = zero_zero_nat ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_mod
% 5.12/5.38 thf(fact_4876_fact__le__power,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_le_power
% 5.12/5.38 thf(fact_4877_fact__le__power,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_le_power
% 5.12/5.38 thf(fact_4878_fact__le__power,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_le_power
% 5.12/5.38 thf(fact_4879_fact__le__power,axiom,
% 5.12/5.38 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_le_power
% 5.12/5.38 thf(fact_4880_fact__diff__Suc,axiom,
% 5.12/5.38 ! [N: nat,M2: nat] :
% 5.12/5.38 ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 5.12/5.38 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) )
% 5.12/5.38 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_diff_Suc
% 5.12/5.38 thf(fact_4881_fact__div__fact__le__pow,axiom,
% 5.12/5.38 ! [R4: nat,N: nat] :
% 5.12/5.38 ( ( ord_less_eq_nat @ R4 @ N )
% 5.12/5.38 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R4 ) ) ) @ ( power_power_nat @ N @ R4 ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % fact_div_fact_le_pow
% 5.12/5.38 thf(fact_4882_le__divide__eq__numeral_I2_J,axiom,
% 5.12/5.38 ! [W: num,B: real,C: real] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.12/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.38 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.38 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_divide_eq_numeral(2)
% 5.12/5.38 thf(fact_4883_le__divide__eq__numeral_I2_J,axiom,
% 5.12/5.38 ! [W: num,B: rat,C: rat] :
% 5.12/5.38 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % le_divide_eq_numeral(2)
% 5.12/5.38 thf(fact_4884_divide__le__eq__numeral_I2_J,axiom,
% 5.12/5.38 ! [B: real,C: real,W: num] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.38 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.12/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % divide_le_eq_numeral(2)
% 5.12/5.38 thf(fact_4885_divide__le__eq__numeral_I2_J,axiom,
% 5.12/5.38 ! [B: rat,C: rat,W: num] :
% 5.12/5.38 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.38 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.12/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % divide_le_eq_numeral(2)
% 5.12/5.38 thf(fact_4886_norm__power__diff,axiom,
% 5.12/5.38 ! [Z2: real,W: real,M2: nat] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 5.12/5.38 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z2 @ M2 ) @ ( power_power_real @ W @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z2 @ W ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_power_diff
% 5.12/5.38 thf(fact_4887_norm__power__diff,axiom,
% 5.12/5.38 ! [Z2: complex,W: complex,M2: nat] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 5.12/5.38 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.12/5.38 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z2 @ M2 ) @ ( power_power_complex @ W @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z2 @ W ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_power_diff
% 5.12/5.38 thf(fact_4888_cppi,axiom,
% 5.12/5.38 ! [D6: int,P: int > $o,P5: int > $o,A2: set_int] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.38 => ( ? [Z5: int] :
% 5.12/5.38 ! [X3: int] :
% 5.12/5.38 ( ( ord_less_int @ Z5 @ X3 )
% 5.12/5.38 => ( ( P @ X3 )
% 5.12/5.38 = ( P5 @ X3 ) ) )
% 5.12/5.38 => ( ! [X3: int] :
% 5.12/5.38 ( ! [Xa2: int] :
% 5.12/5.38 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 => ! [Xb: int] :
% 5.12/5.38 ( ( member_int @ Xb @ A2 )
% 5.12/5.38 => ( X3
% 5.12/5.38 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.38 => ( ( P @ X3 )
% 5.12/5.38 => ( P @ ( plus_plus_int @ X3 @ D6 ) ) ) )
% 5.12/5.38 => ( ! [X3: int,K2: int] :
% 5.12/5.38 ( ( P5 @ X3 )
% 5.12/5.38 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.38 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.12/5.38 = ( ? [X2: int] :
% 5.12/5.38 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 & ( P5 @ X2 ) )
% 5.12/5.38 | ? [X2: int] :
% 5.12/5.38 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 & ? [Y6: int] :
% 5.12/5.38 ( ( member_int @ Y6 @ A2 )
% 5.12/5.38 & ( P @ ( minus_minus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % cppi
% 5.12/5.38 thf(fact_4889_cpmi,axiom,
% 5.12/5.38 ! [D6: int,P: int > $o,P5: int > $o,B5: set_int] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.38 => ( ? [Z5: int] :
% 5.12/5.38 ! [X3: int] :
% 5.12/5.38 ( ( ord_less_int @ X3 @ Z5 )
% 5.12/5.38 => ( ( P @ X3 )
% 5.12/5.38 = ( P5 @ X3 ) ) )
% 5.12/5.38 => ( ! [X3: int] :
% 5.12/5.38 ( ! [Xa2: int] :
% 5.12/5.38 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 => ! [Xb: int] :
% 5.12/5.38 ( ( member_int @ Xb @ B5 )
% 5.12/5.38 => ( X3
% 5.12/5.38 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.38 => ( ( P @ X3 )
% 5.12/5.38 => ( P @ ( minus_minus_int @ X3 @ D6 ) ) ) )
% 5.12/5.38 => ( ! [X3: int,K2: int] :
% 5.12/5.38 ( ( P5 @ X3 )
% 5.12/5.38 = ( P5 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D6 ) ) ) )
% 5.12/5.38 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.12/5.38 = ( ? [X2: int] :
% 5.12/5.38 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 & ( P5 @ X2 ) )
% 5.12/5.38 | ? [X2: int] :
% 5.12/5.38 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 & ? [Y6: int] :
% 5.12/5.38 ( ( member_int @ Y6 @ B5 )
% 5.12/5.38 & ( P @ ( plus_plus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % cpmi
% 5.12/5.38 thf(fact_4890_bset_I6_J,axiom,
% 5.12/5.38 ! [D6: int,B5: set_int,T: int] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.38 => ! [X4: int] :
% 5.12/5.38 ( ! [Xa3: int] :
% 5.12/5.38 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 => ! [Xb2: int] :
% 5.12/5.38 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.38 => ( X4
% 5.12/5.38 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.38 => ( ( ord_less_eq_int @ X4 @ T )
% 5.12/5.38 => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D6 ) @ T ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % bset(6)
% 5.12/5.38 thf(fact_4891_bset_I8_J,axiom,
% 5.12/5.38 ! [D6: int,T: int,B5: set_int] :
% 5.12/5.38 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.38 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 5.12/5.38 => ! [X4: int] :
% 5.12/5.38 ( ! [Xa3: int] :
% 5.12/5.38 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.38 => ! [Xb2: int] :
% 5.12/5.38 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.38 => ( X4
% 5.12/5.38 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.38 => ( ( ord_less_eq_int @ T @ X4 )
% 5.12/5.38 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D6 ) ) ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % bset(8)
% 5.12/5.38 thf(fact_4892_numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( numera6690914467698888265omplex @ M2 )
% 5.12/5.38 = ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_eq_iff
% 5.12/5.38 thf(fact_4893_numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( numeral_numeral_real @ M2 )
% 5.12/5.38 = ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_eq_iff
% 5.12/5.38 thf(fact_4894_numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( numeral_numeral_rat @ M2 )
% 5.12/5.38 = ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_eq_iff
% 5.12/5.38 thf(fact_4895_numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( numeral_numeral_nat @ M2 )
% 5.12/5.38 = ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_eq_iff
% 5.12/5.38 thf(fact_4896_numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( numeral_numeral_int @ M2 )
% 5.12/5.38 = ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_eq_iff
% 5.12/5.38 thf(fact_4897_int__eq__iff__numeral,axiom,
% 5.12/5.38 ! [M2: nat,V: num] :
% 5.12/5.38 ( ( ( semiri1314217659103216013at_int @ M2 )
% 5.12/5.38 = ( numeral_numeral_int @ V ) )
% 5.12/5.38 = ( M2
% 5.12/5.38 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % int_eq_iff_numeral
% 5.12/5.38 thf(fact_4898_nat__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.12/5.38 = ( numeral_numeral_nat @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % nat_numeral
% 5.12/5.38 thf(fact_4899_numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_le_iff
% 5.12/5.38 thf(fact_4900_numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_le_iff
% 5.12/5.38 thf(fact_4901_numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_le_iff
% 5.12/5.38 thf(fact_4902_numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_le_iff
% 5.12/5.38 thf(fact_4903_numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( ord_less_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_less_iff
% 5.12/5.38 thf(fact_4904_numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( ord_less_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_less_iff
% 5.12/5.38 thf(fact_4905_numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( ord_less_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_less_iff
% 5.12/5.38 thf(fact_4906_numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( ord_less_num @ M2 @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_less_iff
% 5.12/5.38 thf(fact_4907_mult__numeral__left__semiring__numeral,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z2 ) )
% 5.12/5.38 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_numeral_left_semiring_numeral
% 5.12/5.38 thf(fact_4908_mult__numeral__left__semiring__numeral,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: real] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z2 ) )
% 5.12/5.38 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_numeral_left_semiring_numeral
% 5.12/5.38 thf(fact_4909_mult__numeral__left__semiring__numeral,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z2 ) )
% 5.12/5.38 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_numeral_left_semiring_numeral
% 5.12/5.38 thf(fact_4910_mult__numeral__left__semiring__numeral,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: nat] :
% 5.12/5.38 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z2 ) )
% 5.12/5.38 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_numeral_left_semiring_numeral
% 5.12/5.38 thf(fact_4911_mult__numeral__left__semiring__numeral,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: int] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z2 ) )
% 5.12/5.38 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_numeral_left_semiring_numeral
% 5.12/5.38 thf(fact_4912_numeral__times__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_times_numeral
% 5.12/5.38 thf(fact_4913_numeral__times__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_times_numeral
% 5.12/5.38 thf(fact_4914_numeral__times__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_times_numeral
% 5.12/5.38 thf(fact_4915_numeral__times__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_times_numeral
% 5.12/5.38 thf(fact_4916_numeral__times__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_times_numeral
% 5.12/5.38 thf(fact_4917_add__numeral__left,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: complex] :
% 5.12/5.38 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z2 ) )
% 5.12/5.38 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_numeral_left
% 5.12/5.38 thf(fact_4918_add__numeral__left,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: real] :
% 5.12/5.38 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z2 ) )
% 5.12/5.38 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_numeral_left
% 5.12/5.38 thf(fact_4919_add__numeral__left,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: rat] :
% 5.12/5.38 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z2 ) )
% 5.12/5.38 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_numeral_left
% 5.12/5.38 thf(fact_4920_add__numeral__left,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: nat] :
% 5.12/5.38 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z2 ) )
% 5.12/5.38 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_numeral_left
% 5.12/5.38 thf(fact_4921_add__numeral__left,axiom,
% 5.12/5.38 ! [V: num,W: num,Z2: int] :
% 5.12/5.38 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z2 ) )
% 5.12/5.38 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_numeral_left
% 5.12/5.38 thf(fact_4922_numeral__plus__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_plus_numeral
% 5.12/5.38 thf(fact_4923_numeral__plus__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_plus_numeral
% 5.12/5.38 thf(fact_4924_numeral__plus__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_plus_numeral
% 5.12/5.38 thf(fact_4925_numeral__plus__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_plus_numeral
% 5.12/5.38 thf(fact_4926_numeral__plus__numeral,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_plus_numeral
% 5.12/5.38 thf(fact_4927_power__zero__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.12/5.38 = zero_zero_rat ) ).
% 5.12/5.38
% 5.12/5.38 % power_zero_numeral
% 5.12/5.38 thf(fact_4928_power__zero__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.12/5.38 = zero_zero_int ) ).
% 5.12/5.38
% 5.12/5.38 % power_zero_numeral
% 5.12/5.38 thf(fact_4929_power__zero__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.12/5.38 = zero_zero_nat ) ).
% 5.12/5.38
% 5.12/5.38 % power_zero_numeral
% 5.12/5.38 thf(fact_4930_power__zero__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.12/5.38 = zero_zero_real ) ).
% 5.12/5.38
% 5.12/5.38 % power_zero_numeral
% 5.12/5.38 thf(fact_4931_power__zero__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.12/5.38 = zero_zero_complex ) ).
% 5.12/5.38
% 5.12/5.38 % power_zero_numeral
% 5.12/5.38 thf(fact_4932_neg__numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.38 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_eq_iff
% 5.12/5.38 thf(fact_4933_neg__numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 5.12/5.38 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_eq_iff
% 5.12/5.38 thf(fact_4934_neg__numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_eq_iff
% 5.12/5.38 thf(fact_4935_neg__numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 5.12/5.38 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_eq_iff
% 5.12/5.38 thf(fact_4936_neg__numeral__eq__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 5.12/5.38 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( M2 = N ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_eq_iff
% 5.12/5.38 thf(fact_4937_of__nat__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_numeral
% 5.12/5.38 thf(fact_4938_of__nat__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_numeral
% 5.12/5.38 thf(fact_4939_of__nat__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_numeral
% 5.12/5.38 thf(fact_4940_of__nat__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_numeral
% 5.12/5.38 thf(fact_4941_of__nat__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_nat_numeral
% 5.12/5.38 thf(fact_4942_abs__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.38 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % abs_numeral
% 5.12/5.38 thf(fact_4943_abs__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( numeral_numeral_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % abs_numeral
% 5.12/5.38 thf(fact_4944_abs__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % abs_numeral
% 5.12/5.38 thf(fact_4945_abs__numeral,axiom,
% 5.12/5.38 ! [N: num] :
% 5.12/5.38 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % abs_numeral
% 5.12/5.38 thf(fact_4946_of__int__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.12/5.38 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_numeral
% 5.12/5.38 thf(fact_4947_of__int__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.12/5.38 = ( numeral_numeral_real @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_numeral
% 5.12/5.38 thf(fact_4948_of__int__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.12/5.38 = ( numeral_numeral_rat @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_numeral
% 5.12/5.38 thf(fact_4949_of__int__numeral,axiom,
% 5.12/5.38 ! [K: num] :
% 5.12/5.38 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.12/5.38 = ( numeral_numeral_int @ K ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_numeral
% 5.12/5.38 thf(fact_4950_of__int__eq__numeral__iff,axiom,
% 5.12/5.38 ! [Z2: int,N: num] :
% 5.12/5.38 ( ( ( ring_17405671764205052669omplex @ Z2 )
% 5.12/5.38 = ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( Z2
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_eq_numeral_iff
% 5.12/5.38 thf(fact_4951_of__int__eq__numeral__iff,axiom,
% 5.12/5.38 ! [Z2: int,N: num] :
% 5.12/5.38 ( ( ( ring_1_of_int_real @ Z2 )
% 5.12/5.38 = ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( Z2
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_eq_numeral_iff
% 5.12/5.38 thf(fact_4952_of__int__eq__numeral__iff,axiom,
% 5.12/5.38 ! [Z2: int,N: num] :
% 5.12/5.38 ( ( ( ring_1_of_int_rat @ Z2 )
% 5.12/5.38 = ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( Z2
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_eq_numeral_iff
% 5.12/5.38 thf(fact_4953_of__int__eq__numeral__iff,axiom,
% 5.12/5.38 ! [Z2: int,N: num] :
% 5.12/5.38 ( ( ( ring_1_of_int_int @ Z2 )
% 5.12/5.38 = ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( Z2
% 5.12/5.38 = ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % of_int_eq_numeral_iff
% 5.12/5.38 thf(fact_4954_norm__minus__cancel,axiom,
% 5.12/5.38 ! [X: real] :
% 5.12/5.38 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.38 = ( real_V7735802525324610683m_real @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_minus_cancel
% 5.12/5.38 thf(fact_4955_norm__minus__cancel,axiom,
% 5.12/5.38 ! [X: complex] :
% 5.12/5.38 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.38 = ( real_V1022390504157884413omplex @ X ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_minus_cancel
% 5.12/5.38 thf(fact_4956_floor__numeral,axiom,
% 5.12/5.38 ! [V: num] :
% 5.12/5.38 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.12/5.38 = ( numeral_numeral_int @ V ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_numeral
% 5.12/5.38 thf(fact_4957_floor__numeral,axiom,
% 5.12/5.38 ! [V: num] :
% 5.12/5.38 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.12/5.38 = ( numeral_numeral_int @ V ) ) ).
% 5.12/5.38
% 5.12/5.38 % floor_numeral
% 5.12/5.38 thf(fact_4958_ceiling__numeral,axiom,
% 5.12/5.38 ! [V: num] :
% 5.12/5.38 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.12/5.38 = ( numeral_numeral_int @ V ) ) ).
% 5.12/5.38
% 5.12/5.38 % ceiling_numeral
% 5.12/5.38 thf(fact_4959_ceiling__numeral,axiom,
% 5.12/5.38 ! [V: num] :
% 5.12/5.38 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.12/5.38 = ( numeral_numeral_int @ V ) ) ).
% 5.12/5.38
% 5.12/5.38 % ceiling_numeral
% 5.12/5.38 thf(fact_4960_norm__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( real_V1022390504157884413omplex @ ( semiri5044797733671781792omplex @ N ) )
% 5.12/5.38 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_fact
% 5.12/5.38 thf(fact_4961_norm__fact,axiom,
% 5.12/5.38 ! [N: nat] :
% 5.12/5.38 ( ( real_V7735802525324610683m_real @ ( semiri2265585572941072030t_real @ N ) )
% 5.12/5.38 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.38
% 5.12/5.38 % norm_fact
% 5.12/5.38 thf(fact_4962_numeral__powr__numeral__real,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( powr_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( power_power_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % numeral_powr_numeral_real
% 5.12/5.38 thf(fact_4963_neg__numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_le_iff
% 5.12/5.38 thf(fact_4964_neg__numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_le_iff
% 5.12/5.38 thf(fact_4965_neg__numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_le_iff
% 5.12/5.38 thf(fact_4966_neg__numeral__le__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_le_iff
% 5.12/5.38 thf(fact_4967_distrib__right__numeral,axiom,
% 5.12/5.38 ! [A: complex,B: complex,V: num] :
% 5.12/5.38 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.12/5.38 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_right_numeral
% 5.12/5.38 thf(fact_4968_distrib__right__numeral,axiom,
% 5.12/5.38 ! [A: real,B: real,V: num] :
% 5.12/5.38 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.12/5.38 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_right_numeral
% 5.12/5.38 thf(fact_4969_distrib__right__numeral,axiom,
% 5.12/5.38 ! [A: rat,B: rat,V: num] :
% 5.12/5.38 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.12/5.38 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_right_numeral
% 5.12/5.38 thf(fact_4970_distrib__right__numeral,axiom,
% 5.12/5.38 ! [A: nat,B: nat,V: num] :
% 5.12/5.38 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.12/5.38 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_right_numeral
% 5.12/5.38 thf(fact_4971_distrib__right__numeral,axiom,
% 5.12/5.38 ! [A: int,B: int,V: num] :
% 5.12/5.38 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.38 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_right_numeral
% 5.12/5.38 thf(fact_4972_distrib__left__numeral,axiom,
% 5.12/5.38 ! [V: num,B: complex,C: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.12/5.38 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_left_numeral
% 5.12/5.38 thf(fact_4973_distrib__left__numeral,axiom,
% 5.12/5.38 ! [V: num,B: real,C: real] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.12/5.38 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_left_numeral
% 5.12/5.38 thf(fact_4974_distrib__left__numeral,axiom,
% 5.12/5.38 ! [V: num,B: rat,C: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.38 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_left_numeral
% 5.12/5.38 thf(fact_4975_distrib__left__numeral,axiom,
% 5.12/5.38 ! [V: num,B: nat,C: nat] :
% 5.12/5.38 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.38 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_left_numeral
% 5.12/5.38 thf(fact_4976_distrib__left__numeral,axiom,
% 5.12/5.38 ! [V: num,B: int,C: int] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.12/5.38 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % distrib_left_numeral
% 5.12/5.38 thf(fact_4977_neg__numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( ord_less_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_less_iff
% 5.12/5.38 thf(fact_4978_neg__numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( ord_less_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_less_iff
% 5.12/5.38 thf(fact_4979_neg__numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( ord_less_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_less_iff
% 5.12/5.38 thf(fact_4980_neg__numeral__less__iff,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( ord_less_num @ N @ M2 ) ) ).
% 5.12/5.38
% 5.12/5.38 % neg_numeral_less_iff
% 5.12/5.38 thf(fact_4981_left__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [A: complex,B: complex,V: num] :
% 5.12/5.38 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.12/5.38 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % left_diff_distrib_numeral
% 5.12/5.38 thf(fact_4982_left__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [A: real,B: real,V: num] :
% 5.12/5.38 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.12/5.38 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % left_diff_distrib_numeral
% 5.12/5.38 thf(fact_4983_left__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [A: rat,B: rat,V: num] :
% 5.12/5.38 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.12/5.38 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % left_diff_distrib_numeral
% 5.12/5.38 thf(fact_4984_left__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [A: int,B: int,V: num] :
% 5.12/5.38 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.38 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % left_diff_distrib_numeral
% 5.12/5.38 thf(fact_4985_right__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [V: num,B: complex,C: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.12/5.38 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % right_diff_distrib_numeral
% 5.12/5.38 thf(fact_4986_right__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [V: num,B: real,C: real] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.12/5.38 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % right_diff_distrib_numeral
% 5.12/5.38 thf(fact_4987_right__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [V: num,B: rat,C: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.12/5.38 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % right_diff_distrib_numeral
% 5.12/5.38 thf(fact_4988_right__diff__distrib__numeral,axiom,
% 5.12/5.38 ! [V: num,B: int,C: int] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.12/5.38 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % right_diff_distrib_numeral
% 5.12/5.38 thf(fact_4989_mult__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_4990_mult__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_4991_mult__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_4992_mult__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_4993_mult__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_4994_mult__neg__numeral__simps_I2_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(2)
% 5.12/5.38 thf(fact_4995_mult__neg__numeral__simps_I2_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(2)
% 5.12/5.38 thf(fact_4996_mult__neg__numeral__simps_I2_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(2)
% 5.12/5.38 thf(fact_4997_mult__neg__numeral__simps_I2_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.38 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(2)
% 5.12/5.38 thf(fact_4998_mult__neg__numeral__simps_I2_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.38 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(2)
% 5.12/5.38 thf(fact_4999_mult__neg__numeral__simps_I1_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(1)
% 5.12/5.38 thf(fact_5000_mult__neg__numeral__simps_I1_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(1)
% 5.12/5.38 thf(fact_5001_mult__neg__numeral__simps_I1_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.38 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(1)
% 5.12/5.38 thf(fact_5002_mult__neg__numeral__simps_I1_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(1)
% 5.12/5.38 thf(fact_5003_mult__neg__numeral__simps_I1_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % mult_neg_numeral_simps(1)
% 5.12/5.38 thf(fact_5004_semiring__norm_I170_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: int] :
% 5.12/5.38 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.12/5.38 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(170)
% 5.12/5.38 thf(fact_5005_semiring__norm_I170_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: real] :
% 5.12/5.38 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.12/5.38 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(170)
% 5.12/5.38 thf(fact_5006_semiring__norm_I170_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.12/5.38 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(170)
% 5.12/5.38 thf(fact_5007_semiring__norm_I170_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: code_integer] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(170)
% 5.12/5.38 thf(fact_5008_semiring__norm_I170_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.12/5.38 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(170)
% 5.12/5.38 thf(fact_5009_semiring__norm_I171_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: int] :
% 5.12/5.38 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(171)
% 5.12/5.38 thf(fact_5010_semiring__norm_I171_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: real] :
% 5.12/5.38 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(171)
% 5.12/5.38 thf(fact_5011_semiring__norm_I171_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(171)
% 5.12/5.38 thf(fact_5012_semiring__norm_I171_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: code_integer] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(171)
% 5.12/5.38 thf(fact_5013_semiring__norm_I171_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(171)
% 5.12/5.38 thf(fact_5014_semiring__norm_I172_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: int] :
% 5.12/5.38 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(172)
% 5.12/5.38 thf(fact_5015_semiring__norm_I172_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: real] :
% 5.12/5.38 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(172)
% 5.12/5.38 thf(fact_5016_semiring__norm_I172_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: complex] :
% 5.12/5.38 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(172)
% 5.12/5.38 thf(fact_5017_semiring__norm_I172_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: code_integer] :
% 5.12/5.38 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(172)
% 5.12/5.38 thf(fact_5018_semiring__norm_I172_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: rat] :
% 5.12/5.38 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.12/5.38 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(172)
% 5.12/5.38 thf(fact_5019_add__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_5020_add__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_5021_add__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_5022_add__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.38 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_5023_add__neg__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.38 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % add_neg_numeral_simps(3)
% 5.12/5.38 thf(fact_5024_semiring__norm_I168_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: int] :
% 5.12/5.38 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.12/5.38 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(168)
% 5.12/5.38 thf(fact_5025_semiring__norm_I168_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: real] :
% 5.12/5.38 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.12/5.38 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(168)
% 5.12/5.38 thf(fact_5026_semiring__norm_I168_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: complex] :
% 5.12/5.38 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.12/5.38 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(168)
% 5.12/5.38 thf(fact_5027_semiring__norm_I168_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: code_integer] :
% 5.12/5.38 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.12/5.38 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(168)
% 5.12/5.38 thf(fact_5028_semiring__norm_I168_J,axiom,
% 5.12/5.38 ! [V: num,W: num,Y: rat] :
% 5.12/5.38 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.12/5.38 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.12/5.38
% 5.12/5.38 % semiring_norm(168)
% 5.12/5.38 thf(fact_5029_diff__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.38 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % diff_numeral_simps(3)
% 5.12/5.38 thf(fact_5030_diff__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.38 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % diff_numeral_simps(3)
% 5.12/5.38 thf(fact_5031_diff__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.38 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.38 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.12/5.38
% 5.12/5.38 % diff_numeral_simps(3)
% 5.12/5.38 thf(fact_5032_diff__numeral__simps_I3_J,axiom,
% 5.12/5.38 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(3)
% 5.12/5.39 thf(fact_5033_diff__numeral__simps_I3_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(3)
% 5.12/5.39 thf(fact_5034_diff__numeral__simps_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(2)
% 5.12/5.39 thf(fact_5035_diff__numeral__simps_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(2)
% 5.12/5.39 thf(fact_5036_diff__numeral__simps_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.39 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(2)
% 5.12/5.39 thf(fact_5037_diff__numeral__simps_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.39 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(2)
% 5.12/5.39 thf(fact_5038_diff__numeral__simps_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_simps(2)
% 5.12/5.39 thf(fact_5039_abs__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % abs_neg_numeral
% 5.12/5.39 thf(fact_5040_abs__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % abs_neg_numeral
% 5.12/5.39 thf(fact_5041_abs__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.39 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % abs_neg_numeral
% 5.12/5.39 thf(fact_5042_abs__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.39 = ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % abs_neg_numeral
% 5.12/5.39 thf(fact_5043_norm__zero,axiom,
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.12/5.39 = zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % norm_zero
% 5.12/5.39 thf(fact_5044_norm__zero,axiom,
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.12/5.39 = zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % norm_zero
% 5.12/5.39 thf(fact_5045_norm__eq__zero,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( real_V7735802525324610683m_real @ X )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 = ( X = zero_zero_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_eq_zero
% 5.12/5.39 thf(fact_5046_norm__eq__zero,axiom,
% 5.12/5.39 ! [X: complex] :
% 5.12/5.39 ( ( ( real_V1022390504157884413omplex @ X )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 = ( X = zero_zero_complex ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_eq_zero
% 5.12/5.39 thf(fact_5047_norm__neg__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( numeral_numeral_real @ W ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_neg_numeral
% 5.12/5.39 thf(fact_5048_norm__neg__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = ( numeral_numeral_real @ W ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_neg_numeral
% 5.12/5.39 thf(fact_5049_norm__one,axiom,
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.12/5.39 = one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % norm_one
% 5.12/5.39 thf(fact_5050_norm__one,axiom,
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.12/5.39 = one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % norm_one
% 5.12/5.39 thf(fact_5051_numeral__less__real__of__nat__iff,axiom,
% 5.12/5.39 ! [W: num,N: nat] :
% 5.12/5.39 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.39 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_less_real_of_nat_iff
% 5.12/5.39 thf(fact_5052_real__of__nat__less__numeral__iff,axiom,
% 5.12/5.39 ! [N: nat,W: num] :
% 5.12/5.39 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_less_numeral_iff
% 5.12/5.39 thf(fact_5053_numeral__le__real__of__nat__iff,axiom,
% 5.12/5.39 ! [N: num,M2: nat] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 5.12/5.39 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_le_real_of_nat_iff
% 5.12/5.39 thf(fact_5054_nat__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = zero_zero_nat ) ).
% 5.12/5.39
% 5.12/5.39 % nat_neg_numeral
% 5.12/5.39 thf(fact_5055_norm__of__nat,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.39 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_of_nat
% 5.12/5.39 thf(fact_5056_norm__of__nat,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( semiri8010041392384452111omplex @ N ) )
% 5.12/5.39 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_of_nat
% 5.12/5.39 thf(fact_5057_diff__nat__numeral,axiom,
% 5.12/5.39 ! [V: num,V2: num] :
% 5.12/5.39 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 5.12/5.39 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_nat_numeral
% 5.12/5.39 thf(fact_5058_numeral__power__eq__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = ( nat2 @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_nat_cancel_iff
% 5.12/5.39 thf(fact_5059_nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( nat2 @ Y )
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5060_floor__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [A: num,B: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.12/5.39 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5061_le__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5062_le__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5063_divide__le__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.12/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral1(1)
% 5.12/5.39 thf(fact_5064_divide__le__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.12/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral1(1)
% 5.12/5.39 thf(fact_5065_divide__eq__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: complex,W: num,A: complex] :
% 5.12/5.39 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 != zero_zero_complex )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.12/5.39 & ( ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 = zero_zero_complex )
% 5.12/5.39 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(1)
% 5.12/5.39 thf(fact_5066_divide__eq__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( numeral_numeral_real @ W )
% 5.12/5.39 != zero_zero_real )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.12/5.39 & ( ( ( numeral_numeral_real @ W )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(1)
% 5.12/5.39 thf(fact_5067_divide__eq__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( numeral_numeral_rat @ W )
% 5.12/5.39 != zero_zero_rat )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.12/5.39 & ( ( ( numeral_numeral_rat @ W )
% 5.12/5.39 = zero_zero_rat )
% 5.12/5.39 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(1)
% 5.12/5.39 thf(fact_5068_eq__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: complex,B: complex,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 != zero_zero_complex )
% 5.12/5.39 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 = zero_zero_complex )
% 5.12/5.39 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5069_eq__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( ( ( ( numeral_numeral_real @ W )
% 5.12/5.39 != zero_zero_real )
% 5.12/5.39 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( numeral_numeral_real @ W )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5070_eq__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( ( ( ( numeral_numeral_rat @ W )
% 5.12/5.39 != zero_zero_rat )
% 5.12/5.39 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( numeral_numeral_rat @ W )
% 5.12/5.39 = zero_zero_rat )
% 5.12/5.39 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5071_divide__less__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.12/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral1(1)
% 5.12/5.39 thf(fact_5072_divide__less__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.12/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral1(1)
% 5.12/5.39 thf(fact_5073_less__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5074_less__divide__eq__numeral1_I1_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral1(1)
% 5.12/5.39 thf(fact_5075_inverse__eq__divide__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_numeral
% 5.12/5.39 thf(fact_5076_inverse__eq__divide__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_numeral
% 5.12/5.39 thf(fact_5077_inverse__eq__divide__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_numeral
% 5.12/5.39 thf(fact_5078_zero__less__norm__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.12/5.39 = ( X != zero_zero_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_norm_iff
% 5.12/5.39 thf(fact_5079_zero__less__norm__iff,axiom,
% 5.12/5.39 ! [X: complex] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.12/5.39 = ( X != zero_zero_complex ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_norm_iff
% 5.12/5.39 thf(fact_5080_norm__le__zero__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.12/5.39 = ( X = zero_zero_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_le_zero_iff
% 5.12/5.39 thf(fact_5081_norm__le__zero__iff,axiom,
% 5.12/5.39 ! [X: complex] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.12/5.39 = ( X = zero_zero_complex ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_le_zero_iff
% 5.12/5.39 thf(fact_5082_of__int__numeral__le__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_le_iff
% 5.12/5.39 thf(fact_5083_of__int__numeral__le__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_le_iff
% 5.12/5.39 thf(fact_5084_of__int__numeral__le__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_le_iff
% 5.12/5.39 thf(fact_5085_of__int__le__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_iff
% 5.12/5.39 thf(fact_5086_of__int__le__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_iff
% 5.12/5.39 thf(fact_5087_of__int__le__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_iff
% 5.12/5.39 thf(fact_5088_of__int__numeral__less__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z2 ) )
% 5.12/5.39 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_less_iff
% 5.12/5.39 thf(fact_5089_of__int__numeral__less__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z2 ) )
% 5.12/5.39 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_less_iff
% 5.12/5.39 thf(fact_5090_of__int__numeral__less__iff,axiom,
% 5.12/5.39 ! [N: num,Z2: int] :
% 5.12/5.39 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z2 ) )
% 5.12/5.39 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_numeral_less_iff
% 5.12/5.39 thf(fact_5091_of__int__less__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_iff
% 5.12/5.39 thf(fact_5092_of__int__less__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_iff
% 5.12/5.39 thf(fact_5093_of__int__less__numeral__iff,axiom,
% 5.12/5.39 ! [Z2: int,N: num] :
% 5.12/5.39 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.39 = ( ord_less_int @ Z2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_iff
% 5.12/5.39 thf(fact_5094_norm__divide__numeral,axiom,
% 5.12/5.39 ! [A: real,W: num] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_divide_numeral
% 5.12/5.39 thf(fact_5095_norm__divide__numeral,axiom,
% 5.12/5.39 ! [A: complex,W: num] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_divide_numeral
% 5.12/5.39 thf(fact_5096_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: nat] :
% 5.12/5.39 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.12/5.39 = ( semiri8010041392384452111omplex @ Y ) )
% 5.12/5.39 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5097_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: nat] :
% 5.12/5.39 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.12/5.39 = ( semiri5074537144036343181t_real @ Y ) )
% 5.12/5.39 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5098_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: nat] :
% 5.12/5.39 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.12/5.39 = ( semiri681578069525770553at_rat @ Y ) )
% 5.12/5.39 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5099_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: nat] :
% 5.12/5.39 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.12/5.39 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5100_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: nat] :
% 5.12/5.39 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = ( semiri1314217659103216013at_int @ Y ) )
% 5.12/5.39 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5101_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: nat,X: num,N: nat] :
% 5.12/5.39 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.12/5.39 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5102_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: nat,X: num,N: nat] :
% 5.12/5.39 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.12/5.39 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5103_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: nat,X: num,N: nat] :
% 5.12/5.39 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.12/5.39 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5104_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: nat,X: num,N: nat] :
% 5.12/5.39 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5105_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: nat,X: num,N: nat] :
% 5.12/5.39 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % real_of_nat_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5106_numeral__le__floor,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.39 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_le_floor
% 5.12/5.39 thf(fact_5107_numeral__le__floor,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.39 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_le_floor
% 5.12/5.39 thf(fact_5108_floor__less__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_less_numeral
% 5.12/5.39 thf(fact_5109_floor__less__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_less_numeral
% 5.12/5.39 thf(fact_5110_ceiling__le__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_le_numeral
% 5.12/5.39 thf(fact_5111_ceiling__le__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_le_numeral
% 5.12/5.39 thf(fact_5112_numeral__less__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.39 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_less_ceiling
% 5.12/5.39 thf(fact_5113_numeral__less__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.39 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_less_ceiling
% 5.12/5.39 thf(fact_5114_floor__neg__numeral,axiom,
% 5.12/5.39 ! [V: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_neg_numeral
% 5.12/5.39 thf(fact_5115_floor__neg__numeral,axiom,
% 5.12/5.39 ! [V: num] :
% 5.12/5.39 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_neg_numeral
% 5.12/5.39 thf(fact_5116_ceiling__add__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.12/5.39 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_add_numeral
% 5.12/5.39 thf(fact_5117_ceiling__add__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.12/5.39 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_add_numeral
% 5.12/5.39 thf(fact_5118_floor__diff__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.12/5.39 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_diff_numeral
% 5.12/5.39 thf(fact_5119_floor__diff__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.12/5.39 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_diff_numeral
% 5.12/5.39 thf(fact_5120_ceiling__neg__numeral,axiom,
% 5.12/5.39 ! [V: num] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_neg_numeral
% 5.12/5.39 thf(fact_5121_ceiling__neg__numeral,axiom,
% 5.12/5.39 ! [V: num] :
% 5.12/5.39 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_neg_numeral
% 5.12/5.39 thf(fact_5122_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.12/5.39 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5123_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_real @ Y )
% 5.12/5.39 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5124_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_rat @ Y )
% 5.12/5.39 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5125_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_int @ Y )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5126_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.12/5.39 = ( ring_17405671764205052669omplex @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5127_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.12/5.39 = ( ring_1_of_int_real @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5128_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.12/5.39 = ( ring_1_of_int_rat @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5129_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = ( ring_1_of_int_int @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5130_ceiling__diff__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.12/5.39 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_diff_numeral
% 5.12/5.39 thf(fact_5131_ceiling__diff__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.12/5.39 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_diff_numeral
% 5.12/5.39 thf(fact_5132_powr__numeral,axiom,
% 5.12/5.39 ! [X: real,N: num] :
% 5.12/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.39 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % powr_numeral
% 5.12/5.39 thf(fact_5133_Suc__times__numeral__mod__eq,axiom,
% 5.12/5.39 ! [K: num,N: nat] :
% 5.12/5.39 ( ( ( numeral_numeral_nat @ K )
% 5.12/5.39 != one_one_nat )
% 5.12/5.39 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.39 = one_one_nat ) ) ).
% 5.12/5.39
% 5.12/5.39 % Suc_times_numeral_mod_eq
% 5.12/5.39 thf(fact_5134_floor__numeral__power,axiom,
% 5.12/5.39 ! [X: num,N: nat] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_numeral_power
% 5.12/5.39 thf(fact_5135_floor__numeral__power,axiom,
% 5.12/5.39 ! [X: num,N: nat] :
% 5.12/5.39 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_numeral_power
% 5.12/5.39 thf(fact_5136_ceiling__numeral__power,axiom,
% 5.12/5.39 ! [X: num,N: nat] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_numeral_power
% 5.12/5.39 thf(fact_5137_ceiling__numeral__power,axiom,
% 5.12/5.39 ! [X: num,N: nat] :
% 5.12/5.39 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_numeral_power
% 5.12/5.39 thf(fact_5138_ceiling__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [A: num,B: num] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5139_le__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.12/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5140_le__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.12/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5141_divide__le__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.12/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral1(2)
% 5.12/5.39 thf(fact_5142_divide__le__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.12/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral1(2)
% 5.12/5.39 thf(fact_5143_divide__eq__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 != zero_zero_real )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.12/5.39 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(2)
% 5.12/5.39 thf(fact_5144_divide__eq__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: complex,W: num,A: complex] :
% 5.12/5.39 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 != zero_zero_complex )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.12/5.39 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = zero_zero_complex )
% 5.12/5.39 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(2)
% 5.12/5.39 thf(fact_5145_divide__eq__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = A )
% 5.12/5.39 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 != zero_zero_rat )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.12/5.39 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = zero_zero_rat )
% 5.12/5.39 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral1(2)
% 5.12/5.39 thf(fact_5146_eq__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.12/5.39 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 != zero_zero_real )
% 5.12/5.39 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 => ( A = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5147_eq__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: complex,B: complex,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.12/5.39 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 != zero_zero_complex )
% 5.12/5.39 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = zero_zero_complex )
% 5.12/5.39 => ( A = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5148_eq__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( A
% 5.12/5.39 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.12/5.39 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 != zero_zero_rat )
% 5.12/5.39 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = zero_zero_rat )
% 5.12/5.39 => ( A = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5149_divide__less__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: real,W: num,A: real] :
% 5.12/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.12/5.39 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral1(2)
% 5.12/5.39 thf(fact_5150_divide__less__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [B: rat,W: num,A: rat] :
% 5.12/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.12/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral1(2)
% 5.12/5.39 thf(fact_5151_less__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: real,B: real,W: num] :
% 5.12/5.39 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.12/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5152_less__divide__eq__numeral1_I2_J,axiom,
% 5.12/5.39 ! [A: rat,B: rat,W: num] :
% 5.12/5.39 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.12/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral1(2)
% 5.12/5.39 thf(fact_5153_dbl__inc__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_inc_simps(1)
% 5.12/5.39 thf(fact_5154_dbl__inc__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_inc_simps(1)
% 5.12/5.39 thf(fact_5155_dbl__inc__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_inc_simps(1)
% 5.12/5.39 thf(fact_5156_dbl__inc__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_inc_simps(1)
% 5.12/5.39 thf(fact_5157_dbl__inc__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_inc_simps(1)
% 5.12/5.39 thf(fact_5158_dbl__dec__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_dec_simps(1)
% 5.12/5.39 thf(fact_5159_dbl__dec__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_dec_simps(1)
% 5.12/5.39 thf(fact_5160_dbl__dec__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_dec_simps(1)
% 5.12/5.39 thf(fact_5161_dbl__dec__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_dec_simps(1)
% 5.12/5.39 thf(fact_5162_dbl__dec__simps_I1_J,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % dbl_dec_simps(1)
% 5.12/5.39 thf(fact_5163_inverse__eq__divide__neg__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_neg_numeral
% 5.12/5.39 thf(fact_5164_inverse__eq__divide__neg__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_neg_numeral
% 5.12/5.39 thf(fact_5165_inverse__eq__divide__neg__numeral,axiom,
% 5.12/5.39 ! [W: num] :
% 5.12/5.39 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inverse_eq_divide_neg_numeral
% 5.12/5.39 thf(fact_5166_nat__numeral__diff__1,axiom,
% 5.12/5.39 ! [V: num] :
% 5.12/5.39 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.12/5.39 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nat_numeral_diff_1
% 5.12/5.39 thf(fact_5167_numeral__power__less__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_nat_cancel_iff
% 5.12/5.39 thf(fact_5168_nat__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nat_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5169_numeral__power__le__nat__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_nat_cancel_iff
% 5.12/5.39 thf(fact_5170_nat__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nat_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5171_floor__one__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [B: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.12/5.39 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_one_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5172_floor__minus__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [A: num,B: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.12/5.39 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_minus_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5173_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [A: num,B: num] :
% 5.12/5.39 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_minus_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5174_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.12/5.39 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5175_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.12/5.39 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5176_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.12/5.39 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5177_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.12/5.39 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5178_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5179_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5180_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5181_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5182_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.12/5.39 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5183_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.12/5.39 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5184_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.12/5.39 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5185_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.12/5.39 ! [I: num,N: nat,X: nat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.12/5.39 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_nat_cancel_iff
% 5.12/5.39 thf(fact_5186_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5187_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5188_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5189_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [X: nat,I: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_nat_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5190_numeral__less__floor,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.39 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_less_floor
% 5.12/5.39 thf(fact_5191_numeral__less__floor,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.39 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_less_floor
% 5.12/5.39 thf(fact_5192_floor__le__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_le_numeral
% 5.12/5.39 thf(fact_5193_floor__le__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_le_numeral
% 5.12/5.39 thf(fact_5194_ceiling__less__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_less_numeral
% 5.12/5.39 thf(fact_5195_ceiling__less__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.12/5.39 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_less_numeral
% 5.12/5.39 thf(fact_5196_numeral__le__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.39 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_le_ceiling
% 5.12/5.39 thf(fact_5197_numeral__le__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.39 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_le_ceiling
% 5.12/5.39 thf(fact_5198_neg__numeral__le__floor,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.39 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_floor
% 5.12/5.39 thf(fact_5199_neg__numeral__le__floor,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.39 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_floor
% 5.12/5.39 thf(fact_5200_floor__less__neg__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_less_neg_numeral
% 5.12/5.39 thf(fact_5201_floor__less__neg__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_less_neg_numeral
% 5.12/5.39 thf(fact_5202_ceiling__le__neg__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_le_neg_numeral
% 5.12/5.39 thf(fact_5203_ceiling__le__neg__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_le_neg_numeral
% 5.12/5.39 thf(fact_5204_of__int__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5205_of__int__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5206_of__int__le__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5207_numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5208_numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5209_numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5210_neg__numeral__less__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.39 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_ceiling
% 5.12/5.39 thf(fact_5211_neg__numeral__less__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.39 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_ceiling
% 5.12/5.39 thf(fact_5212_of__int__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5213_of__int__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5214_of__int__less__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5215_numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5216_numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5217_numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5218_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_int @ Y )
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5219_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_real @ Y )
% 5.12/5.39 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5220_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.12/5.39 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5221_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.12/5.39 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5222_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [Y: int,X: num,N: nat] :
% 5.12/5.39 ( ( ( ring_1_of_int_rat @ Y )
% 5.12/5.39 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.12/5.39 = ( Y
% 5.12/5.39 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_eq_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5223_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = ( ring_1_of_int_int @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5224_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 5.12/5.39 = ( ring_1_of_int_real @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5225_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 5.12/5.39 = ( ring_17405671764205052669omplex @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5226_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 5.12/5.39 = ( ring_18347121197199848620nteger @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5227_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,Y: int] :
% 5.12/5.39 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 5.12/5.39 = ( ring_1_of_int_rat @ Y ) )
% 5.12/5.39 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_eq_of_int_cancel_iff
% 5.12/5.39 thf(fact_5228_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.12/5.39 ! [B: num] :
% 5.12/5.39 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.12/5.39 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_minus_one_divide_eq_div_numeral
% 5.12/5.39 thf(fact_5229_neg__numeral__less__floor,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.39 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_floor
% 5.12/5.39 thf(fact_5230_neg__numeral__less__floor,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.39 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_floor
% 5.12/5.39 thf(fact_5231_floor__le__neg__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_le_neg_numeral
% 5.12/5.39 thf(fact_5232_floor__le__neg__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % floor_le_neg_numeral
% 5.12/5.39 thf(fact_5233_ceiling__less__neg__numeral,axiom,
% 5.12/5.39 ! [X: real,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_less_neg_numeral
% 5.12/5.39 thf(fact_5234_ceiling__less__neg__numeral,axiom,
% 5.12/5.39 ! [X: rat,V: num] :
% 5.12/5.39 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.12/5.39 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_less_neg_numeral
% 5.12/5.39 thf(fact_5235_neg__numeral__le__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: real] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.12/5.39 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_ceiling
% 5.12/5.39 thf(fact_5236_neg__numeral__le__ceiling,axiom,
% 5.12/5.39 ! [V: num,X: rat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.12/5.39 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_ceiling
% 5.12/5.39 thf(fact_5237_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5238_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5239_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5240_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_le_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5241_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5242_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5243_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5244_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.12/5.39 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_le_of_int_cancel_iff
% 5.12/5.39 thf(fact_5245_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5246_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5247_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5248_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.12/5.39 ! [A: int,X: num,N: nat] :
% 5.12/5.39 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.12/5.39 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_less_neg_numeral_power_cancel_iff
% 5.12/5.39 thf(fact_5249_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5250_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5251_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5252_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.12/5.39 ! [X: num,N: nat,A: int] :
% 5.12/5.39 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.12/5.39 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_power_less_of_int_cancel_iff
% 5.12/5.39 thf(fact_5253_int__ops_I3_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.12/5.39 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % int_ops(3)
% 5.12/5.39 thf(fact_5254_nat__numeral__as__int,axiom,
% 5.12/5.39 ( numeral_numeral_nat
% 5.12/5.39 = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nat_numeral_as_int
% 5.12/5.39 thf(fact_5255_norm__minus__commute,axiom,
% 5.12/5.39 ! [A: complex,B: complex] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.12/5.39 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_minus_commute
% 5.12/5.39 thf(fact_5256_zero__neq__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_complex
% 5.12/5.39 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_numeral
% 5.12/5.39 thf(fact_5257_zero__neq__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_real
% 5.12/5.39 != ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_numeral
% 5.12/5.39 thf(fact_5258_zero__neq__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_rat
% 5.12/5.39 != ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_numeral
% 5.12/5.39 thf(fact_5259_zero__neq__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_nat
% 5.12/5.39 != ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_numeral
% 5.12/5.39 thf(fact_5260_zero__neq__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_int
% 5.12/5.39 != ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_numeral
% 5.12/5.39 thf(fact_5261_div__mult2__numeral__eq,axiom,
% 5.12/5.39 ! [A: nat,K: num,L: num] :
% 5.12/5.39 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.12/5.39 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % div_mult2_numeral_eq
% 5.12/5.39 thf(fact_5262_div__mult2__numeral__eq,axiom,
% 5.12/5.39 ! [A: int,K: num,L: num] :
% 5.12/5.39 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.12/5.39 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % div_mult2_numeral_eq
% 5.12/5.39 thf(fact_5263_numeral__neq__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( numeral_numeral_int @ M2 )
% 5.12/5.39 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_numeral
% 5.12/5.39 thf(fact_5264_numeral__neq__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( numeral_numeral_real @ M2 )
% 5.12/5.39 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_numeral
% 5.12/5.39 thf(fact_5265_numeral__neq__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( numera6690914467698888265omplex @ M2 )
% 5.12/5.39 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_numeral
% 5.12/5.39 thf(fact_5266_numeral__neq__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( numera6620942414471956472nteger @ M2 )
% 5.12/5.39 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_numeral
% 5.12/5.39 thf(fact_5267_numeral__neq__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( numeral_numeral_rat @ M2 )
% 5.12/5.39 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_numeral
% 5.12/5.39 thf(fact_5268_neg__numeral__neq__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.39 != ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_neq_numeral
% 5.12/5.39 thf(fact_5269_neg__numeral__neq__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 5.12/5.39 != ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_neq_numeral
% 5.12/5.39 thf(fact_5270_neg__numeral__neq__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 5.12/5.39 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_neq_numeral
% 5.12/5.39 thf(fact_5271_neg__numeral__neq__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 5.12/5.39 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_neq_numeral
% 5.12/5.39 thf(fact_5272_neg__numeral__neq__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 5.12/5.39 != ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_neq_numeral
% 5.12/5.39 thf(fact_5273_Ints__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( member_complex @ ( numera6690914467698888265omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.12/5.39
% 5.12/5.39 % Ints_numeral
% 5.12/5.39 thf(fact_5274_Ints__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( member_real @ ( numeral_numeral_real @ N ) @ ring_1_Ints_real ) ).
% 5.12/5.39
% 5.12/5.39 % Ints_numeral
% 5.12/5.39 thf(fact_5275_Ints__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.12/5.39
% 5.12/5.39 % Ints_numeral
% 5.12/5.39 thf(fact_5276_Ints__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 5.12/5.39
% 5.12/5.39 % Ints_numeral
% 5.12/5.39 thf(fact_5277_of__int__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_neg_numeral
% 5.12/5.39 thf(fact_5278_of__int__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_neg_numeral
% 5.12/5.39 thf(fact_5279_of__int__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_neg_numeral
% 5.12/5.39 thf(fact_5280_of__int__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_neg_numeral
% 5.12/5.39 thf(fact_5281_of__int__neg__numeral,axiom,
% 5.12/5.39 ! [K: num] :
% 5.12/5.39 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_int_neg_numeral
% 5.12/5.39 thf(fact_5282_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.12/5.39 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.12/5.39 & ( ord_less_eq_set_nat @ B @ D )
% 5.12/5.39 & ( ( ord_less_set_nat @ C @ A )
% 5.12/5.39 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5283_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.39 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_rat @ C @ A )
% 5.12/5.39 & ( ord_less_eq_rat @ B @ D )
% 5.12/5.39 & ( ( ord_less_rat @ C @ A )
% 5.12/5.39 | ( ord_less_rat @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5284_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: num,B: num,C: num,D: num] :
% 5.12/5.39 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_num @ C @ A )
% 5.12/5.39 & ( ord_less_eq_num @ B @ D )
% 5.12/5.39 & ( ( ord_less_num @ C @ A )
% 5.12/5.39 | ( ord_less_num @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5285_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.39 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_int @ C @ A )
% 5.12/5.39 & ( ord_less_eq_int @ B @ D )
% 5.12/5.39 & ( ( ord_less_int @ C @ A )
% 5.12/5.39 | ( ord_less_int @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5286_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.39 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_nat @ C @ A )
% 5.12/5.39 & ( ord_less_eq_nat @ B @ D )
% 5.12/5.39 & ( ( ord_less_nat @ C @ A )
% 5.12/5.39 | ( ord_less_nat @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5287_atLeastatMost__psubset__iff,axiom,
% 5.12/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.39 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.12/5.39 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.12/5.39 | ( ( ord_less_eq_real @ C @ A )
% 5.12/5.39 & ( ord_less_eq_real @ B @ D )
% 5.12/5.39 & ( ( ord_less_real @ C @ A )
% 5.12/5.39 | ( ord_less_real @ B @ D ) ) ) )
% 5.12/5.39 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % atLeastatMost_psubset_iff
% 5.12/5.39 thf(fact_5288_norm__divide,axiom,
% 5.12/5.39 ! [A: real,B: real] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_divide
% 5.12/5.39 thf(fact_5289_norm__divide,axiom,
% 5.12/5.39 ! [A: complex,B: complex] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_divide
% 5.12/5.39 thf(fact_5290_zero__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_le_numeral
% 5.12/5.39 thf(fact_5291_zero__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_le_numeral
% 5.12/5.39 thf(fact_5292_zero__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_le_numeral
% 5.12/5.39 thf(fact_5293_zero__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_le_numeral
% 5.12/5.39 thf(fact_5294_not__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_zero
% 5.12/5.39 thf(fact_5295_not__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_zero
% 5.12/5.39 thf(fact_5296_not__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_zero
% 5.12/5.39 thf(fact_5297_not__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_zero
% 5.12/5.39 thf(fact_5298_zero__less__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_numeral
% 5.12/5.39 thf(fact_5299_zero__less__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_numeral
% 5.12/5.39 thf(fact_5300_zero__less__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_numeral
% 5.12/5.39 thf(fact_5301_zero__less__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_less_numeral
% 5.12/5.39 thf(fact_5302_not__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_zero
% 5.12/5.39 thf(fact_5303_not__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_zero
% 5.12/5.39 thf(fact_5304_not__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_zero
% 5.12/5.39 thf(fact_5305_not__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_zero
% 5.12/5.39 thf(fact_5306_one__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_le_numeral
% 5.12/5.39 thf(fact_5307_one__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_le_numeral
% 5.12/5.39 thf(fact_5308_one__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_le_numeral
% 5.12/5.39 thf(fact_5309_one__le__numeral,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_le_numeral
% 5.12/5.39 thf(fact_5310_not__numeral__less__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_one
% 5.12/5.39 thf(fact_5311_not__numeral__less__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_one
% 5.12/5.39 thf(fact_5312_not__numeral__less__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_one
% 5.12/5.39 thf(fact_5313_not__numeral__less__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_one
% 5.12/5.39 thf(fact_5314_not__numeral__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_numeral
% 5.12/5.39 thf(fact_5315_not__numeral__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_numeral
% 5.12/5.39 thf(fact_5316_not__numeral__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_numeral
% 5.12/5.39 thf(fact_5317_not__numeral__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_numeral
% 5.12/5.39 thf(fact_5318_neg__numeral__le__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_numeral
% 5.12/5.39 thf(fact_5319_neg__numeral__le__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_numeral
% 5.12/5.39 thf(fact_5320_neg__numeral__le__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_numeral
% 5.12/5.39 thf(fact_5321_neg__numeral__le__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_numeral
% 5.12/5.39 thf(fact_5322_zero__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_int
% 5.12/5.39 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_neg_numeral
% 5.12/5.39 thf(fact_5323_zero__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_real
% 5.12/5.39 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_neg_numeral
% 5.12/5.39 thf(fact_5324_zero__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_complex
% 5.12/5.39 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_neg_numeral
% 5.12/5.39 thf(fact_5325_zero__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_z3403309356797280102nteger
% 5.12/5.39 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_neg_numeral
% 5.12/5.39 thf(fact_5326_zero__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( zero_zero_rat
% 5.12/5.39 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zero_neq_neg_numeral
% 5.12/5.39 thf(fact_5327_neg__numeral__less__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_numeral
% 5.12/5.39 thf(fact_5328_neg__numeral__less__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_numeral
% 5.12/5.39 thf(fact_5329_neg__numeral__less__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_numeral
% 5.12/5.39 thf(fact_5330_neg__numeral__less__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_numeral
% 5.12/5.39 thf(fact_5331_not__numeral__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_numeral
% 5.12/5.39 thf(fact_5332_not__numeral__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_numeral
% 5.12/5.39 thf(fact_5333_not__numeral__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_numeral
% 5.12/5.39 thf(fact_5334_not__numeral__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_numeral
% 5.12/5.39 thf(fact_5335_one__plus__numeral__commute,axiom,
% 5.12/5.39 ! [X: num] :
% 5.12/5.39 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.12/5.39 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_plus_numeral_commute
% 5.12/5.39 thf(fact_5336_one__plus__numeral__commute,axiom,
% 5.12/5.39 ! [X: num] :
% 5.12/5.39 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.12/5.39 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_plus_numeral_commute
% 5.12/5.39 thf(fact_5337_one__plus__numeral__commute,axiom,
% 5.12/5.39 ! [X: num] :
% 5.12/5.39 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.12/5.39 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_plus_numeral_commute
% 5.12/5.39 thf(fact_5338_one__plus__numeral__commute,axiom,
% 5.12/5.39 ! [X: num] :
% 5.12/5.39 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.12/5.39 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_plus_numeral_commute
% 5.12/5.39 thf(fact_5339_one__plus__numeral__commute,axiom,
% 5.12/5.39 ! [X: num] :
% 5.12/5.39 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.12/5.39 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_plus_numeral_commute
% 5.12/5.39 thf(fact_5340_numeral__times__minus__swap,axiom,
% 5.12/5.39 ! [W: num,X: int] :
% 5.12/5.39 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.12/5.39 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_times_minus_swap
% 5.12/5.39 thf(fact_5341_numeral__times__minus__swap,axiom,
% 5.12/5.39 ! [W: num,X: real] :
% 5.12/5.39 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.12/5.39 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_times_minus_swap
% 5.12/5.39 thf(fact_5342_numeral__times__minus__swap,axiom,
% 5.12/5.39 ! [W: num,X: complex] :
% 5.12/5.39 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.39 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_times_minus_swap
% 5.12/5.39 thf(fact_5343_numeral__times__minus__swap,axiom,
% 5.12/5.39 ! [W: num,X: code_integer] :
% 5.12/5.39 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.12/5.39 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_times_minus_swap
% 5.12/5.39 thf(fact_5344_numeral__times__minus__swap,axiom,
% 5.12/5.39 ! [W: num,X: rat] :
% 5.12/5.39 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.12/5.39 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_times_minus_swap
% 5.12/5.39 thf(fact_5345_numeral__neq__neg__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( numeral_numeral_int @ N )
% 5.12/5.39 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_one
% 5.12/5.39 thf(fact_5346_numeral__neq__neg__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( numeral_numeral_real @ N )
% 5.12/5.39 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_one
% 5.12/5.39 thf(fact_5347_numeral__neq__neg__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( numera6690914467698888265omplex @ N )
% 5.12/5.39 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_one
% 5.12/5.39 thf(fact_5348_numeral__neq__neg__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( numera6620942414471956472nteger @ N )
% 5.12/5.39 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_one
% 5.12/5.39 thf(fact_5349_numeral__neq__neg__one,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( numeral_numeral_rat @ N )
% 5.12/5.39 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_neq_neg_one
% 5.12/5.39 thf(fact_5350_one__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( one_one_int
% 5.12/5.39 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_neq_neg_numeral
% 5.12/5.39 thf(fact_5351_one__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( one_one_real
% 5.12/5.39 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_neq_neg_numeral
% 5.12/5.39 thf(fact_5352_one__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( one_one_complex
% 5.12/5.39 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_neq_neg_numeral
% 5.12/5.39 thf(fact_5353_one__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( one_one_Code_integer
% 5.12/5.39 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_neq_neg_numeral
% 5.12/5.39 thf(fact_5354_one__neq__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( one_one_rat
% 5.12/5.39 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_neq_neg_numeral
% 5.12/5.39 thf(fact_5355_norm__uminus__minus,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 5.12/5.39 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_uminus_minus
% 5.12/5.39 thf(fact_5356_norm__uminus__minus,axiom,
% 5.12/5.39 ! [X: complex,Y: complex] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 5.12/5.39 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_uminus_minus
% 5.12/5.39 thf(fact_5357_nonzero__norm__divide,axiom,
% 5.12/5.39 ! [B: real,A: real] :
% 5.12/5.39 ( ( B != zero_zero_real )
% 5.12/5.39 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nonzero_norm_divide
% 5.12/5.39 thf(fact_5358_nonzero__norm__divide,axiom,
% 5.12/5.39 ! [B: complex,A: complex] :
% 5.12/5.39 ( ( B != zero_zero_complex )
% 5.12/5.39 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nonzero_norm_divide
% 5.12/5.39 thf(fact_5359_power__eq__imp__eq__norm,axiom,
% 5.12/5.39 ! [W: real,N: nat,Z2: real] :
% 5.12/5.39 ( ( ( power_power_real @ W @ N )
% 5.12/5.39 = ( power_power_real @ Z2 @ N ) )
% 5.12/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.39 => ( ( real_V7735802525324610683m_real @ W )
% 5.12/5.39 = ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % power_eq_imp_eq_norm
% 5.12/5.39 thf(fact_5360_power__eq__imp__eq__norm,axiom,
% 5.12/5.39 ! [W: complex,N: nat,Z2: complex] :
% 5.12/5.39 ( ( ( power_power_complex @ W @ N )
% 5.12/5.39 = ( power_power_complex @ Z2 @ N ) )
% 5.12/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.39 => ( ( real_V1022390504157884413omplex @ W )
% 5.12/5.39 = ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % power_eq_imp_eq_norm
% 5.12/5.39 thf(fact_5361_norm__diff__triangle__less,axiom,
% 5.12/5.39 ! [X: complex,Y: complex,E1: real,Z2: complex,E22: real] :
% 5.12/5.39 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.12/5.39 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z2 ) ) @ E22 )
% 5.12/5.39 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_triangle_less
% 5.12/5.39 thf(fact_5362_norm__triangle__sub,axiom,
% 5.12/5.39 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_triangle_sub
% 5.12/5.39 thf(fact_5363_norm__triangle__ineq4,axiom,
% 5.12/5.39 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_triangle_ineq4
% 5.12/5.39 thf(fact_5364_norm__diff__triangle__le,axiom,
% 5.12/5.39 ! [X: complex,Y: complex,E1: real,Z2: complex,E22: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.12/5.39 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z2 ) ) @ E22 )
% 5.12/5.39 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z2 ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_triangle_le
% 5.12/5.39 thf(fact_5365_norm__triangle__le__diff,axiom,
% 5.12/5.39 ! [X: complex,Y: complex,E2: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.12/5.39 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_triangle_le_diff
% 5.12/5.39 thf(fact_5366_neg__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_zero
% 5.12/5.39 thf(fact_5367_neg__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_zero
% 5.12/5.39 thf(fact_5368_neg__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_zero
% 5.12/5.39 thf(fact_5369_neg__numeral__le__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_zero
% 5.12/5.39 thf(fact_5370_not__zero__le__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_le_neg_numeral
% 5.12/5.39 thf(fact_5371_not__zero__le__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_le_neg_numeral
% 5.12/5.39 thf(fact_5372_not__zero__le__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_le_neg_numeral
% 5.12/5.39 thf(fact_5373_not__zero__le__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_le_neg_numeral
% 5.12/5.39 thf(fact_5374_neg__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_zero
% 5.12/5.39 thf(fact_5375_neg__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_zero
% 5.12/5.39 thf(fact_5376_neg__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_zero
% 5.12/5.39 thf(fact_5377_neg__numeral__less__zero,axiom,
% 5.12/5.39 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_zero
% 5.12/5.39 thf(fact_5378_not__zero__less__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_less_neg_numeral
% 5.12/5.39 thf(fact_5379_not__zero__less__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_less_neg_numeral
% 5.12/5.39 thf(fact_5380_not__zero__less__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_less_neg_numeral
% 5.12/5.39 thf(fact_5381_not__zero__less__neg__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_zero_less_neg_numeral
% 5.12/5.39 thf(fact_5382_bset_I1_J,axiom,
% 5.12/5.39 ! [D6: int,B5: set_int,P: int > $o,Q: int > $o] :
% 5.12/5.39 ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ B5 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( P @ X3 )
% 5.12/5.39 => ( P @ ( minus_minus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ B5 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( Q @ X3 )
% 5.12/5.39 => ( Q @ ( minus_minus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ( P @ X4 )
% 5.12/5.39 & ( Q @ X4 ) )
% 5.12/5.39 => ( ( P @ ( minus_minus_int @ X4 @ D6 ) )
% 5.12/5.39 & ( Q @ ( minus_minus_int @ X4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(1)
% 5.12/5.39 thf(fact_5383_bset_I2_J,axiom,
% 5.12/5.39 ! [D6: int,B5: set_int,P: int > $o,Q: int > $o] :
% 5.12/5.39 ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ B5 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( P @ X3 )
% 5.12/5.39 => ( P @ ( minus_minus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ B5 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( Q @ X3 )
% 5.12/5.39 => ( Q @ ( minus_minus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ( P @ X4 )
% 5.12/5.39 | ( Q @ X4 ) )
% 5.12/5.39 => ( ( P @ ( minus_minus_int @ X4 @ D6 ) )
% 5.12/5.39 | ( Q @ ( minus_minus_int @ X4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(2)
% 5.12/5.39 thf(fact_5384_aset_I1_J,axiom,
% 5.12/5.39 ! [D6: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.12/5.39 ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ A2 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( P @ X3 )
% 5.12/5.39 => ( P @ ( plus_plus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ A2 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( Q @ X3 )
% 5.12/5.39 => ( Q @ ( plus_plus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ( P @ X4 )
% 5.12/5.39 & ( Q @ X4 ) )
% 5.12/5.39 => ( ( P @ ( plus_plus_int @ X4 @ D6 ) )
% 5.12/5.39 & ( Q @ ( plus_plus_int @ X4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(1)
% 5.12/5.39 thf(fact_5385_aset_I2_J,axiom,
% 5.12/5.39 ! [D6: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.12/5.39 ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ A2 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( P @ X3 )
% 5.12/5.39 => ( P @ ( plus_plus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ( ! [X3: int] :
% 5.12/5.39 ( ! [Xa2: int] :
% 5.12/5.39 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb: int] :
% 5.12/5.39 ( ( member_int @ Xb @ A2 )
% 5.12/5.39 => ( X3
% 5.12/5.39 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.12/5.39 => ( ( Q @ X3 )
% 5.12/5.39 => ( Q @ ( plus_plus_int @ X3 @ D6 ) ) ) )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ( P @ X4 )
% 5.12/5.39 | ( Q @ X4 ) )
% 5.12/5.39 => ( ( P @ ( plus_plus_int @ X4 @ D6 ) )
% 5.12/5.39 | ( Q @ ( plus_plus_int @ X4 @ D6 ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(2)
% 5.12/5.39 thf(fact_5386_norm__diff__ineq,axiom,
% 5.12/5.39 ! [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 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_ineq
% 5.12/5.39 thf(fact_5387_norm__diff__ineq,axiom,
% 5.12/5.39 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_ineq
% 5.12/5.39 thf(fact_5388_divide__eq__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: complex,C: complex,W: num] :
% 5.12/5.39 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.12/5.39 = ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = ( ( ( C != zero_zero_complex )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_complex )
% 5.12/5.39 => ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(1)
% 5.12/5.39 thf(fact_5389_divide__eq__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: real,C: real,W: num] :
% 5.12/5.39 ( ( ( divide_divide_real @ B @ C )
% 5.12/5.39 = ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( ( ( C != zero_zero_real )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_real )
% 5.12/5.39 => ( ( numeral_numeral_real @ W )
% 5.12/5.39 = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(1)
% 5.12/5.39 thf(fact_5390_divide__eq__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: rat,C: rat,W: num] :
% 5.12/5.39 ( ( ( divide_divide_rat @ B @ C )
% 5.12/5.39 = ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = ( ( ( C != zero_zero_rat )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_rat )
% 5.12/5.39 => ( ( numeral_numeral_rat @ W )
% 5.12/5.39 = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(1)
% 5.12/5.39 thf(fact_5391_eq__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: complex,C: complex] :
% 5.12/5.39 ( ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_complex )
% 5.12/5.39 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_complex )
% 5.12/5.39 => ( ( numera6690914467698888265omplex @ W )
% 5.12/5.39 = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5392_eq__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: real,C: real] :
% 5.12/5.39 ( ( ( numeral_numeral_real @ W )
% 5.12/5.39 = ( divide_divide_real @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_real )
% 5.12/5.39 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_real )
% 5.12/5.39 => ( ( numeral_numeral_real @ W )
% 5.12/5.39 = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5393_eq__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: rat,C: rat] :
% 5.12/5.39 ( ( ( numeral_numeral_rat @ W )
% 5.12/5.39 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_rat )
% 5.12/5.39 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_rat )
% 5.12/5.39 => ( ( numeral_numeral_rat @ W )
% 5.12/5.39 = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5394_norm__triangle__ineq2,axiom,
% 5.12/5.39 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_triangle_ineq2
% 5.12/5.39 thf(fact_5395_neg__numeral__le__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_one
% 5.12/5.39 thf(fact_5396_neg__numeral__le__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_one
% 5.12/5.39 thf(fact_5397_neg__numeral__le__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_one
% 5.12/5.39 thf(fact_5398_neg__numeral__le__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_one
% 5.12/5.39 thf(fact_5399_neg__one__le__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_le_numeral
% 5.12/5.39 thf(fact_5400_neg__one__le__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_le_numeral
% 5.12/5.39 thf(fact_5401_neg__one__le__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_le_numeral
% 5.12/5.39 thf(fact_5402_neg__one__le__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_le_numeral
% 5.12/5.39 thf(fact_5403_neg__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_neg_one
% 5.12/5.39 thf(fact_5404_neg__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_neg_one
% 5.12/5.39 thf(fact_5405_neg__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_neg_one
% 5.12/5.39 thf(fact_5406_neg__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_le_neg_one
% 5.12/5.39 thf(fact_5407_not__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_one
% 5.12/5.39 thf(fact_5408_not__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_one
% 5.12/5.39 thf(fact_5409_not__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_one
% 5.12/5.39 thf(fact_5410_not__numeral__le__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_le_neg_one
% 5.12/5.39 thf(fact_5411_not__one__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_le_neg_numeral
% 5.12/5.39 thf(fact_5412_not__one__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_le_neg_numeral
% 5.12/5.39 thf(fact_5413_not__one__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_le_neg_numeral
% 5.12/5.39 thf(fact_5414_not__one__le__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_le_neg_numeral
% 5.12/5.39 thf(fact_5415_neg__numeral__less__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_one
% 5.12/5.39 thf(fact_5416_neg__numeral__less__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_one
% 5.12/5.39 thf(fact_5417_neg__numeral__less__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_one
% 5.12/5.39 thf(fact_5418_neg__numeral__less__one,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 5.12/5.39
% 5.12/5.39 % neg_numeral_less_one
% 5.12/5.39 thf(fact_5419_neg__one__less__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_less_numeral
% 5.12/5.39 thf(fact_5420_neg__one__less__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_less_numeral
% 5.12/5.39 thf(fact_5421_neg__one__less__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_less_numeral
% 5.12/5.39 thf(fact_5422_neg__one__less__numeral,axiom,
% 5.12/5.39 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_less_numeral
% 5.12/5.39 thf(fact_5423_not__numeral__less__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_one
% 5.12/5.39 thf(fact_5424_not__numeral__less__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_one
% 5.12/5.39 thf(fact_5425_not__numeral__less__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_one
% 5.12/5.39 thf(fact_5426_not__numeral__less__neg__one,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_numeral_less_neg_one
% 5.12/5.39 thf(fact_5427_not__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_less_neg_numeral
% 5.12/5.39 thf(fact_5428_not__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_less_neg_numeral
% 5.12/5.39 thf(fact_5429_not__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_less_neg_numeral
% 5.12/5.39 thf(fact_5430_not__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_one_less_neg_numeral
% 5.12/5.39 thf(fact_5431_not__neg__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_less_neg_numeral
% 5.12/5.39 thf(fact_5432_not__neg__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_less_neg_numeral
% 5.12/5.39 thf(fact_5433_not__neg__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_less_neg_numeral
% 5.12/5.39 thf(fact_5434_not__neg__one__less__neg__numeral,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_less_neg_numeral
% 5.12/5.39 thf(fact_5435_nonzero__norm__inverse,axiom,
% 5.12/5.39 ! [A: real] :
% 5.12/5.39 ( ( A != zero_zero_real )
% 5.12/5.39 => ( ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ A ) )
% 5.12/5.39 = ( inverse_inverse_real @ ( real_V7735802525324610683m_real @ A ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nonzero_norm_inverse
% 5.12/5.39 thf(fact_5436_nonzero__norm__inverse,axiom,
% 5.12/5.39 ! [A: complex] :
% 5.12/5.39 ( ( A != zero_zero_complex )
% 5.12/5.39 => ( ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.12/5.39 = ( inverse_inverse_real @ ( real_V1022390504157884413omplex @ A ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % nonzero_norm_inverse
% 5.12/5.39 thf(fact_5437_norm__exp,axiom,
% 5.12/5.39 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_exp
% 5.12/5.39 thf(fact_5438_norm__exp,axiom,
% 5.12/5.39 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_exp
% 5.12/5.39 thf(fact_5439_powr__neg__numeral,axiom,
% 5.12/5.39 ! [X: real,N: num] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.39 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.39 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % powr_neg_numeral
% 5.12/5.39 thf(fact_5440_power__eq__1__iff,axiom,
% 5.12/5.39 ! [W: real,N: nat] :
% 5.12/5.39 ( ( ( power_power_real @ W @ N )
% 5.12/5.39 = one_one_real )
% 5.12/5.39 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.12/5.39 = one_one_real )
% 5.12/5.39 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % power_eq_1_iff
% 5.12/5.39 thf(fact_5441_power__eq__1__iff,axiom,
% 5.12/5.39 ! [W: complex,N: nat] :
% 5.12/5.39 ( ( ( power_power_complex @ W @ N )
% 5.12/5.39 = one_one_complex )
% 5.12/5.39 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.12/5.39 = one_one_real )
% 5.12/5.39 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % power_eq_1_iff
% 5.12/5.39 thf(fact_5442_norm__diff__triangle__ineq,axiom,
% 5.12/5.39 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_triangle_ineq
% 5.12/5.39 thf(fact_5443_norm__diff__triangle__ineq,axiom,
% 5.12/5.39 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_diff_triangle_ineq
% 5.12/5.39 thf(fact_5444_norm__sgn,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( X = zero_zero_real )
% 5.12/5.39 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 5.12/5.39 = zero_zero_real ) )
% 5.12/5.39 & ( ( X != zero_zero_real )
% 5.12/5.39 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 5.12/5.39 = one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_sgn
% 5.12/5.39 thf(fact_5445_norm__sgn,axiom,
% 5.12/5.39 ! [X: complex] :
% 5.12/5.39 ( ( ( X = zero_zero_complex )
% 5.12/5.39 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 5.12/5.39 = zero_zero_real ) )
% 5.12/5.39 & ( ( X != zero_zero_complex )
% 5.12/5.39 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 5.12/5.39 = one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_sgn
% 5.12/5.39 thf(fact_5446_divide__less__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: real,C: real,W: num] :
% 5.12/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral(1)
% 5.12/5.39 thf(fact_5447_divide__less__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: rat,C: rat,W: num] :
% 5.12/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral(1)
% 5.12/5.39 thf(fact_5448_less__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: real,C: real] :
% 5.12/5.39 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5449_less__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: rat,C: rat] :
% 5.12/5.39 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5450_divide__eq__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [B: real,C: real,W: num] :
% 5.12/5.39 ( ( ( divide_divide_real @ B @ C )
% 5.12/5.39 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( ( ( C != zero_zero_real )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_real )
% 5.12/5.39 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(2)
% 5.12/5.39 thf(fact_5451_divide__eq__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [B: complex,C: complex,W: num] :
% 5.12/5.39 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.39 = ( ( ( C != zero_zero_complex )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_complex )
% 5.12/5.39 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(2)
% 5.12/5.39 thf(fact_5452_divide__eq__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [B: rat,C: rat,W: num] :
% 5.12/5.39 ( ( ( divide_divide_rat @ B @ C )
% 5.12/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( ( ( C != zero_zero_rat )
% 5.12/5.39 => ( B
% 5.12/5.39 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ( C = zero_zero_rat )
% 5.12/5.39 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_eq_eq_numeral(2)
% 5.12/5.39 thf(fact_5453_eq__divide__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [W: num,B: real,C: real] :
% 5.12/5.39 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( divide_divide_real @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_real )
% 5.12/5.39 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_real )
% 5.12/5.39 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = zero_zero_real ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(2)
% 5.12/5.39 thf(fact_5454_eq__divide__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [W: num,B: complex,C: complex] :
% 5.12/5.39 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_complex )
% 5.12/5.39 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_complex )
% 5.12/5.39 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.12/5.39 = zero_zero_complex ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(2)
% 5.12/5.39 thf(fact_5455_eq__divide__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [W: num,B: rat,C: rat] :
% 5.12/5.39 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.39 = ( ( ( C != zero_zero_rat )
% 5.12/5.39 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.12/5.39 = B ) )
% 5.12/5.39 & ( ( C = zero_zero_rat )
% 5.12/5.39 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = zero_zero_rat ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % eq_divide_eq_numeral(2)
% 5.12/5.39 thf(fact_5456_norm__triangle__ineq3,axiom,
% 5.12/5.39 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_triangle_ineq3
% 5.12/5.39 thf(fact_5457_periodic__finite__ex,axiom,
% 5.12/5.39 ! [D: int,P: int > $o] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D )
% 5.12/5.39 => ( ! [X3: int,K2: int] :
% 5.12/5.39 ( ( P @ X3 )
% 5.12/5.39 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.12/5.39 => ( ( ? [X7: int] : ( P @ X7 ) )
% 5.12/5.39 = ( ? [X2: int] :
% 5.12/5.39 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.12/5.39 & ( P @ X2 ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % periodic_finite_ex
% 5.12/5.39 thf(fact_5458_bset_I3_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,B5: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B5 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( X4 = T )
% 5.12/5.39 => ( ( minus_minus_int @ X4 @ D6 )
% 5.12/5.39 = T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(3)
% 5.12/5.39 thf(fact_5459_bset_I4_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,B5: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ T @ B5 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( X4 != T )
% 5.12/5.39 => ( ( minus_minus_int @ X4 @ D6 )
% 5.12/5.39 != T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(4)
% 5.12/5.39 thf(fact_5460_bset_I5_J,axiom,
% 5.12/5.39 ! [D6: int,B5: set_int,T: int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_int @ X4 @ T )
% 5.12/5.39 => ( ord_less_int @ ( minus_minus_int @ X4 @ D6 ) @ T ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(5)
% 5.12/5.39 thf(fact_5461_bset_I7_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,B5: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ T @ B5 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_int @ T @ X4 )
% 5.12/5.39 => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D6 ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bset(7)
% 5.12/5.39 thf(fact_5462_aset_I3_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,A2: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( X4 = T )
% 5.12/5.39 => ( ( plus_plus_int @ X4 @ D6 )
% 5.12/5.39 = T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(3)
% 5.12/5.39 thf(fact_5463_aset_I4_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,A2: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ T @ A2 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( X4 != T )
% 5.12/5.39 => ( ( plus_plus_int @ X4 @ D6 )
% 5.12/5.39 != T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(4)
% 5.12/5.39 thf(fact_5464_aset_I5_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,A2: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ T @ A2 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_int @ X4 @ T )
% 5.12/5.39 => ( ord_less_int @ ( plus_plus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(5)
% 5.12/5.39 thf(fact_5465_aset_I7_J,axiom,
% 5.12/5.39 ! [D6: int,A2: set_int,T: int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_int @ T @ X4 )
% 5.12/5.39 => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D6 ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(7)
% 5.12/5.39 thf(fact_5466_divide__le__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: real,C: real,W: num] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral(1)
% 5.12/5.39 thf(fact_5467_divide__le__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [B: rat,C: rat,W: num] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_le_eq_numeral(1)
% 5.12/5.39 thf(fact_5468_le__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: real,C: real] :
% 5.12/5.39 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5469_le__divide__eq__numeral_I1_J,axiom,
% 5.12/5.39 ! [W: num,B: rat,C: rat] :
% 5.12/5.39 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % le_divide_eq_numeral(1)
% 5.12/5.39 thf(fact_5470_divide__less__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [B: real,C: real,W: num] :
% 5.12/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral(2)
% 5.12/5.39 thf(fact_5471_divide__less__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [B: rat,C: rat,W: num] :
% 5.12/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % divide_less_eq_numeral(2)
% 5.12/5.39 thf(fact_5472_less__divide__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [W: num,B: real,C: real] :
% 5.12/5.39 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.12/5.39 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral(2)
% 5.12/5.39 thf(fact_5473_less__divide__eq__numeral_I2_J,axiom,
% 5.12/5.39 ! [W: num,B: rat,C: rat] :
% 5.12/5.39 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.12/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.12/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.12/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.12/5.39 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % less_divide_eq_numeral(2)
% 5.12/5.39 thf(fact_5474_Cauchy__iff,axiom,
% 5.12/5.39 ( topolo6517432010174082258omplex
% 5.12/5.39 = ( ^ [X7: nat > complex] :
% 5.12/5.39 ! [E3: real] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.12/5.39 => ? [M7: nat] :
% 5.12/5.39 ! [M5: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.12/5.39 => ! [N4: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.12/5.39 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X7 @ M5 ) @ ( X7 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % Cauchy_iff
% 5.12/5.39 thf(fact_5475_Cauchy__iff,axiom,
% 5.12/5.39 ( topolo4055970368930404560y_real
% 5.12/5.39 = ( ^ [X7: nat > real] :
% 5.12/5.39 ! [E3: real] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.12/5.39 => ? [M7: nat] :
% 5.12/5.39 ! [M5: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.12/5.39 => ! [N4: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.12/5.39 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X7 @ M5 ) @ ( X7 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % Cauchy_iff
% 5.12/5.39 thf(fact_5476_CauchyI,axiom,
% 5.12/5.39 ! [X8: nat > complex] :
% 5.12/5.39 ( ! [E: real] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ E )
% 5.12/5.39 => ? [M8: nat] :
% 5.12/5.39 ! [M3: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.12/5.39 => ! [N2: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.12/5.39 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M3 ) @ ( X8 @ N2 ) ) ) @ E ) ) ) )
% 5.12/5.39 => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 5.12/5.39
% 5.12/5.39 % CauchyI
% 5.12/5.39 thf(fact_5477_CauchyI,axiom,
% 5.12/5.39 ! [X8: nat > real] :
% 5.12/5.39 ( ! [E: real] :
% 5.12/5.39 ( ( ord_less_real @ zero_zero_real @ E )
% 5.12/5.39 => ? [M8: nat] :
% 5.12/5.39 ! [M3: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.12/5.39 => ! [N2: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.12/5.39 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M3 ) @ ( X8 @ N2 ) ) ) @ E ) ) ) )
% 5.12/5.39 => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 5.12/5.39
% 5.12/5.39 % CauchyI
% 5.12/5.39 thf(fact_5478_CauchyD,axiom,
% 5.12/5.39 ! [X8: nat > complex,E2: real] :
% 5.12/5.39 ( ( topolo6517432010174082258omplex @ X8 )
% 5.12/5.39 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.12/5.39 => ? [M9: nat] :
% 5.12/5.39 ! [M: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M9 @ M )
% 5.12/5.39 => ! [N6: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.12/5.39 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % CauchyD
% 5.12/5.39 thf(fact_5479_CauchyD,axiom,
% 5.12/5.39 ! [X8: nat > real,E2: real] :
% 5.12/5.39 ( ( topolo4055970368930404560y_real @ X8 )
% 5.12/5.39 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.12/5.39 => ? [M9: nat] :
% 5.12/5.39 ! [M: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M9 @ M )
% 5.12/5.39 => ! [N6: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.12/5.39 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % CauchyD
% 5.12/5.39 thf(fact_5480_aset_I8_J,axiom,
% 5.12/5.39 ! [D6: int,A2: set_int,T: int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_eq_int @ T @ X4 )
% 5.12/5.39 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D6 ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(8)
% 5.12/5.39 thf(fact_5481_aset_I6_J,axiom,
% 5.12/5.39 ! [D6: int,T: int,A2: set_int] :
% 5.12/5.39 ( ( ord_less_int @ zero_zero_int @ D6 )
% 5.12/5.39 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.12/5.39 => ! [X4: int] :
% 5.12/5.39 ( ! [Xa3: int] :
% 5.12/5.39 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.39 => ! [Xb2: int] :
% 5.12/5.39 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.39 => ( X4
% 5.12/5.39 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.39 => ( ( ord_less_eq_int @ X4 @ T )
% 5.12/5.39 => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % aset(6)
% 5.12/5.39 thf(fact_5482_enat__ord__number_I2_J,axiom,
% 5.12/5.39 ! [M2: num,N: num] :
% 5.12/5.39 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.12/5.39 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % enat_ord_number(2)
% 5.12/5.39 thf(fact_5483_lemma__termdiff3,axiom,
% 5.12/5.39 ! [H: real,Z2: real,K5: real,N: nat] :
% 5.12/5.39 ( ( H != zero_zero_real )
% 5.12/5.39 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ K5 )
% 5.12/5.39 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z2 @ H ) ) @ K5 )
% 5.12/5.39 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z2 @ H ) @ N ) @ ( power_power_real @ Z2 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z2 @ ( 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 @ H ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % lemma_termdiff3
% 5.12/5.39 thf(fact_5484_lemma__termdiff3,axiom,
% 5.12/5.39 ! [H: complex,Z2: complex,K5: real,N: nat] :
% 5.12/5.39 ( ( H != zero_zero_complex )
% 5.12/5.39 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ K5 )
% 5.12/5.39 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z2 @ H ) ) @ K5 )
% 5.12/5.39 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z2 @ H ) @ N ) @ ( power_power_complex @ Z2 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z2 @ ( 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 @ H ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % lemma_termdiff3
% 5.12/5.39 thf(fact_5485_complex__mod__triangle__ineq2,axiom,
% 5.12/5.39 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.12/5.39
% 5.12/5.39 % complex_mod_triangle_ineq2
% 5.12/5.39 thf(fact_5486_complex__mod__minus__le__complex__mod,axiom,
% 5.12/5.39 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.12/5.39
% 5.12/5.39 % complex_mod_minus_le_complex_mod
% 5.12/5.39 thf(fact_5487_norm__of__real__add1,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 5.12/5.39 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_of_real_add1
% 5.12/5.39 thf(fact_5488_norm__of__real__add1,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 5.12/5.39 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % norm_of_real_add1
% 5.12/5.39 thf(fact_5489_ceiling__log__nat__eq__powr__iff,axiom,
% 5.12/5.39 ! [B: nat,K: nat,N: nat] :
% 5.12/5.39 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.39 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.39 => ( ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.12/5.39 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.12/5.39 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.12/5.39 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % ceiling_log_nat_eq_powr_iff
% 5.12/5.39 thf(fact_5490_diff__numeral__special_I5_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_special(5)
% 5.12/5.39 thf(fact_5491_diff__numeral__special_I5_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_special(5)
% 5.12/5.39 thf(fact_5492_diff__numeral__special_I5_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_special(5)
% 5.12/5.39 thf(fact_5493_diff__numeral__special_I5_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_special(5)
% 5.12/5.39 thf(fact_5494_diff__numeral__special_I5_J,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % diff_numeral_special(5)
% 5.12/5.39 thf(fact_5495_verit__eq__simplify_I8_J,axiom,
% 5.12/5.39 ! [X23: num,Y2: num] :
% 5.12/5.39 ( ( ( bit0 @ X23 )
% 5.12/5.39 = ( bit0 @ Y2 ) )
% 5.12/5.39 = ( X23 = Y2 ) ) ).
% 5.12/5.39
% 5.12/5.39 % verit_eq_simplify(8)
% 5.12/5.39 thf(fact_5496_pow__sum,axiom,
% 5.12/5.39 ! [A: nat,B: nat] :
% 5.12/5.39 ( ( 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 ) )
% 5.12/5.39 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.12/5.39
% 5.12/5.39 % pow_sum
% 5.12/5.39 thf(fact_5497_member__bound,axiom,
% 5.12/5.39 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 5.12/5.39 ( ( vEBT_vebt_member @ Tree @ X )
% 5.12/5.39 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.12/5.39 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % member_bound
% 5.12/5.39 thf(fact_5498_bit__concat__def,axiom,
% 5.12/5.39 ( vEBT_VEBT_bit_concat
% 5.12/5.39 = ( ^ [H2: nat,L2: nat,D4: nat] : ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D4 ) ) @ L2 ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % bit_concat_def
% 5.12/5.39 thf(fact_5499_numeral__eq__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( numera6690914467698888265omplex @ N )
% 5.12/5.39 = one_one_complex )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_one_iff
% 5.12/5.39 thf(fact_5500_numeral__eq__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( numeral_numeral_real @ N )
% 5.12/5.39 = one_one_real )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_one_iff
% 5.12/5.39 thf(fact_5501_numeral__eq__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( numeral_numeral_rat @ N )
% 5.12/5.39 = one_one_rat )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_one_iff
% 5.12/5.39 thf(fact_5502_numeral__eq__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( numeral_numeral_nat @ N )
% 5.12/5.39 = one_one_nat )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_one_iff
% 5.12/5.39 thf(fact_5503_numeral__eq__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( numeral_numeral_int @ N )
% 5.12/5.39 = one_one_int )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_one_iff
% 5.12/5.39 thf(fact_5504_one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( one_one_complex
% 5.12/5.39 = ( numera6690914467698888265omplex @ N ) )
% 5.12/5.39 = ( one = N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_eq_numeral_iff
% 5.12/5.39 thf(fact_5505_one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( one_one_real
% 5.12/5.39 = ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( one = N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_eq_numeral_iff
% 5.12/5.39 thf(fact_5506_one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( one_one_rat
% 5.12/5.39 = ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( one = N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_eq_numeral_iff
% 5.12/5.39 thf(fact_5507_one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( one_one_nat
% 5.12/5.39 = ( numeral_numeral_nat @ N ) )
% 5.12/5.39 = ( one = N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_eq_numeral_iff
% 5.12/5.39 thf(fact_5508_one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( one_one_int
% 5.12/5.39 = ( numeral_numeral_int @ N ) )
% 5.12/5.39 = ( one = N ) ) ).
% 5.12/5.39
% 5.12/5.39 % one_eq_numeral_iff
% 5.12/5.39 thf(fact_5509_of__real__eq__0__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( real_V1803761363581548252l_real @ X )
% 5.12/5.39 = zero_zero_real )
% 5.12/5.39 = ( X = zero_zero_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_0_iff
% 5.12/5.39 thf(fact_5510_of__real__eq__0__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( real_V4546457046886955230omplex @ X )
% 5.12/5.39 = zero_zero_complex )
% 5.12/5.39 = ( X = zero_zero_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_0_iff
% 5.12/5.39 thf(fact_5511_of__real__0,axiom,
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 5.12/5.39 = zero_zero_real ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_0
% 5.12/5.39 thf(fact_5512_of__real__0,axiom,
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 5.12/5.39 = zero_zero_complex ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_0
% 5.12/5.39 thf(fact_5513_of__real__eq__1__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( real_V1803761363581548252l_real @ X )
% 5.12/5.39 = one_one_real )
% 5.12/5.39 = ( X = one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_1_iff
% 5.12/5.39 thf(fact_5514_of__real__eq__1__iff,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( ( real_V4546457046886955230omplex @ X )
% 5.12/5.39 = one_one_complex )
% 5.12/5.39 = ( X = one_one_real ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_1_iff
% 5.12/5.39 thf(fact_5515_of__real__1,axiom,
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.12/5.39 = one_one_real ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_1
% 5.12/5.39 thf(fact_5516_of__real__1,axiom,
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.12/5.39 = one_one_complex ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_1
% 5.12/5.39 thf(fact_5517_zdiv__numeral__Bit0,axiom,
% 5.12/5.39 ! [V: num,W: num] :
% 5.12/5.39 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.12/5.39 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % zdiv_numeral_Bit0
% 5.12/5.39 thf(fact_5518_of__real__divide,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.39 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_divide
% 5.12/5.39 thf(fact_5519_of__real__divide,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.39 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_divide
% 5.12/5.39 thf(fact_5520_of__real__eq__minus__of__real__iff,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( ( real_V1803761363581548252l_real @ X )
% 5.12/5.39 = ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ Y ) ) )
% 5.12/5.39 = ( X
% 5.12/5.39 = ( uminus_uminus_real @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_minus_of_real_iff
% 5.12/5.39 thf(fact_5521_of__real__eq__minus__of__real__iff,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( ( real_V4546457046886955230omplex @ X )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ Y ) ) )
% 5.12/5.39 = ( X
% 5.12/5.39 = ( uminus_uminus_real @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_eq_minus_of_real_iff
% 5.12/5.39 thf(fact_5522_minus__of__real__eq__of__real__iff,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ X ) )
% 5.12/5.39 = ( real_V1803761363581548252l_real @ Y ) )
% 5.12/5.39 = ( ( uminus_uminus_real @ X )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % minus_of_real_eq_of_real_iff
% 5.12/5.39 thf(fact_5523_minus__of__real__eq__of__real__iff,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ X ) )
% 5.12/5.39 = ( real_V4546457046886955230omplex @ Y ) )
% 5.12/5.39 = ( ( uminus_uminus_real @ X )
% 5.12/5.39 = Y ) ) ).
% 5.12/5.39
% 5.12/5.39 % minus_of_real_eq_of_real_iff
% 5.12/5.39 thf(fact_5524_of__real__minus,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.39 = ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ X ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_minus
% 5.12/5.39 thf(fact_5525_of__real__minus,axiom,
% 5.12/5.39 ! [X: real] :
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ X ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ X ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_minus
% 5.12/5.39 thf(fact_5526_of__real__diff,axiom,
% 5.12/5.39 ! [X: real,Y: real] :
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.39 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_diff
% 5.12/5.39 thf(fact_5527_of__real__of__nat__eq,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.39 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_of_nat_eq
% 5.12/5.39 thf(fact_5528_of__real__of__nat__eq,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.39 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_of_nat_eq
% 5.12/5.39 thf(fact_5529_num__double,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.12/5.39 = ( bit0 @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % num_double
% 5.12/5.39 thf(fact_5530_of__real__fact,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V4546457046886955230omplex @ ( semiri2265585572941072030t_real @ N ) )
% 5.12/5.39 = ( semiri5044797733671781792omplex @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_fact
% 5.12/5.39 thf(fact_5531_of__real__fact,axiom,
% 5.12/5.39 ! [N: nat] :
% 5.12/5.39 ( ( real_V1803761363581548252l_real @ ( semiri2265585572941072030t_real @ N ) )
% 5.12/5.39 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.12/5.39
% 5.12/5.39 % of_real_fact
% 5.12/5.39 thf(fact_5532_numeral__eq__neg__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.12/5.39 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_neg_one_iff
% 5.12/5.39 thf(fact_5533_numeral__eq__neg__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.12/5.39 = ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_neg_one_iff
% 5.12/5.39 thf(fact_5534_numeral__eq__neg__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_neg_one_iff
% 5.12/5.39 thf(fact_5535_numeral__eq__neg__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_neg_one_iff
% 5.12/5.39 thf(fact_5536_numeral__eq__neg__one__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.12/5.39 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % numeral_eq_neg_one_iff
% 5.12/5.39 thf(fact_5537_neg__one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_int @ one_one_int )
% 5.12/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_eq_numeral_iff
% 5.12/5.39 thf(fact_5538_neg__one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_real @ one_one_real )
% 5.12/5.39 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_eq_numeral_iff
% 5.12/5.39 thf(fact_5539_neg__one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.12/5.39 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_eq_numeral_iff
% 5.12/5.39 thf(fact_5540_neg__one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.12/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_eq_numeral_iff
% 5.12/5.39 thf(fact_5541_neg__one__eq__numeral__iff,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.12/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.39 = ( N = one ) ) ).
% 5.12/5.39
% 5.12/5.39 % neg_one_eq_numeral_iff
% 5.12/5.39 thf(fact_5542_Suc__numeral,axiom,
% 5.12/5.39 ! [N: num] :
% 5.12/5.39 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.12/5.39 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % Suc_numeral
% 5.12/5.39 thf(fact_5543_inrange,axiom,
% 5.12/5.39 ! [T: vEBT_VEBT,N: nat] :
% 5.12/5.39 ( ( vEBT_invar_vebt @ T @ N )
% 5.12/5.39 => ( 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 ) ) ) ) ).
% 5.12/5.39
% 5.12/5.39 % inrange
% 5.12/5.39 thf(fact_5544_not__neg__one__le__neg__numeral__iff,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 5.12/5.39 = ( M2 != one ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_le_neg_numeral_iff
% 5.12/5.39 thf(fact_5545_not__neg__one__le__neg__numeral__iff,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 5.12/5.39 = ( M2 != one ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_le_neg_numeral_iff
% 5.12/5.39 thf(fact_5546_not__neg__one__le__neg__numeral__iff,axiom,
% 5.12/5.39 ! [M2: num] :
% 5.12/5.39 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 5.12/5.39 = ( M2 != one ) ) ).
% 5.12/5.39
% 5.12/5.39 % not_neg_one_le_neg_numeral_iff
% 5.12/5.39 thf(fact_5547_not__neg__one__le__neg__numeral__iff,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 5.12/5.40 = ( M2 != one ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_neg_one_le_neg_numeral_iff
% 5.12/5.40 thf(fact_5548_neg__numeral__less__neg__one__iff,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( M2 != one ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_numeral_less_neg_one_iff
% 5.12/5.40 thf(fact_5549_neg__numeral__less__neg__one__iff,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( M2 != one ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_numeral_less_neg_one_iff
% 5.12/5.40 thf(fact_5550_neg__numeral__less__neg__one__iff,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( M2 != one ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_numeral_less_neg_one_iff
% 5.12/5.40 thf(fact_5551_neg__numeral__less__neg__one__iff,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( M2 != one ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_numeral_less_neg_one_iff
% 5.12/5.40 thf(fact_5552_one__add__one,axiom,
% 5.12/5.40 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_add_one
% 5.12/5.40 thf(fact_5553_one__add__one,axiom,
% 5.12/5.40 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_add_one
% 5.12/5.40 thf(fact_5554_one__add__one,axiom,
% 5.12/5.40 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_add_one
% 5.12/5.40 thf(fact_5555_one__add__one,axiom,
% 5.12/5.40 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.12/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_add_one
% 5.12/5.40 thf(fact_5556_one__add__one,axiom,
% 5.12/5.40 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_add_one
% 5.12/5.40 thf(fact_5557_zero__eq__power2,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_rat )
% 5.12/5.40 = ( A = zero_zero_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_eq_power2
% 5.12/5.40 thf(fact_5558_zero__eq__power2,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_int )
% 5.12/5.40 = ( A = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_eq_power2
% 5.12/5.40 thf(fact_5559_zero__eq__power2,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat )
% 5.12/5.40 = ( A = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_eq_power2
% 5.12/5.40 thf(fact_5560_zero__eq__power2,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_real )
% 5.12/5.40 = ( A = zero_zero_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_eq_power2
% 5.12/5.40 thf(fact_5561_zero__eq__power2,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_complex )
% 5.12/5.40 = ( A = zero_zero_complex ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_eq_power2
% 5.12/5.40 thf(fact_5562_one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % one_mod_two_eq_one
% 5.12/5.40 thf(fact_5563_one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % one_mod_two_eq_one
% 5.12/5.40 thf(fact_5564_one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer ) ).
% 5.12/5.40
% 5.12/5.40 % one_mod_two_eq_one
% 5.12/5.40 thf(fact_5565_one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_natural ) ).
% 5.12/5.40
% 5.12/5.40 % one_mod_two_eq_one
% 5.12/5.40 thf(fact_5566_bits__one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % bits_one_mod_two_eq_one
% 5.12/5.40 thf(fact_5567_bits__one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % bits_one_mod_two_eq_one
% 5.12/5.40 thf(fact_5568_bits__one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer ) ).
% 5.12/5.40
% 5.12/5.40 % bits_one_mod_two_eq_one
% 5.12/5.40 thf(fact_5569_bits__one__mod__two__eq__one,axiom,
% 5.12/5.40 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_natural ) ).
% 5.12/5.40
% 5.12/5.40 % bits_one_mod_two_eq_one
% 5.12/5.40 thf(fact_5570_power2__minus,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_minus
% 5.12/5.40 thf(fact_5571_power2__minus,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_minus
% 5.12/5.40 thf(fact_5572_power2__minus,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_minus
% 5.12/5.40 thf(fact_5573_power2__minus,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_minus
% 5.12/5.40 thf(fact_5574_power2__minus,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_minus
% 5.12/5.40 thf(fact_5575_add__2__eq__Suc_H,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( suc @ ( suc @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_2_eq_Suc'
% 5.12/5.40 thf(fact_5576_add__2__eq__Suc,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 = ( suc @ ( suc @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_2_eq_Suc
% 5.12/5.40 thf(fact_5577_Suc__1,axiom,
% 5.12/5.40 ( ( suc @ one_one_nat )
% 5.12/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_1
% 5.12/5.40 thf(fact_5578_div2__Suc__Suc,axiom,
% 5.12/5.40 ! [M2: nat] :
% 5.12/5.40 ( ( divide_divide_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( suc @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div2_Suc_Suc
% 5.12/5.40 thf(fact_5579_add__self__div__2,axiom,
% 5.12/5.40 ! [M2: nat] :
% 5.12/5.40 ( ( divide_divide_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = M2 ) ).
% 5.12/5.40
% 5.12/5.40 % add_self_div_2
% 5.12/5.40 thf(fact_5580_mod2__Suc__Suc,axiom,
% 5.12/5.40 ! [M2: nat] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod2_Suc_Suc
% 5.12/5.40 thf(fact_5581_one__plus__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_plus_numeral
% 5.12/5.40 thf(fact_5582_one__plus__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_plus_numeral
% 5.12/5.40 thf(fact_5583_one__plus__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_plus_numeral
% 5.12/5.40 thf(fact_5584_one__plus__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.40 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_plus_numeral
% 5.12/5.40 thf(fact_5585_one__plus__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_plus_numeral
% 5.12/5.40 thf(fact_5586_numeral__plus__one,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_plus_one
% 5.12/5.40 thf(fact_5587_numeral__plus__one,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.12/5.40 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_plus_one
% 5.12/5.40 thf(fact_5588_numeral__plus__one,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.12/5.40 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_plus_one
% 5.12/5.40 thf(fact_5589_numeral__plus__one,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.12/5.40 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_plus_one
% 5.12/5.40 thf(fact_5590_numeral__plus__one,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.12/5.40 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_plus_one
% 5.12/5.40 thf(fact_5591_of__real__neg__numeral,axiom,
% 5.12/5.40 ! [W: num] :
% 5.12/5.40 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_real_neg_numeral
% 5.12/5.40 thf(fact_5592_of__real__neg__numeral,axiom,
% 5.12/5.40 ! [W: num] :
% 5.12/5.40 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_real_neg_numeral
% 5.12/5.40 thf(fact_5593_numeral__le__one__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.12/5.40 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_le_one_iff
% 5.12/5.40 thf(fact_5594_numeral__le__one__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.12/5.40 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_le_one_iff
% 5.12/5.40 thf(fact_5595_numeral__le__one__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.12/5.40 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_le_one_iff
% 5.12/5.40 thf(fact_5596_numeral__le__one__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.12/5.40 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_le_one_iff
% 5.12/5.40 thf(fact_5597_one__less__numeral__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.12/5.40 = ( ord_less_num @ one @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_numeral_iff
% 5.12/5.40 thf(fact_5598_one__less__numeral__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.12/5.40 = ( ord_less_num @ one @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_numeral_iff
% 5.12/5.40 thf(fact_5599_one__less__numeral__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.40 = ( ord_less_num @ one @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_numeral_iff
% 5.12/5.40 thf(fact_5600_one__less__numeral__iff,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.12/5.40 = ( ord_less_num @ one @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_numeral_iff
% 5.12/5.40 thf(fact_5601_add__neg__numeral__special_I5_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(5)
% 5.12/5.40 thf(fact_5602_add__neg__numeral__special_I5_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(5)
% 5.12/5.40 thf(fact_5603_add__neg__numeral__special_I5_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(5)
% 5.12/5.40 thf(fact_5604_add__neg__numeral__special_I5_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(5)
% 5.12/5.40 thf(fact_5605_add__neg__numeral__special_I5_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(5)
% 5.12/5.40 thf(fact_5606_add__neg__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(6)
% 5.12/5.40 thf(fact_5607_add__neg__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(6)
% 5.12/5.40 thf(fact_5608_add__neg__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(6)
% 5.12/5.40 thf(fact_5609_add__neg__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(6)
% 5.12/5.40 thf(fact_5610_add__neg__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(6)
% 5.12/5.40 thf(fact_5611_diff__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( inc @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(6)
% 5.12/5.40 thf(fact_5612_diff__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( inc @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(6)
% 5.12/5.40 thf(fact_5613_diff__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( inc @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(6)
% 5.12/5.40 thf(fact_5614_diff__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(6)
% 5.12/5.40 thf(fact_5615_diff__numeral__special_I6_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(6)
% 5.12/5.40 thf(fact_5616_one__div__two__eq__zero,axiom,
% 5.12/5.40 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % one_div_two_eq_zero
% 5.12/5.40 thf(fact_5617_one__div__two__eq__zero,axiom,
% 5.12/5.40 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % one_div_two_eq_zero
% 5.12/5.40 thf(fact_5618_bits__1__div__2,axiom,
% 5.12/5.40 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % bits_1_div_2
% 5.12/5.40 thf(fact_5619_bits__1__div__2,axiom,
% 5.12/5.40 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % bits_1_div_2
% 5.12/5.40 thf(fact_5620_power2__less__eq__zero__iff,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.12/5.40 = ( A = zero_zero_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_eq_zero_iff
% 5.12/5.40 thf(fact_5621_power2__less__eq__zero__iff,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.12/5.40 = ( A = zero_zero_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_eq_zero_iff
% 5.12/5.40 thf(fact_5622_power2__less__eq__zero__iff,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.12/5.40 = ( A = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_eq_zero_iff
% 5.12/5.40 thf(fact_5623_power2__eq__iff__nonneg,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff_nonneg
% 5.12/5.40 thf(fact_5624_power2__eq__iff__nonneg,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff_nonneg
% 5.12/5.40 thf(fact_5625_power2__eq__iff__nonneg,axiom,
% 5.12/5.40 ! [X: nat,Y: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.12/5.40 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff_nonneg
% 5.12/5.40 thf(fact_5626_power2__eq__iff__nonneg,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.40 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff_nonneg
% 5.12/5.40 thf(fact_5627_add__neg__numeral__special_I9_J,axiom,
% 5.12/5.40 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(9)
% 5.12/5.40 thf(fact_5628_add__neg__numeral__special_I9_J,axiom,
% 5.12/5.40 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(9)
% 5.12/5.40 thf(fact_5629_add__neg__numeral__special_I9_J,axiom,
% 5.12/5.40 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(9)
% 5.12/5.40 thf(fact_5630_add__neg__numeral__special_I9_J,axiom,
% 5.12/5.40 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(9)
% 5.12/5.40 thf(fact_5631_add__neg__numeral__special_I9_J,axiom,
% 5.12/5.40 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_neg_numeral_special(9)
% 5.12/5.40 thf(fact_5632_zero__less__power2,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( A != zero_zero_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_less_power2
% 5.12/5.40 thf(fact_5633_zero__less__power2,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( A != zero_zero_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_less_power2
% 5.12/5.40 thf(fact_5634_zero__less__power2,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( A != zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_less_power2
% 5.12/5.40 thf(fact_5635_diff__numeral__special_I11_J,axiom,
% 5.12/5.40 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(11)
% 5.12/5.40 thf(fact_5636_diff__numeral__special_I11_J,axiom,
% 5.12/5.40 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(11)
% 5.12/5.40 thf(fact_5637_diff__numeral__special_I11_J,axiom,
% 5.12/5.40 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(11)
% 5.12/5.40 thf(fact_5638_diff__numeral__special_I11_J,axiom,
% 5.12/5.40 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(11)
% 5.12/5.40 thf(fact_5639_diff__numeral__special_I11_J,axiom,
% 5.12/5.40 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(11)
% 5.12/5.40 thf(fact_5640_diff__numeral__special_I10_J,axiom,
% 5.12/5.40 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(10)
% 5.12/5.40 thf(fact_5641_diff__numeral__special_I10_J,axiom,
% 5.12/5.40 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(10)
% 5.12/5.40 thf(fact_5642_diff__numeral__special_I10_J,axiom,
% 5.12/5.40 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(10)
% 5.12/5.40 thf(fact_5643_diff__numeral__special_I10_J,axiom,
% 5.12/5.40 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(10)
% 5.12/5.40 thf(fact_5644_diff__numeral__special_I10_J,axiom,
% 5.12/5.40 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(10)
% 5.12/5.40 thf(fact_5645_minus__1__div__2__eq,axiom,
% 5.12/5.40 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_1_div_2_eq
% 5.12/5.40 thf(fact_5646_minus__1__div__2__eq,axiom,
% 5.12/5.40 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_1_div_2_eq
% 5.12/5.40 thf(fact_5647_sum__power2__eq__zero__iff,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_zero_rat )
% 5.12/5.40 = ( ( X = zero_zero_rat )
% 5.12/5.40 & ( Y = zero_zero_rat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_eq_zero_iff
% 5.12/5.40 thf(fact_5648_sum__power2__eq__zero__iff,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_zero_int )
% 5.12/5.40 = ( ( X = zero_zero_int )
% 5.12/5.40 & ( Y = zero_zero_int ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_eq_zero_iff
% 5.12/5.40 thf(fact_5649_sum__power2__eq__zero__iff,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_zero_real )
% 5.12/5.40 = ( ( X = zero_zero_real )
% 5.12/5.40 & ( Y = zero_zero_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_eq_zero_iff
% 5.12/5.40 thf(fact_5650_not__mod__2__eq__0__eq__1,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 != zero_zero_int )
% 5.12/5.40 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_0_eq_1
% 5.12/5.40 thf(fact_5651_not__mod__2__eq__0__eq__1,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 != zero_zero_nat )
% 5.12/5.40 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_0_eq_1
% 5.12/5.40 thf(fact_5652_not__mod__2__eq__0__eq__1,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 != zero_z3403309356797280102nteger )
% 5.12/5.40 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_0_eq_1
% 5.12/5.40 thf(fact_5653_not__mod__2__eq__0__eq__1,axiom,
% 5.12/5.40 ! [A: code_natural] :
% 5.12/5.40 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 != zero_z2226904508553997617atural )
% 5.12/5.40 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_natural ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_0_eq_1
% 5.12/5.40 thf(fact_5654_not__mod__2__eq__1__eq__0,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 != one_one_int )
% 5.12/5.40 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_1_eq_0
% 5.12/5.40 thf(fact_5655_not__mod__2__eq__1__eq__0,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 != one_one_nat )
% 5.12/5.40 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_1_eq_0
% 5.12/5.40 thf(fact_5656_not__mod__2__eq__1__eq__0,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 != one_one_Code_integer )
% 5.12/5.40 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_1_eq_0
% 5.12/5.40 thf(fact_5657_not__mod__2__eq__1__eq__0,axiom,
% 5.12/5.40 ! [A: code_natural] :
% 5.12/5.40 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 != one_one_Code_natural )
% 5.12/5.40 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod_2_eq_1_eq_0
% 5.12/5.40 thf(fact_5658_bits__minus__1__mod__2__eq,axiom,
% 5.12/5.40 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % bits_minus_1_mod_2_eq
% 5.12/5.40 thf(fact_5659_bits__minus__1__mod__2__eq,axiom,
% 5.12/5.40 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer ) ).
% 5.12/5.40
% 5.12/5.40 % bits_minus_1_mod_2_eq
% 5.12/5.40 thf(fact_5660_minus__1__mod__2__eq,axiom,
% 5.12/5.40 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % minus_1_mod_2_eq
% 5.12/5.40 thf(fact_5661_minus__1__mod__2__eq,axiom,
% 5.12/5.40 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer ) ).
% 5.12/5.40
% 5.12/5.40 % minus_1_mod_2_eq
% 5.12/5.40 thf(fact_5662_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.40 ! [A: int,N: nat] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Power.ring_1_class.power_minus_even
% 5.12/5.40 thf(fact_5663_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.40 ! [A: real,N: nat] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Power.ring_1_class.power_minus_even
% 5.12/5.40 thf(fact_5664_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.40 ! [A: complex,N: nat] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Power.ring_1_class.power_minus_even
% 5.12/5.40 thf(fact_5665_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.40 ! [A: code_integer,N: nat] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Power.ring_1_class.power_minus_even
% 5.12/5.40 thf(fact_5666_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.40 ! [A: rat,N: nat] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Power.ring_1_class.power_minus_even
% 5.12/5.40 thf(fact_5667_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 != ( suc @ zero_zero_nat ) )
% 5.12/5.40 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % not_mod2_eq_Suc_0_eq_0
% 5.12/5.40 thf(fact_5668_diff__numeral__special_I4_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(4)
% 5.12/5.40 thf(fact_5669_diff__numeral__special_I4_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(4)
% 5.12/5.40 thf(fact_5670_diff__numeral__special_I4_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ one_one_complex )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(4)
% 5.12/5.40 thf(fact_5671_diff__numeral__special_I4_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(4)
% 5.12/5.40 thf(fact_5672_diff__numeral__special_I4_J,axiom,
% 5.12/5.40 ! [M2: num] :
% 5.12/5.40 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(4)
% 5.12/5.40 thf(fact_5673_diff__numeral__special_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(3)
% 5.12/5.40 thf(fact_5674_diff__numeral__special_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(3)
% 5.12/5.40 thf(fact_5675_diff__numeral__special_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(3)
% 5.12/5.40 thf(fact_5676_diff__numeral__special_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.40 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(3)
% 5.12/5.40 thf(fact_5677_diff__numeral__special_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_numeral_special(3)
% 5.12/5.40 thf(fact_5678_add__self__mod__2,axiom,
% 5.12/5.40 ! [M2: nat] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % add_self_mod_2
% 5.12/5.40 thf(fact_5679_half__nonnegative__int__iff,axiom,
% 5.12/5.40 ! [K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_nonnegative_int_iff
% 5.12/5.40 thf(fact_5680_half__negative__int__iff,axiom,
% 5.12/5.40 ! [K: int] :
% 5.12/5.40 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.12/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_negative_int_iff
% 5.12/5.40 thf(fact_5681_real__average__minus__first,axiom,
% 5.12/5.40 ! [A: real,B: real] :
% 5.12/5.40 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.12/5.40 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % real_average_minus_first
% 5.12/5.40 thf(fact_5682_real__average__minus__second,axiom,
% 5.12/5.40 ! [B: real,A: real] :
% 5.12/5.40 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.12/5.40 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % real_average_minus_second
% 5.12/5.40 thf(fact_5683_power__minus1__even,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_even
% 5.12/5.40 thf(fact_5684_power__minus1__even,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = one_one_real ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_even
% 5.12/5.40 thf(fact_5685_power__minus1__even,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = one_one_complex ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_even
% 5.12/5.40 thf(fact_5686_power__minus1__even,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = one_one_Code_integer ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_even
% 5.12/5.40 thf(fact_5687_power__minus1__even,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = one_one_rat ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_even
% 5.12/5.40 thf(fact_5688_one__less__floor,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.12/5.40 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_floor
% 5.12/5.40 thf(fact_5689_one__less__floor,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.12/5.40 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % one_less_floor
% 5.12/5.40 thf(fact_5690_floor__le__one,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.12/5.40 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_le_one
% 5.12/5.40 thf(fact_5691_floor__le__one,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.12/5.40 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_le_one
% 5.12/5.40 thf(fact_5692_mod2__gr__0,axiom,
% 5.12/5.40 ! [M2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod2_gr_0
% 5.12/5.40 thf(fact_5693_square__powr__half,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( abs_abs_real @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_powr_half
% 5.12/5.40 thf(fact_5694_sgn__eq,axiom,
% 5.12/5.40 ( sgn_sgn_complex
% 5.12/5.40 = ( ^ [Z6: complex] : ( divide1717551699836669952omplex @ Z6 @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ Z6 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sgn_eq
% 5.12/5.40 thf(fact_5695_mult__inc,axiom,
% 5.12/5.40 ! [X: num,Y: num] :
% 5.12/5.40 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.12/5.40 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_inc
% 5.12/5.40 thf(fact_5696_add__One,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( plus_plus_num @ X @ one )
% 5.12/5.40 = ( inc @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_One
% 5.12/5.40 thf(fact_5697_add__inc,axiom,
% 5.12/5.40 ! [X: num,Y: num] :
% 5.12/5.40 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.12/5.40 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_inc
% 5.12/5.40 thf(fact_5698_add__One__commute,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( plus_plus_num @ one @ N )
% 5.12/5.40 = ( plus_plus_num @ N @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % add_One_commute
% 5.12/5.40 thf(fact_5699_le__num__One__iff,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( ord_less_eq_num @ X @ one )
% 5.12/5.40 = ( X = one ) ) ).
% 5.12/5.40
% 5.12/5.40 % le_num_One_iff
% 5.12/5.40 thf(fact_5700_verit__eq__simplify_I10_J,axiom,
% 5.12/5.40 ! [X23: num] :
% 5.12/5.40 ( one
% 5.12/5.40 != ( bit0 @ X23 ) ) ).
% 5.12/5.40
% 5.12/5.40 % verit_eq_simplify(10)
% 5.12/5.40 thf(fact_5701_inc_Osimps_I1_J,axiom,
% 5.12/5.40 ( ( inc @ one )
% 5.12/5.40 = ( bit0 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % inc.simps(1)
% 5.12/5.40 thf(fact_5702_num__induct,axiom,
% 5.12/5.40 ! [P: num > $o,X: num] :
% 5.12/5.40 ( ( P @ one )
% 5.12/5.40 => ( ! [X3: num] :
% 5.12/5.40 ( ( P @ X3 )
% 5.12/5.40 => ( P @ ( inc @ X3 ) ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % num_induct
% 5.12/5.40 thf(fact_5703_zero__power2,axiom,
% 5.12/5.40 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_rat ) ).
% 5.12/5.40
% 5.12/5.40 % zero_power2
% 5.12/5.40 thf(fact_5704_zero__power2,axiom,
% 5.12/5.40 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % zero_power2
% 5.12/5.40 thf(fact_5705_zero__power2,axiom,
% 5.12/5.40 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % zero_power2
% 5.12/5.40 thf(fact_5706_zero__power2,axiom,
% 5.12/5.40 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % zero_power2
% 5.12/5.40 thf(fact_5707_zero__power2,axiom,
% 5.12/5.40 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = zero_zero_complex ) ).
% 5.12/5.40
% 5.12/5.40 % zero_power2
% 5.12/5.40 thf(fact_5708_numeral__Bit0__div__2,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0_div_2
% 5.12/5.40 thf(fact_5709_numeral__Bit0__div__2,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0_div_2
% 5.12/5.40 thf(fact_5710_one__power2,axiom,
% 5.12/5.40 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_rat ) ).
% 5.12/5.40
% 5.12/5.40 % one_power2
% 5.12/5.40 thf(fact_5711_one__power2,axiom,
% 5.12/5.40 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % one_power2
% 5.12/5.40 thf(fact_5712_one__power2,axiom,
% 5.12/5.40 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % one_power2
% 5.12/5.40 thf(fact_5713_one__power2,axiom,
% 5.12/5.40 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_real ) ).
% 5.12/5.40
% 5.12/5.40 % one_power2
% 5.12/5.40 thf(fact_5714_one__power2,axiom,
% 5.12/5.40 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_complex ) ).
% 5.12/5.40
% 5.12/5.40 % one_power2
% 5.12/5.40 thf(fact_5715_power2__commute,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_commute
% 5.12/5.40 thf(fact_5716_power2__commute,axiom,
% 5.12/5.40 ! [X: complex,Y: complex] :
% 5.12/5.40 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_commute
% 5.12/5.40 thf(fact_5717_power2__commute,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_commute
% 5.12/5.40 thf(fact_5718_power2__commute,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_commute
% 5.12/5.40 thf(fact_5719_power2__eq__iff,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( X = Y )
% 5.12/5.40 | ( X
% 5.12/5.40 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff
% 5.12/5.40 thf(fact_5720_power2__eq__iff,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( X = Y )
% 5.12/5.40 | ( X
% 5.12/5.40 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff
% 5.12/5.40 thf(fact_5721_power2__eq__iff,axiom,
% 5.12/5.40 ! [X: complex,Y: complex] :
% 5.12/5.40 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( X = Y )
% 5.12/5.40 | ( X
% 5.12/5.40 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff
% 5.12/5.40 thf(fact_5722_power2__eq__iff,axiom,
% 5.12/5.40 ! [X: code_integer,Y: code_integer] :
% 5.12/5.40 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( X = Y )
% 5.12/5.40 | ( X
% 5.12/5.40 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff
% 5.12/5.40 thf(fact_5723_power2__eq__iff,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ( X = Y )
% 5.12/5.40 | ( X
% 5.12/5.40 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_iff
% 5.12/5.40 thf(fact_5724_numeral__2__eq__2,axiom,
% 5.12/5.40 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.12/5.40 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_2_eq_2
% 5.12/5.40 thf(fact_5725_pos2,axiom,
% 5.12/5.40 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % pos2
% 5.12/5.40 thf(fact_5726_double__not__eq__Suc__double,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.12/5.40 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % double_not_eq_Suc_double
% 5.12/5.40 thf(fact_5727_Suc__double__not__eq__double,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_double_not_eq_double
% 5.12/5.40 thf(fact_5728_nat__1__add__1,axiom,
% 5.12/5.40 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.12/5.40 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nat_1_add_1
% 5.12/5.40 thf(fact_5729_less__exp,axiom,
% 5.12/5.40 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % less_exp
% 5.12/5.40 thf(fact_5730_pochhammer__of__real,axiom,
% 5.12/5.40 ! [X: real,N: nat] :
% 5.12/5.40 ( ( comm_s2602460028002588243omplex @ ( real_V4546457046886955230omplex @ X ) @ N )
% 5.12/5.40 = ( real_V4546457046886955230omplex @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pochhammer_of_real
% 5.12/5.40 thf(fact_5731_num_Osize_I4_J,axiom,
% 5.12/5.40 ( ( size_size_num @ one )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % num.size(4)
% 5.12/5.40 thf(fact_5732_numerals_I1_J,axiom,
% 5.12/5.40 ( ( numeral_numeral_nat @ one )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % numerals(1)
% 5.12/5.40 thf(fact_5733_zero__le__power2,axiom,
% 5.12/5.40 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_power2
% 5.12/5.40 thf(fact_5734_zero__le__power2,axiom,
% 5.12/5.40 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_power2
% 5.12/5.40 thf(fact_5735_zero__le__power2,axiom,
% 5.12/5.40 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_power2
% 5.12/5.40 thf(fact_5736_power2__eq__imp__eq,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_imp_eq
% 5.12/5.40 thf(fact_5737_power2__eq__imp__eq,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_imp_eq
% 5.12/5.40 thf(fact_5738_power2__eq__imp__eq,axiom,
% 5.12/5.40 ! [X: nat,Y: nat] :
% 5.12/5.40 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.12/5.40 => ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_imp_eq
% 5.12/5.40 thf(fact_5739_power2__eq__imp__eq,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.40 => ( X = Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_imp_eq
% 5.12/5.40 thf(fact_5740_power2__le__imp__le,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_imp_le
% 5.12/5.40 thf(fact_5741_power2__le__imp__le,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_imp_le
% 5.12/5.40 thf(fact_5742_power2__le__imp__le,axiom,
% 5.12/5.40 ! [X: nat,Y: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.12/5.40 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_imp_le
% 5.12/5.40 thf(fact_5743_power2__le__imp__le,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.40 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_imp_le
% 5.12/5.40 thf(fact_5744_power2__less__0,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_0
% 5.12/5.40 thf(fact_5745_power2__less__0,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_0
% 5.12/5.40 thf(fact_5746_power2__less__0,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_0
% 5.12/5.40 thf(fact_5747_mult__2,axiom,
% 5.12/5.40 ! [Z2: complex] :
% 5.12/5.40 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 )
% 5.12/5.40 = ( plus_plus_complex @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2
% 5.12/5.40 thf(fact_5748_mult__2,axiom,
% 5.12/5.40 ! [Z2: real] :
% 5.12/5.40 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 )
% 5.12/5.40 = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2
% 5.12/5.40 thf(fact_5749_mult__2,axiom,
% 5.12/5.40 ! [Z2: rat] :
% 5.12/5.40 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 )
% 5.12/5.40 = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2
% 5.12/5.40 thf(fact_5750_mult__2,axiom,
% 5.12/5.40 ! [Z2: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z2 )
% 5.12/5.40 = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2
% 5.12/5.40 thf(fact_5751_mult__2,axiom,
% 5.12/5.40 ! [Z2: int] :
% 5.12/5.40 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z2 )
% 5.12/5.40 = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2
% 5.12/5.40 thf(fact_5752_mult__2__right,axiom,
% 5.12/5.40 ! [Z2: complex] :
% 5.12/5.40 ( ( times_times_complex @ Z2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( plus_plus_complex @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2_right
% 5.12/5.40 thf(fact_5753_mult__2__right,axiom,
% 5.12/5.40 ! [Z2: real] :
% 5.12/5.40 ( ( times_times_real @ Z2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( plus_plus_real @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2_right
% 5.12/5.40 thf(fact_5754_mult__2__right,axiom,
% 5.12/5.40 ! [Z2: rat] :
% 5.12/5.40 ( ( times_times_rat @ Z2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( plus_plus_rat @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2_right
% 5.12/5.40 thf(fact_5755_mult__2__right,axiom,
% 5.12/5.40 ! [Z2: nat] :
% 5.12/5.40 ( ( times_times_nat @ Z2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( plus_plus_nat @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2_right
% 5.12/5.40 thf(fact_5756_mult__2__right,axiom,
% 5.12/5.40 ! [Z2: int] :
% 5.12/5.40 ( ( times_times_int @ Z2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( plus_plus_int @ Z2 @ Z2 ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_2_right
% 5.12/5.40 thf(fact_5757_left__add__twice,axiom,
% 5.12/5.40 ! [A: complex,B: complex] :
% 5.12/5.40 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.12/5.40 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % left_add_twice
% 5.12/5.40 thf(fact_5758_left__add__twice,axiom,
% 5.12/5.40 ! [A: real,B: real] :
% 5.12/5.40 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.12/5.40 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % left_add_twice
% 5.12/5.40 thf(fact_5759_left__add__twice,axiom,
% 5.12/5.40 ! [A: rat,B: rat] :
% 5.12/5.40 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.40 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % left_add_twice
% 5.12/5.40 thf(fact_5760_left__add__twice,axiom,
% 5.12/5.40 ! [A: nat,B: nat] :
% 5.12/5.40 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.40 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % left_add_twice
% 5.12/5.40 thf(fact_5761_left__add__twice,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.12/5.40 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % left_add_twice
% 5.12/5.40 thf(fact_5762_field__sum__of__halves,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = X ) ).
% 5.12/5.40
% 5.12/5.40 % field_sum_of_halves
% 5.12/5.40 thf(fact_5763_field__sum__of__halves,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = X ) ).
% 5.12/5.40
% 5.12/5.40 % field_sum_of_halves
% 5.12/5.40 thf(fact_5764_power2__eq__1__iff,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int )
% 5.12/5.40 = ( ( A = one_one_int )
% 5.12/5.40 | ( A
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_1_iff
% 5.12/5.40 thf(fact_5765_power2__eq__1__iff,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_real )
% 5.12/5.40 = ( ( A = one_one_real )
% 5.12/5.40 | ( A
% 5.12/5.40 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_1_iff
% 5.12/5.40 thf(fact_5766_power2__eq__1__iff,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_complex )
% 5.12/5.40 = ( ( A = one_one_complex )
% 5.12/5.40 | ( A
% 5.12/5.40 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_1_iff
% 5.12/5.40 thf(fact_5767_power2__eq__1__iff,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer )
% 5.12/5.40 = ( ( A = one_one_Code_integer )
% 5.12/5.40 | ( A
% 5.12/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_1_iff
% 5.12/5.40 thf(fact_5768_power2__eq__1__iff,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_rat )
% 5.12/5.40 = ( ( A = one_one_rat )
% 5.12/5.40 | ( A
% 5.12/5.40 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_eq_1_iff
% 5.12/5.40 thf(fact_5769_less__2__cases__iff,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( ( N = zero_zero_nat )
% 5.12/5.40 | ( N
% 5.12/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % less_2_cases_iff
% 5.12/5.40 thf(fact_5770_less__2__cases,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 => ( ( N = zero_zero_nat )
% 5.12/5.40 | ( N
% 5.12/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % less_2_cases
% 5.12/5.40 thf(fact_5771_abs__square__eq__1,axiom,
% 5.12/5.40 ! [X: code_integer] :
% 5.12/5.40 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_Code_integer )
% 5.12/5.40 = ( ( abs_abs_Code_integer @ X )
% 5.12/5.40 = one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_eq_1
% 5.12/5.40 thf(fact_5772_abs__square__eq__1,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_rat )
% 5.12/5.40 = ( ( abs_abs_rat @ X )
% 5.12/5.40 = one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_eq_1
% 5.12/5.40 thf(fact_5773_abs__square__eq__1,axiom,
% 5.12/5.40 ! [X: int] :
% 5.12/5.40 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_int )
% 5.12/5.40 = ( ( abs_abs_int @ X )
% 5.12/5.40 = one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_eq_1
% 5.12/5.40 thf(fact_5774_abs__square__eq__1,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_real )
% 5.12/5.40 = ( ( abs_abs_real @ X )
% 5.12/5.40 = one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_eq_1
% 5.12/5.40 thf(fact_5775_abs__sqrt__wlog,axiom,
% 5.12/5.40 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.12/5.40 ( ! [X3: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.12/5.40 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_sqrt_wlog
% 5.12/5.40 thf(fact_5776_abs__sqrt__wlog,axiom,
% 5.12/5.40 ! [P: real > real > $o,X: real] :
% 5.12/5.40 ( ! [X3: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.12/5.40 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_sqrt_wlog
% 5.12/5.40 thf(fact_5777_abs__sqrt__wlog,axiom,
% 5.12/5.40 ! [P: rat > rat > $o,X: rat] :
% 5.12/5.40 ( ! [X3: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.12/5.40 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_sqrt_wlog
% 5.12/5.40 thf(fact_5778_abs__sqrt__wlog,axiom,
% 5.12/5.40 ! [P: int > int > $o,X: int] :
% 5.12/5.40 ( ! [X3: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.12/5.40 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_sqrt_wlog
% 5.12/5.40 thf(fact_5779_nat__2,axiom,
% 5.12/5.40 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nat_2
% 5.12/5.40 thf(fact_5780_nat__induct2,axiom,
% 5.12/5.40 ! [P: nat > $o,N: nat] :
% 5.12/5.40 ( ( P @ zero_zero_nat )
% 5.12/5.40 => ( ( P @ one_one_nat )
% 5.12/5.40 => ( ! [N2: nat] :
% 5.12/5.40 ( ( P @ N2 )
% 5.12/5.40 => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( P @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nat_induct2
% 5.12/5.40 thf(fact_5781_two__realpow__ge__one,axiom,
% 5.12/5.40 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % two_realpow_ge_one
% 5.12/5.40 thf(fact_5782_square__fact__le__2__fact,axiom,
% 5.12/5.40 ! [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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_fact_le_2_fact
% 5.12/5.40 thf(fact_5783_realpow__square__minus__le,axiom,
% 5.12/5.40 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % realpow_square_minus_le
% 5.12/5.40 thf(fact_5784_diff__le__diff__pow,axiom,
% 5.12/5.40 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.12/5.40 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % diff_le_diff_pow
% 5.12/5.40 thf(fact_5785_ln__2__less__1,axiom,
% 5.12/5.40 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.12/5.40
% 5.12/5.40 % ln_2_less_1
% 5.12/5.40 thf(fact_5786_not__exp__less__eq__0__int,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % not_exp_less_eq_0_int
% 5.12/5.40 thf(fact_5787_log2__of__power__eq,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( M2
% 5.12/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( semiri5074537144036343181t_real @ N )
% 5.12/5.40 = ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % log2_of_power_eq
% 5.12/5.40 thf(fact_5788_power2__less__imp__less,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_imp_less
% 5.12/5.40 thf(fact_5789_power2__less__imp__less,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_imp_less
% 5.12/5.40 thf(fact_5790_power2__less__imp__less,axiom,
% 5.12/5.40 ! [X: nat,Y: nat] :
% 5.12/5.40 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.12/5.40 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_imp_less
% 5.12/5.40 thf(fact_5791_power2__less__imp__less,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.40 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_less_imp_less
% 5.12/5.40 thf(fact_5792_half__gt__zero,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.12/5.40 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_gt_zero
% 5.12/5.40 thf(fact_5793_half__gt__zero,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.12/5.40 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_gt_zero
% 5.12/5.40 thf(fact_5794_half__gt__zero__iff,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_gt_zero_iff
% 5.12/5.40 thf(fact_5795_half__gt__zero__iff,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.40
% 5.12/5.40 % half_gt_zero_iff
% 5.12/5.40 thf(fact_5796_sum__power2__ge__zero,axiom,
% 5.12/5.40 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_ge_zero
% 5.12/5.40 thf(fact_5797_sum__power2__ge__zero,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_ge_zero
% 5.12/5.40 thf(fact_5798_sum__power2__ge__zero,axiom,
% 5.12/5.40 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_ge_zero
% 5.12/5.40 thf(fact_5799_sum__power2__le__zero__iff,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.12/5.40 = ( ( X = zero_zero_real )
% 5.12/5.40 & ( Y = zero_zero_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_le_zero_iff
% 5.12/5.40 thf(fact_5800_sum__power2__le__zero__iff,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.12/5.40 = ( ( X = zero_zero_rat )
% 5.12/5.40 & ( Y = zero_zero_rat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_le_zero_iff
% 5.12/5.40 thf(fact_5801_sum__power2__le__zero__iff,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.12/5.40 = ( ( X = zero_zero_int )
% 5.12/5.40 & ( Y = zero_zero_int ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_le_zero_iff
% 5.12/5.40 thf(fact_5802_not__sum__power2__lt__zero,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % not_sum_power2_lt_zero
% 5.12/5.40 thf(fact_5803_not__sum__power2__lt__zero,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.12/5.40
% 5.12/5.40 % not_sum_power2_lt_zero
% 5.12/5.40 thf(fact_5804_not__sum__power2__lt__zero,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % not_sum_power2_lt_zero
% 5.12/5.40 thf(fact_5805_sum__power2__gt__zero__iff,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 = ( ( X != zero_zero_real )
% 5.12/5.40 | ( Y != zero_zero_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_gt_zero_iff
% 5.12/5.40 thf(fact_5806_sum__power2__gt__zero__iff,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 = ( ( X != zero_zero_rat )
% 5.12/5.40 | ( Y != zero_zero_rat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_gt_zero_iff
% 5.12/5.40 thf(fact_5807_sum__power2__gt__zero__iff,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 = ( ( X != zero_zero_int )
% 5.12/5.40 | ( Y != zero_zero_int ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % sum_power2_gt_zero_iff
% 5.12/5.40 thf(fact_5808_field__less__half__sum,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( ord_less_real @ X @ Y )
% 5.12/5.40 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % field_less_half_sum
% 5.12/5.40 thf(fact_5809_field__less__half__sum,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_rat @ X @ Y )
% 5.12/5.40 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % field_less_half_sum
% 5.12/5.40 thf(fact_5810_square__le__1,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.40 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_le_1
% 5.12/5.40 thf(fact_5811_square__le__1,axiom,
% 5.12/5.40 ! [X: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.12/5.40 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.12/5.40 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_le_1
% 5.12/5.40 thf(fact_5812_square__le__1,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.12/5.40 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.12/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_le_1
% 5.12/5.40 thf(fact_5813_square__le__1,axiom,
% 5.12/5.40 ! [X: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.12/5.40 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.12/5.40 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_le_1
% 5.12/5.40 thf(fact_5814_power2__le__iff__abs__le,axiom,
% 5.12/5.40 ! [Y: code_integer,X: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.12/5.40 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_iff_abs_le
% 5.12/5.40 thf(fact_5815_power2__le__iff__abs__le,axiom,
% 5.12/5.40 ! [Y: real,X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_iff_abs_le
% 5.12/5.40 thf(fact_5816_power2__le__iff__abs__le,axiom,
% 5.12/5.40 ! [Y: rat,X: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_iff_abs_le
% 5.12/5.40 thf(fact_5817_power2__le__iff__abs__le,axiom,
% 5.12/5.40 ! [Y: int,X: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.40 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_le_iff_abs_le
% 5.12/5.40 thf(fact_5818_of__nat__less__two__power,axiom,
% 5.12/5.40 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_nat_less_two_power
% 5.12/5.40 thf(fact_5819_of__nat__less__two__power,axiom,
% 5.12/5.40 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_nat_less_two_power
% 5.12/5.40 thf(fact_5820_of__nat__less__two__power,axiom,
% 5.12/5.40 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_nat_less_two_power
% 5.12/5.40 thf(fact_5821_exp__add__not__zero__imp__left,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.40 != zero_zero_nat )
% 5.12/5.40 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.12/5.40 != zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_add_not_zero_imp_left
% 5.12/5.40 thf(fact_5822_exp__add__not__zero__imp__left,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.40 != zero_zero_int )
% 5.12/5.40 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 5.12/5.40 != zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_add_not_zero_imp_left
% 5.12/5.40 thf(fact_5823_exp__add__not__zero__imp__right,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.40 != zero_zero_nat )
% 5.12/5.40 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 != zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_add_not_zero_imp_right
% 5.12/5.40 thf(fact_5824_exp__add__not__zero__imp__right,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.40 != zero_zero_int )
% 5.12/5.40 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 != zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_add_not_zero_imp_right
% 5.12/5.40 thf(fact_5825_zero__le__even__power_H,axiom,
% 5.12/5.40 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_even_power'
% 5.12/5.40 thf(fact_5826_zero__le__even__power_H,axiom,
% 5.12/5.40 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_even_power'
% 5.12/5.40 thf(fact_5827_zero__le__even__power_H,axiom,
% 5.12/5.40 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_le_even_power'
% 5.12/5.40 thf(fact_5828_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.12/5.40 ! [N: nat,M2: nat] :
% 5.12/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 != zero_zero_nat )
% 5.12/5.40 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.40 != zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_not_zero_imp_exp_diff_not_zero
% 5.12/5.40 thf(fact_5829_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.12/5.40 ! [N: nat,M2: nat] :
% 5.12/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 != zero_zero_int )
% 5.12/5.40 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.40 != zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_not_zero_imp_exp_diff_not_zero
% 5.12/5.40 thf(fact_5830_abs__square__le__1,axiom,
% 5.12/5.40 ! [X: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.12/5.40 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_le_1
% 5.12/5.40 thf(fact_5831_abs__square__le__1,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.12/5.40 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_le_1
% 5.12/5.40 thf(fact_5832_abs__square__le__1,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.12/5.40 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_le_1
% 5.12/5.40 thf(fact_5833_abs__square__le__1,axiom,
% 5.12/5.40 ! [X: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.12/5.40 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_le_1
% 5.12/5.40 thf(fact_5834_abs__square__less__1,axiom,
% 5.12/5.40 ! [X: code_integer] :
% 5.12/5.40 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.12/5.40 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_less_1
% 5.12/5.40 thf(fact_5835_abs__square__less__1,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.12/5.40 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_less_1
% 5.12/5.40 thf(fact_5836_abs__square__less__1,axiom,
% 5.12/5.40 ! [X: rat] :
% 5.12/5.40 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.12/5.40 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_less_1
% 5.12/5.40 thf(fact_5837_abs__square__less__1,axiom,
% 5.12/5.40 ! [X: int] :
% 5.12/5.40 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.12/5.40 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_square_less_1
% 5.12/5.40 thf(fact_5838_div__exp__eq,axiom,
% 5.12/5.40 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.40 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_eq
% 5.12/5.40 thf(fact_5839_div__exp__eq,axiom,
% 5.12/5.40 ! [A: int,M2: nat,N: nat] :
% 5.12/5.40 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_eq
% 5.12/5.40 thf(fact_5840_ex__nat__less,axiom,
% 5.12/5.40 ! [N: nat,P: nat > $o] :
% 5.12/5.40 ( ( ? [M5: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M5 @ N )
% 5.12/5.40 & ( P @ M5 ) ) )
% 5.12/5.40 = ( ? [X2: nat] :
% 5.12/5.40 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.40 & ( P @ X2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ex_nat_less
% 5.12/5.40 thf(fact_5841_all__nat__less,axiom,
% 5.12/5.40 ! [N: nat,P: nat > $o] :
% 5.12/5.40 ( ( ! [M5: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M5 @ N )
% 5.12/5.40 => ( P @ M5 ) ) )
% 5.12/5.40 = ( ! [X2: nat] :
% 5.12/5.40 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.40 => ( P @ X2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nat_less
% 5.12/5.40 thf(fact_5842_minus__power__mult__self,axiom,
% 5.12/5.40 ! [A: int,N: nat] :
% 5.12/5.40 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.12/5.40 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_power_mult_self
% 5.12/5.40 thf(fact_5843_minus__power__mult__self,axiom,
% 5.12/5.40 ! [A: real,N: nat] :
% 5.12/5.40 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.12/5.40 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_power_mult_self
% 5.12/5.40 thf(fact_5844_minus__power__mult__self,axiom,
% 5.12/5.40 ! [A: complex,N: nat] :
% 5.12/5.40 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.12/5.40 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_power_mult_self
% 5.12/5.40 thf(fact_5845_minus__power__mult__self,axiom,
% 5.12/5.40 ! [A: code_integer,N: nat] :
% 5.12/5.40 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.12/5.40 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_power_mult_self
% 5.12/5.40 thf(fact_5846_minus__power__mult__self,axiom,
% 5.12/5.40 ! [A: rat,N: nat] :
% 5.12/5.40 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.12/5.40 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_power_mult_self
% 5.12/5.40 thf(fact_5847_power__odd__eq,axiom,
% 5.12/5.40 ! [A: complex,N: nat] :
% 5.12/5.40 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_odd_eq
% 5.12/5.40 thf(fact_5848_power__odd__eq,axiom,
% 5.12/5.40 ! [A: real,N: nat] :
% 5.12/5.40 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_odd_eq
% 5.12/5.40 thf(fact_5849_power__odd__eq,axiom,
% 5.12/5.40 ! [A: rat,N: nat] :
% 5.12/5.40 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_odd_eq
% 5.12/5.40 thf(fact_5850_power__odd__eq,axiom,
% 5.12/5.40 ! [A: nat,N: nat] :
% 5.12/5.40 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_odd_eq
% 5.12/5.40 thf(fact_5851_power__odd__eq,axiom,
% 5.12/5.40 ! [A: int,N: nat] :
% 5.12/5.40 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_odd_eq
% 5.12/5.40 thf(fact_5852_exp__double,axiom,
% 5.12/5.40 ! [Z2: complex] :
% 5.12/5.40 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) )
% 5.12/5.40 = ( power_power_complex @ ( exp_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_double
% 5.12/5.40 thf(fact_5853_exp__double,axiom,
% 5.12/5.40 ! [Z2: real] :
% 5.12/5.40 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) )
% 5.12/5.40 = ( power_power_real @ ( exp_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_double
% 5.12/5.40 thf(fact_5854_nat__bit__induct,axiom,
% 5.12/5.40 ! [P: nat > $o,N: nat] :
% 5.12/5.40 ( ( P @ zero_zero_nat )
% 5.12/5.40 => ( ! [N2: nat] :
% 5.12/5.40 ( ( P @ N2 )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.12/5.40 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.12/5.40 => ( ! [N2: nat] :
% 5.12/5.40 ( ( P @ N2 )
% 5.12/5.40 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.12/5.40 => ( P @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nat_bit_induct
% 5.12/5.40 thf(fact_5855_square__norm__one,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_real )
% 5.12/5.40 => ( ( real_V7735802525324610683m_real @ X )
% 5.12/5.40 = one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_norm_one
% 5.12/5.40 thf(fact_5856_square__norm__one,axiom,
% 5.12/5.40 ! [X: complex] :
% 5.12/5.40 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = one_one_complex )
% 5.12/5.40 => ( ( real_V1022390504157884413omplex @ X )
% 5.12/5.40 = one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % square_norm_one
% 5.12/5.40 thf(fact_5857_Suc__n__div__2__gt__zero,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_n_div_2_gt_zero
% 5.12/5.40 thf(fact_5858_div__2__gt__zero,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_2_gt_zero
% 5.12/5.40 thf(fact_5859_of__real__exp,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( real_V1803761363581548252l_real @ ( exp_real @ X ) )
% 5.12/5.40 = ( exp_real @ ( real_V1803761363581548252l_real @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_real_exp
% 5.12/5.40 thf(fact_5860_of__real__exp,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( real_V4546457046886955230omplex @ ( exp_real @ X ) )
% 5.12/5.40 = ( exp_complex @ ( real_V4546457046886955230omplex @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_real_exp
% 5.12/5.40 thf(fact_5861_numeral__Bit0,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.12/5.40 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0
% 5.12/5.40 thf(fact_5862_numeral__Bit0,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.12/5.40 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0
% 5.12/5.40 thf(fact_5863_numeral__Bit0,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.12/5.40 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0
% 5.12/5.40 thf(fact_5864_numeral__Bit0,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.12/5.40 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0
% 5.12/5.40 thf(fact_5865_numeral__Bit0,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.12/5.40 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit0
% 5.12/5.40 thf(fact_5866_exp__half__le2,axiom,
% 5.12/5.40 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_half_le2
% 5.12/5.40 thf(fact_5867_power__minus__Bit0,axiom,
% 5.12/5.40 ! [X: int,K: num] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit0
% 5.12/5.40 thf(fact_5868_power__minus__Bit0,axiom,
% 5.12/5.40 ! [X: real,K: num] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit0
% 5.12/5.40 thf(fact_5869_power__minus__Bit0,axiom,
% 5.12/5.40 ! [X: complex,K: num] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit0
% 5.12/5.40 thf(fact_5870_power__minus__Bit0,axiom,
% 5.12/5.40 ! [X: code_integer,K: num] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit0
% 5.12/5.40 thf(fact_5871_power__minus__Bit0,axiom,
% 5.12/5.40 ! [X: rat,K: num] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit0
% 5.12/5.40 thf(fact_5872_minus__1__div__exp__eq__int,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % minus_1_div_exp_eq_int
% 5.12/5.40 thf(fact_5873_exp__plus__inverse__exp,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_plus_inverse_exp
% 5.12/5.40 thf(fact_5874_mult__numeral__1,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1
% 5.12/5.40 thf(fact_5875_mult__numeral__1,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1
% 5.12/5.40 thf(fact_5876_mult__numeral__1,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1
% 5.12/5.40 thf(fact_5877_mult__numeral__1,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1
% 5.12/5.40 thf(fact_5878_mult__numeral__1,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1
% 5.12/5.40 thf(fact_5879_mult__numeral__1__right,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1_right
% 5.12/5.40 thf(fact_5880_mult__numeral__1__right,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1_right
% 5.12/5.40 thf(fact_5881_mult__numeral__1__right,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1_right
% 5.12/5.40 thf(fact_5882_mult__numeral__1__right,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1_right
% 5.12/5.40 thf(fact_5883_mult__numeral__1__right,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % mult_numeral_1_right
% 5.12/5.40 thf(fact_5884_numeral__One,axiom,
% 5.12/5.40 ( ( numera6690914467698888265omplex @ one )
% 5.12/5.40 = one_one_complex ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_One
% 5.12/5.40 thf(fact_5885_numeral__One,axiom,
% 5.12/5.40 ( ( numeral_numeral_real @ one )
% 5.12/5.40 = one_one_real ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_One
% 5.12/5.40 thf(fact_5886_numeral__One,axiom,
% 5.12/5.40 ( ( numeral_numeral_rat @ one )
% 5.12/5.40 = one_one_rat ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_One
% 5.12/5.40 thf(fact_5887_numeral__One,axiom,
% 5.12/5.40 ( ( numeral_numeral_nat @ one )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_One
% 5.12/5.40 thf(fact_5888_numeral__One,axiom,
% 5.12/5.40 ( ( numeral_numeral_int @ one )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_One
% 5.12/5.40 thf(fact_5889_divide__numeral__1,axiom,
% 5.12/5.40 ! [A: complex] :
% 5.12/5.40 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % divide_numeral_1
% 5.12/5.40 thf(fact_5890_divide__numeral__1,axiom,
% 5.12/5.40 ! [A: real] :
% 5.12/5.40 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % divide_numeral_1
% 5.12/5.40 thf(fact_5891_divide__numeral__1,axiom,
% 5.12/5.40 ! [A: rat] :
% 5.12/5.40 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.12/5.40 = A ) ).
% 5.12/5.40
% 5.12/5.40 % divide_numeral_1
% 5.12/5.40 thf(fact_5892_numeral__1__eq__Suc__0,axiom,
% 5.12/5.40 ( ( numeral_numeral_nat @ one )
% 5.12/5.40 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_1_eq_Suc_0
% 5.12/5.40 thf(fact_5893_Suc__nat__number__of__add,axiom,
% 5.12/5.40 ! [V: num,N: nat] :
% 5.12/5.40 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.12/5.40 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_nat_number_of_add
% 5.12/5.40 thf(fact_5894_inverse__numeral__1,axiom,
% 5.12/5.40 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.12/5.40 = ( numeral_numeral_real @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % inverse_numeral_1
% 5.12/5.40 thf(fact_5895_inverse__numeral__1,axiom,
% 5.12/5.40 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % inverse_numeral_1
% 5.12/5.40 thf(fact_5896_inverse__numeral__1,axiom,
% 5.12/5.40 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.12/5.40 = ( numeral_numeral_rat @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % inverse_numeral_1
% 5.12/5.40 thf(fact_5897_triangle__def,axiom,
% 5.12/5.40 ( nat_triangle
% 5.12/5.40 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % triangle_def
% 5.12/5.40 thf(fact_5898_divmod__digit__0_I2_J,axiom,
% 5.12/5.40 ! [B: int,A: int] :
% 5.12/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.40 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.12/5.40 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(2)
% 5.12/5.40 thf(fact_5899_divmod__digit__0_I2_J,axiom,
% 5.12/5.40 ! [B: nat,A: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.40 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.12/5.40 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(2)
% 5.12/5.40 thf(fact_5900_divmod__digit__0_I2_J,axiom,
% 5.12/5.40 ! [B: code_integer,A: code_integer] :
% 5.12/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.40 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.12/5.40 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(2)
% 5.12/5.40 thf(fact_5901_power2__diff,axiom,
% 5.12/5.40 ! [X: complex,Y: complex] :
% 5.12/5.40 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_diff
% 5.12/5.40 thf(fact_5902_power2__diff,axiom,
% 5.12/5.40 ! [X: real,Y: real] :
% 5.12/5.40 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_diff
% 5.12/5.40 thf(fact_5903_power2__diff,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_diff
% 5.12/5.40 thf(fact_5904_power2__diff,axiom,
% 5.12/5.40 ! [X: int,Y: int] :
% 5.12/5.40 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power2_diff
% 5.12/5.40 thf(fact_5905_bits__stable__imp__add__self,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = A )
% 5.12/5.40 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % bits_stable_imp_add_self
% 5.12/5.40 thf(fact_5906_bits__stable__imp__add__self,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = A )
% 5.12/5.40 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % bits_stable_imp_add_self
% 5.12/5.40 thf(fact_5907_bits__stable__imp__add__self,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.40 = A )
% 5.12/5.40 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.40
% 5.12/5.40 % bits_stable_imp_add_self
% 5.12/5.40 thf(fact_5908_bits__stable__imp__add__self,axiom,
% 5.12/5.40 ! [A: code_natural] :
% 5.12/5.40 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.40 = A )
% 5.12/5.40 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.40
% 5.12/5.40 % bits_stable_imp_add_self
% 5.12/5.40 thf(fact_5909_odd__0__le__power__imp__0__le,axiom,
% 5.12/5.40 ! [A: real,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_0_le_power_imp_0_le
% 5.12/5.40 thf(fact_5910_odd__0__le__power__imp__0__le,axiom,
% 5.12/5.40 ! [A: rat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_0_le_power_imp_0_le
% 5.12/5.40 thf(fact_5911_odd__0__le__power__imp__0__le,axiom,
% 5.12/5.40 ! [A: int,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.40 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_0_le_power_imp_0_le
% 5.12/5.40 thf(fact_5912_odd__power__less__zero,axiom,
% 5.12/5.40 ! [A: real,N: nat] :
% 5.12/5.40 ( ( ord_less_real @ A @ zero_zero_real )
% 5.12/5.40 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_power_less_zero
% 5.12/5.40 thf(fact_5913_odd__power__less__zero,axiom,
% 5.12/5.40 ! [A: rat,N: nat] :
% 5.12/5.40 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.12/5.40 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_power_less_zero
% 5.12/5.40 thf(fact_5914_odd__power__less__zero,axiom,
% 5.12/5.40 ! [A: int,N: nat] :
% 5.12/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.12/5.40 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % odd_power_less_zero
% 5.12/5.40 thf(fact_5915_power__minus1__odd,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_odd
% 5.12/5.40 thf(fact_5916_power__minus1__odd,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_odd
% 5.12/5.40 thf(fact_5917_power__minus1__odd,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_odd
% 5.12/5.40 thf(fact_5918_power__minus1__odd,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_odd
% 5.12/5.40 thf(fact_5919_power__minus1__odd,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus1_odd
% 5.12/5.40 thf(fact_5920_div__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [A: int,N: nat,M2: nat] :
% 5.12/5.40 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5921_div__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [A: nat,N: nat,M2: nat] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5922_div__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [A: code_integer,N: nat,M2: nat] :
% 5.12/5.40 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5923_div__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [A: code_natural,N: nat,M2: nat] :
% 5.12/5.40 ( ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5924_ex__power__ivl2,axiom,
% 5.12/5.40 ! [B: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.12/5.40 => ? [N2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.12/5.40 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ex_power_ivl2
% 5.12/5.40 thf(fact_5925_ex__power__ivl1,axiom,
% 5.12/5.40 ! [B: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.40 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.12/5.40 => ? [N2: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.12/5.40 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ex_power_ivl1
% 5.12/5.40 thf(fact_5926_plus__inverse__ge__2,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % plus_inverse_ge_2
% 5.12/5.40 thf(fact_5927_exp__bound__half,axiom,
% 5.12/5.40 ! [Z2: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_bound_half
% 5.12/5.40 thf(fact_5928_exp__bound__half,axiom,
% 5.12/5.40 ! [Z2: complex] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_bound_half
% 5.12/5.40 thf(fact_5929_int__bit__induct,axiom,
% 5.12/5.40 ! [P: int > $o,K: int] :
% 5.12/5.40 ( ( P @ zero_zero_int )
% 5.12/5.40 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 => ( ! [K2: int] :
% 5.12/5.40 ( ( P @ K2 )
% 5.12/5.40 => ( ( K2 != zero_zero_int )
% 5.12/5.40 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.40 => ( ! [K2: int] :
% 5.12/5.40 ( ( P @ K2 )
% 5.12/5.40 => ( ( K2
% 5.12/5.40 != ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.12/5.40 => ( P @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % int_bit_induct
% 5.12/5.40 thf(fact_5930_less__log2__of__power,axiom,
% 5.12/5.40 ! [N: nat,M2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 5.12/5.40 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % less_log2_of_power
% 5.12/5.40 thf(fact_5931_le__log2__of__power,axiom,
% 5.12/5.40 ! [N: nat,M2: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 5.12/5.40 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % le_log2_of_power
% 5.12/5.40 thf(fact_5932_arsinh__def,axiom,
% 5.12/5.40 ( arsinh_real
% 5.12/5.40 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arsinh_def
% 5.12/5.40 thf(fact_5933_nonzero__of__real__divide,axiom,
% 5.12/5.40 ! [Y: real,X: real] :
% 5.12/5.40 ( ( Y != zero_zero_real )
% 5.12/5.40 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.40 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nonzero_of_real_divide
% 5.12/5.40 thf(fact_5934_nonzero__of__real__divide,axiom,
% 5.12/5.40 ! [Y: real,X: real] :
% 5.12/5.40 ( ( Y != zero_zero_real )
% 5.12/5.40 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.40 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nonzero_of_real_divide
% 5.12/5.40 thf(fact_5935_divmod__digit__0_I1_J,axiom,
% 5.12/5.40 ! [B: int,A: int] :
% 5.12/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.40 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(1)
% 5.12/5.40 thf(fact_5936_divmod__digit__0_I1_J,axiom,
% 5.12/5.40 ! [B: nat,A: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.40 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(1)
% 5.12/5.40 thf(fact_5937_divmod__digit__0_I1_J,axiom,
% 5.12/5.40 ! [B: code_integer,A: code_integer] :
% 5.12/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.40 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_0(1)
% 5.12/5.40 thf(fact_5938_arcosh__def,axiom,
% 5.12/5.40 ( arcosh_real
% 5.12/5.40 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arcosh_def
% 5.12/5.40 thf(fact_5939_mult__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [M2: nat,N: nat,A: int] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.40 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5940_mult__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [M2: nat,N: nat,A: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.40 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5941_mult__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [M2: nat,N: nat,A: code_integer] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.40 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5942_mult__exp__mod__exp__eq,axiom,
% 5.12/5.40 ! [M2: nat,N: nat,A: code_natural] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.40 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_exp_mod_exp_eq
% 5.12/5.40 thf(fact_5943_cosh__zero__iff,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ( cosh_real @ X )
% 5.12/5.40 = zero_zero_real )
% 5.12/5.40 = ( ( power_power_real @ ( exp_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % cosh_zero_iff
% 5.12/5.40 thf(fact_5944_cosh__zero__iff,axiom,
% 5.12/5.40 ! [X: complex] :
% 5.12/5.40 ( ( ( cosh_complex @ X )
% 5.12/5.40 = zero_zero_complex )
% 5.12/5.40 = ( ( power_power_complex @ ( exp_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % cosh_zero_iff
% 5.12/5.40 thf(fact_5945_cong__exp__iff__simps_I2_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = zero_zero_int )
% 5.12/5.40 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q5 ) )
% 5.12/5.40 = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(2)
% 5.12/5.40 thf(fact_5946_cong__exp__iff__simps_I2_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = zero_zero_nat )
% 5.12/5.40 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q5 ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(2)
% 5.12/5.40 thf(fact_5947_cong__exp__iff__simps_I2_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = zero_z3403309356797280102nteger )
% 5.12/5.40 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q5 ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(2)
% 5.12/5.40 thf(fact_5948_cosh__field__def,axiom,
% 5.12/5.40 ( cosh_real
% 5.12/5.40 = ( ^ [Z6: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z6 ) @ ( exp_real @ ( uminus_uminus_real @ Z6 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % cosh_field_def
% 5.12/5.40 thf(fact_5949_cosh__field__def,axiom,
% 5.12/5.40 ( cosh_complex
% 5.12/5.40 = ( ^ [Z6: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z6 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z6 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % cosh_field_def
% 5.12/5.40 thf(fact_5950_num_Osize_I5_J,axiom,
% 5.12/5.40 ! [X23: num] :
% 5.12/5.40 ( ( size_size_num @ ( bit0 @ X23 ) )
% 5.12/5.40 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % num.size(5)
% 5.12/5.40 thf(fact_5951_log2__of__power__less,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.40 => ( ord_less_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % log2_of_power_less
% 5.12/5.40 thf(fact_5952_exp__bound,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.40 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_bound
% 5.12/5.40 thf(fact_5953_pos__zdiv__mult__2,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.40 => ( ( 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 ) )
% 5.12/5.40 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pos_zdiv_mult_2
% 5.12/5.40 thf(fact_5954_neg__zdiv__mult__2,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.40 => ( ( 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 ) )
% 5.12/5.40 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_zdiv_mult_2
% 5.12/5.40 thf(fact_5955_pos__zmod__mult__2,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.40 => ( ( 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 ) )
% 5.12/5.40 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pos_zmod_mult_2
% 5.12/5.40 thf(fact_5956_real__le__x__sinh,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % real_le_x_sinh
% 5.12/5.40 thf(fact_5957_mult__1s__ring__1_I1_J,axiom,
% 5.12/5.40 ! [B: int] :
% 5.12/5.40 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.12/5.40 = ( uminus_uminus_int @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(1)
% 5.12/5.40 thf(fact_5958_mult__1s__ring__1_I1_J,axiom,
% 5.12/5.40 ! [B: real] :
% 5.12/5.40 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.12/5.40 = ( uminus_uminus_real @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(1)
% 5.12/5.40 thf(fact_5959_mult__1s__ring__1_I1_J,axiom,
% 5.12/5.40 ! [B: complex] :
% 5.12/5.40 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(1)
% 5.12/5.40 thf(fact_5960_mult__1s__ring__1_I1_J,axiom,
% 5.12/5.40 ! [B: code_integer] :
% 5.12/5.40 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(1)
% 5.12/5.40 thf(fact_5961_mult__1s__ring__1_I1_J,axiom,
% 5.12/5.40 ! [B: rat] :
% 5.12/5.40 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.12/5.40 = ( uminus_uminus_rat @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(1)
% 5.12/5.40 thf(fact_5962_mult__1s__ring__1_I2_J,axiom,
% 5.12/5.40 ! [B: int] :
% 5.12/5.40 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(2)
% 5.12/5.40 thf(fact_5963_mult__1s__ring__1_I2_J,axiom,
% 5.12/5.40 ! [B: real] :
% 5.12/5.40 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(2)
% 5.12/5.40 thf(fact_5964_mult__1s__ring__1_I2_J,axiom,
% 5.12/5.40 ! [B: complex] :
% 5.12/5.40 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(2)
% 5.12/5.40 thf(fact_5965_mult__1s__ring__1_I2_J,axiom,
% 5.12/5.40 ! [B: code_integer] :
% 5.12/5.40 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(2)
% 5.12/5.40 thf(fact_5966_mult__1s__ring__1_I2_J,axiom,
% 5.12/5.40 ! [B: rat] :
% 5.12/5.40 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.12/5.40 = ( uminus_uminus_rat @ B ) ) ).
% 5.12/5.40
% 5.12/5.40 % mult_1s_ring_1(2)
% 5.12/5.40 thf(fact_5967_uminus__numeral__One,axiom,
% 5.12/5.40 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % uminus_numeral_One
% 5.12/5.40 thf(fact_5968_uminus__numeral__One,axiom,
% 5.12/5.40 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.12/5.40 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % uminus_numeral_One
% 5.12/5.40 thf(fact_5969_uminus__numeral__One,axiom,
% 5.12/5.40 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.40
% 5.12/5.40 % uminus_numeral_One
% 5.12/5.40 thf(fact_5970_uminus__numeral__One,axiom,
% 5.12/5.40 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % uminus_numeral_One
% 5.12/5.40 thf(fact_5971_uminus__numeral__One,axiom,
% 5.12/5.40 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.12/5.40 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % uminus_numeral_One
% 5.12/5.40 thf(fact_5972_real__le__abs__sinh,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % real_le_abs_sinh
% 5.12/5.40 thf(fact_5973_cong__exp__iff__simps_I1_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(1)
% 5.12/5.40 thf(fact_5974_cong__exp__iff__simps_I1_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(1)
% 5.12/5.40 thf(fact_5975_cong__exp__iff__simps_I1_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(1)
% 5.12/5.40 thf(fact_5976_arith__geo__mean,axiom,
% 5.12/5.40 ! [U: real,X: real,Y: real] :
% 5.12/5.40 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( times_times_real @ X @ Y ) )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.40 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arith_geo_mean
% 5.12/5.40 thf(fact_5977_arith__geo__mean,axiom,
% 5.12/5.40 ! [U: rat,X: rat,Y: rat] :
% 5.12/5.40 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( times_times_rat @ X @ Y ) )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.12/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.12/5.40 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arith_geo_mean
% 5.12/5.40 thf(fact_5978_mod__double__modulus,axiom,
% 5.12/5.40 ! [M2: code_integer,X: code_integer] :
% 5.12/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M2 )
% 5.12/5.40 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.12/5.40 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( modulo364778990260209775nteger @ X @ M2 ) )
% 5.12/5.40 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod_double_modulus
% 5.12/5.40 thf(fact_5979_mod__double__modulus,axiom,
% 5.12/5.40 ! [M2: nat,X: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.12/5.40 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( modulo_modulo_nat @ X @ M2 ) )
% 5.12/5.40 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod_double_modulus
% 5.12/5.40 thf(fact_5980_mod__double__modulus,axiom,
% 5.12/5.40 ! [M2: int,X: int] :
% 5.12/5.40 ( ( ord_less_int @ zero_zero_int @ M2 )
% 5.12/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.40 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( modulo_modulo_int @ X @ M2 ) )
% 5.12/5.40 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod_double_modulus
% 5.12/5.40 thf(fact_5981_divmod__digit__1_I2_J,axiom,
% 5.12/5.40 ! [A: code_integer,B: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.40 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.40 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(2)
% 5.12/5.40 thf(fact_5982_divmod__digit__1_I2_J,axiom,
% 5.12/5.40 ! [A: nat,B: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.40 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(2)
% 5.12/5.40 thf(fact_5983_divmod__digit__1_I2_J,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.40 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.12/5.40 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(2)
% 5.12/5.40 thf(fact_5984_norm__less__p1,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % norm_less_p1
% 5.12/5.40 thf(fact_5985_norm__less__p1,axiom,
% 5.12/5.40 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % norm_less_p1
% 5.12/5.40 thf(fact_5986_log2__of__power__le,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.40 => ( ord_less_eq_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % log2_of_power_le
% 5.12/5.40 thf(fact_5987_exp__bound__lemma,axiom,
% 5.12/5.40 ! [Z2: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_bound_lemma
% 5.12/5.40 thf(fact_5988_exp__bound__lemma,axiom,
% 5.12/5.40 ! [Z2: complex] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z2 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_bound_lemma
% 5.12/5.40 thf(fact_5989_real__exp__bound__lemma,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % real_exp_bound_lemma
% 5.12/5.40 thf(fact_5990_exp__lower__Taylor__quadratic,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_lower_Taylor_quadratic
% 5.12/5.40 thf(fact_5991_ln__one__plus__pos__lower__bound,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.40 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ln_one_plus_pos_lower_bound
% 5.12/5.40 thf(fact_5992_artanh__def,axiom,
% 5.12/5.40 ( artanh_real
% 5.12/5.40 = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % artanh_def
% 5.12/5.40 thf(fact_5993_neg__zmod__mult__2,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.12/5.40 => ( ( 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 ) )
% 5.12/5.40 = ( 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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % neg_zmod_mult_2
% 5.12/5.40 thf(fact_5994_numeral__inc,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 5.12/5.40 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_inc
% 5.12/5.40 thf(fact_5995_numeral__inc,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( numeral_numeral_real @ ( inc @ X ) )
% 5.12/5.40 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_inc
% 5.12/5.40 thf(fact_5996_numeral__inc,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 5.12/5.40 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_inc
% 5.12/5.40 thf(fact_5997_numeral__inc,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 5.12/5.40 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_inc
% 5.12/5.40 thf(fact_5998_numeral__inc,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( numeral_numeral_int @ ( inc @ X ) )
% 5.12/5.40 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_inc
% 5.12/5.40 thf(fact_5999_cosh__ln__real,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.12/5.40 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % cosh_ln_real
% 5.12/5.40 thf(fact_6000_floor__log2__div2,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 => ( ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.40 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_log2_div2
% 5.12/5.40 thf(fact_6001_fact__double,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % fact_double
% 5.12/5.40 thf(fact_6002_fact__double,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % fact_double
% 5.12/5.40 thf(fact_6003_fact__double,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % fact_double
% 5.12/5.40 thf(fact_6004_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.40 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.12/5.40 thf(fact_6005_arctan__double,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.40 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.12/5.40 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arctan_double
% 5.12/5.40 thf(fact_6006_tanh__real__altdef,axiom,
% 5.12/5.40 ( tanh_real
% 5.12/5.40 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % tanh_real_altdef
% 5.12/5.40 thf(fact_6007_divmod__digit__1_I1_J,axiom,
% 5.12/5.40 ! [A: code_integer,B: code_integer] :
% 5.12/5.40 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.12/5.40 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.12/5.40 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.12/5.40 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(1)
% 5.12/5.40 thf(fact_6008_divmod__digit__1_I1_J,axiom,
% 5.12/5.40 ! [A: nat,B: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.12/5.40 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( 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 )
% 5.12/5.40 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(1)
% 5.12/5.40 thf(fact_6009_divmod__digit__1_I1_J,axiom,
% 5.12/5.40 ! [A: int,B: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.12/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.40 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.12/5.40 => ( ( 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 )
% 5.12/5.40 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divmod_digit_1(1)
% 5.12/5.40 thf(fact_6010_pochhammer__double,axiom,
% 5.12/5.40 ! [Z2: complex,N: nat] :
% 5.12/5.40 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 @ Z2 @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pochhammer_double
% 5.12/5.40 thf(fact_6011_pochhammer__double,axiom,
% 5.12/5.40 ! [Z2: real,N: nat] :
% 5.12/5.40 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 @ Z2 @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pochhammer_double
% 5.12/5.40 thf(fact_6012_pochhammer__double,axiom,
% 5.12/5.40 ! [Z2: rat,N: nat] :
% 5.12/5.40 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 = ( 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 @ Z2 @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pochhammer_double
% 5.12/5.40 thf(fact_6013_norm__of__real__diff,axiom,
% 5.12/5.40 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % norm_of_real_diff
% 5.12/5.40 thf(fact_6014_ln__one__minus__pos__lower__bound,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ln_one_minus_pos_lower_bound
% 5.12/5.40 thf(fact_6015_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_ln_one_plus_x_minus_x_bound
% 5.12/5.40 thf(fact_6016_tanh__ln__real,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.12/5.40 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % tanh_ln_real
% 5.12/5.40 thf(fact_6017_floor__log__nat__eq__if,axiom,
% 5.12/5.40 ! [B: nat,N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.12/5.40 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.40 => ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.12/5.40 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_log_nat_eq_if
% 5.12/5.40 thf(fact_6018_floor__log__nat__eq__powr__iff,axiom,
% 5.12/5.40 ! [B: nat,K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.40 => ( ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.12/5.40 = ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.40 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.12/5.40 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_log_nat_eq_powr_iff
% 5.12/5.40 thf(fact_6019_ceiling__log2__div2,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.40 => ( ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.40 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log2 @ ( 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 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ceiling_log2_div2
% 5.12/5.40 thf(fact_6020_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.40 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.40 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.12/5.40 thf(fact_6021_ceiling__log__nat__eq__if,axiom,
% 5.12/5.40 ! [B: nat,N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.12/5.40 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.12/5.40 => ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.12/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % ceiling_log_nat_eq_if
% 5.12/5.40 thf(fact_6022_set__bit__0,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.12/5.40 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_0
% 5.12/5.40 thf(fact_6023_set__bit__0,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.12/5.40 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_0
% 5.12/5.40 thf(fact_6024_low__inv,axiom,
% 5.12/5.40 ! [X: nat,N: nat,Y: nat] :
% 5.12/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.12/5.40 = X ) ) ).
% 5.12/5.40
% 5.12/5.40 % low_inv
% 5.12/5.40 thf(fact_6025_high__inv,axiom,
% 5.12/5.40 ! [X: nat,N: nat,Y: nat] :
% 5.12/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.12/5.40 = Y ) ) ).
% 5.12/5.40
% 5.12/5.40 % high_inv
% 5.12/5.40 thf(fact_6026_set__n__deg__not__0,axiom,
% 5.12/5.40 ! [TreeList: list_VEBT_VEBT,N: nat,M2: nat] :
% 5.12/5.40 ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.40 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.12/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_n_deg_not_0
% 5.12/5.40 thf(fact_6027_high__bound__aux,axiom,
% 5.12/5.40 ! [Ma: nat,N: nat,M2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.12/5.40 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % high_bound_aux
% 5.12/5.40 thf(fact_6028_unset__bit__0,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.12/5.40 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_0
% 5.12/5.40 thf(fact_6029_unset__bit__0,axiom,
% 5.12/5.40 ! [A: nat] :
% 5.12/5.40 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.12/5.40 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_0
% 5.12/5.40 thf(fact_6030_bit__split__inv,axiom,
% 5.12/5.40 ! [X: nat,D: nat] :
% 5.12/5.40 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.12/5.40 = X ) ).
% 5.12/5.40
% 5.12/5.40 % bit_split_inv
% 5.12/5.40 thf(fact_6031_high__def,axiom,
% 5.12/5.40 ( vEBT_VEBT_high
% 5.12/5.40 = ( ^ [X2: nat,N4: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % high_def
% 5.12/5.40 thf(fact_6032_low__def,axiom,
% 5.12/5.40 ( vEBT_VEBT_low
% 5.12/5.40 = ( ^ [X2: nat,N4: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % low_def
% 5.12/5.40 thf(fact_6033_unset__bit__nonnegative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.12/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_nonnegative_int_iff
% 5.12/5.40 thf(fact_6034_set__bit__nonnegative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.12/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_nonnegative_int_iff
% 5.12/5.40 thf(fact_6035_unset__bit__negative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_negative_int_iff
% 5.12/5.40 thf(fact_6036_set__bit__negative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_negative_int_iff
% 5.12/5.40 thf(fact_6037_divide__complex__def,axiom,
% 5.12/5.40 ( divide1717551699836669952omplex
% 5.12/5.40 = ( ^ [X2: complex,Y6: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y6 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % divide_complex_def
% 5.12/5.40 thf(fact_6038_unset__bit__nat__def,axiom,
% 5.12/5.40 ( bit_se4205575877204974255it_nat
% 5.12/5.40 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M5 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_nat_def
% 5.12/5.40 thf(fact_6039_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: complex,Xs: list_complex] :
% 5.12/5.40 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6040_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: real,Xs: list_real] :
% 5.12/5.40 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6041_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: set_nat,Xs: list_set_nat] :
% 5.12/5.40 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6042_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6043_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: $o,Xs: list_o] :
% 5.12/5.40 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6044_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: nat,Xs: list_nat] :
% 5.12/5.40 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6045_length__pos__if__in__set,axiom,
% 5.12/5.40 ! [X: int,Xs: list_int] :
% 5.12/5.40 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % length_pos_if_in_set
% 5.12/5.40 thf(fact_6046_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.12/5.40 ! [X: nat,N: nat,M2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.40 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % VEBT_internal.exp_split_high_low(1)
% 5.12/5.40 thf(fact_6047_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.12/5.40 ! [X: nat,N: nat,M2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.40 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % VEBT_internal.exp_split_high_low(2)
% 5.12/5.40 thf(fact_6048_invar__vebt_Ointros_I2_J,axiom,
% 5.12/5.40 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 5.12/5.40 ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.40 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.12/5.40 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.12/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 => ( ( M2 = N )
% 5.12/5.40 => ( ( Deg
% 5.12/5.40 = ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.40 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.12/5.40 => ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.40 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.12/5.40 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % invar_vebt.intros(2)
% 5.12/5.40 thf(fact_6049_invar__vebt_Ointros_I3_J,axiom,
% 5.12/5.40 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 5.12/5.40 ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.40 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.12/5.40 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.12/5.40 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.40 => ( ( M2
% 5.12/5.40 = ( suc @ N ) )
% 5.12/5.40 => ( ( Deg
% 5.12/5.40 = ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.40 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.12/5.40 => ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.40 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.12/5.40 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % invar_vebt.intros(3)
% 5.12/5.40 thf(fact_6050_unset__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_integer] :
% 5.12/5.40 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_Suc
% 5.12/5.40 thf(fact_6051_unset__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_natural] :
% 5.12/5.40 ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_Suc
% 5.12/5.40 thf(fact_6052_unset__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: int] :
% 5.12/5.40 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_Suc
% 5.12/5.40 thf(fact_6053_unset__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: nat] :
% 5.12/5.40 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % unset_bit_Suc
% 5.12/5.40 thf(fact_6054_set__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_integer] :
% 5.12/5.40 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_Suc
% 5.12/5.40 thf(fact_6055_set__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_natural] :
% 5.12/5.40 ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_Suc
% 5.12/5.40 thf(fact_6056_set__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: int] :
% 5.12/5.40 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_Suc
% 5.12/5.40 thf(fact_6057_set__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: nat] :
% 5.12/5.40 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % set_bit_Suc
% 5.12/5.40 thf(fact_6058_both__member__options__ding,axiom,
% 5.12/5.40 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.12/5.40 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.12/5.40 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.12/5.40 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % both_member_options_ding
% 5.12/5.40 thf(fact_6059_flip__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_integer] :
% 5.12/5.40 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_Suc
% 5.12/5.40 thf(fact_6060_flip__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_natural] :
% 5.12/5.40 ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_Suc
% 5.12/5.40 thf(fact_6061_flip__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: int] :
% 5.12/5.40 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_Suc
% 5.12/5.40 thf(fact_6062_flip__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: nat] :
% 5.12/5.40 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_Suc
% 5.12/5.40 thf(fact_6063_signed__take__bit__rec,axiom,
% 5.12/5.40 ( bit_ri6519982836138164636nteger
% 5.12/5.40 = ( ^ [N4: nat,A3: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_rec
% 5.12/5.40 thf(fact_6064_signed__take__bit__rec,axiom,
% 5.12/5.40 ( bit_ri631733984087533419it_int
% 5.12/5.40 = ( ^ [N4: nat,A3: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_rec
% 5.12/5.40 thf(fact_6065_round__unique,axiom,
% 5.12/5.40 ! [X: real,Y: int] :
% 5.12/5.40 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.12/5.40 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( ( archim8280529875227126926d_real @ X )
% 5.12/5.40 = Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_unique
% 5.12/5.40 thf(fact_6066_round__unique,axiom,
% 5.12/5.40 ! [X: rat,Y: int] :
% 5.12/5.40 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.12/5.40 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.40 => ( ( archim7778729529865785530nd_rat @ X )
% 5.12/5.40 = Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_unique
% 5.12/5.40 thf(fact_6067_dbl__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(4)
% 5.12/5.40 thf(fact_6068_dbl__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(4)
% 5.12/5.40 thf(fact_6069_dbl__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(4)
% 5.12/5.40 thf(fact_6070_dbl__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(4)
% 5.12/5.40 thf(fact_6071_dbl__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(4)
% 5.12/5.40 thf(fact_6072_round__altdef,axiom,
% 5.12/5.40 ( archim8280529875227126926d_real
% 5.12/5.40 = ( ^ [X2: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X2 ) ) @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_altdef
% 5.12/5.40 thf(fact_6073_round__altdef,axiom,
% 5.12/5.40 ( archim7778729529865785530nd_rat
% 5.12/5.40 = ( ^ [X2: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X2 ) ) @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_altdef
% 5.12/5.40 thf(fact_6074_inthall,axiom,
% 5.12/5.40 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 5.12/5.40 ( ! [X3: complex] :
% 5.12/5.40 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6075_inthall,axiom,
% 5.12/5.40 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.12/5.40 ( ! [X3: real] :
% 5.12/5.40 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6076_inthall,axiom,
% 5.12/5.40 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 5.12/5.40 ( ! [X3: set_nat] :
% 5.12/5.40 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6077_inthall,axiom,
% 5.12/5.40 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.12/5.40 ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6078_inthall,axiom,
% 5.12/5.40 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.12/5.40 ( ! [X3: $o] :
% 5.12/5.40 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6079_inthall,axiom,
% 5.12/5.40 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.12/5.40 ( ! [X3: nat] :
% 5.12/5.40 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6080_inthall,axiom,
% 5.12/5.40 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.12/5.40 ( ! [X3: int] :
% 5.12/5.40 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inthall
% 5.12/5.40 thf(fact_6081_flip__bit__nonnegative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.12/5.40 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_nonnegative_int_iff
% 5.12/5.40 thf(fact_6082_flip__bit__negative__int__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % flip_bit_negative_int_iff
% 5.12/5.40 thf(fact_6083_signed__take__bit__of__0,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_of_0
% 5.12/5.40 thf(fact_6084_round__of__int,axiom,
% 5.12/5.40 ! [N: int] :
% 5.12/5.40 ( ( archim8280529875227126926d_real @ ( ring_1_of_int_real @ N ) )
% 5.12/5.40 = N ) ).
% 5.12/5.40
% 5.12/5.40 % round_of_int
% 5.12/5.40 thf(fact_6085_round__of__int,axiom,
% 5.12/5.40 ! [N: int] :
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ ( ring_1_of_int_rat @ N ) )
% 5.12/5.40 = N ) ).
% 5.12/5.40
% 5.12/5.40 % round_of_int
% 5.12/5.40 thf(fact_6086_dbl__simps_I2_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.12/5.40 = zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(2)
% 5.12/5.40 thf(fact_6087_dbl__simps_I2_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.12/5.40 = zero_zero_rat ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(2)
% 5.12/5.40 thf(fact_6088_dbl__simps_I2_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(2)
% 5.12/5.40 thf(fact_6089_signed__take__bit__of__minus__1,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_of_minus_1
% 5.12/5.40 thf(fact_6090_signed__take__bit__of__minus__1,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_of_minus_1
% 5.12/5.40 thf(fact_6091_signed__take__bit__Suc__1,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc_1
% 5.12/5.40 thf(fact_6092_signed__take__bit__numeral__of__1,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_numeral_of_1
% 5.12/5.40 thf(fact_6093_round__0,axiom,
% 5.12/5.40 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % round_0
% 5.12/5.40 thf(fact_6094_round__0,axiom,
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.12/5.40 = zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % round_0
% 5.12/5.40 thf(fact_6095_round__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.12/5.40 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_numeral
% 5.12/5.40 thf(fact_6096_round__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.12/5.40 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_numeral
% 5.12/5.40 thf(fact_6097_round__1,axiom,
% 5.12/5.40 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % round_1
% 5.12/5.40 thf(fact_6098_round__1,axiom,
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.12/5.40 = one_one_int ) ).
% 5.12/5.40
% 5.12/5.40 % round_1
% 5.12/5.40 thf(fact_6099_round__of__nat,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( archim8280529875227126926d_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.40 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_of_nat
% 5.12/5.40 thf(fact_6100_round__of__nat,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.12/5.40 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_of_nat
% 5.12/5.40 thf(fact_6101_dbl__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(5)
% 5.12/5.40 thf(fact_6102_dbl__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(5)
% 5.12/5.40 thf(fact_6103_dbl__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(5)
% 5.12/5.40 thf(fact_6104_dbl__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(5)
% 5.12/5.40 thf(fact_6105_dbl__simps_I1_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(1)
% 5.12/5.40 thf(fact_6106_dbl__simps_I1_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(1)
% 5.12/5.40 thf(fact_6107_dbl__simps_I1_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(1)
% 5.12/5.40 thf(fact_6108_dbl__simps_I1_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(1)
% 5.12/5.40 thf(fact_6109_dbl__simps_I1_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(1)
% 5.12/5.40 thf(fact_6110_signed__take__bit__Suc__bit0,axiom,
% 5.12/5.40 ! [N: nat,K: num] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.12/5.40 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc_bit0
% 5.12/5.40 thf(fact_6111_round__neg__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_neg_numeral
% 5.12/5.40 thf(fact_6112_round__neg__numeral,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_neg_numeral
% 5.12/5.40 thf(fact_6113_dbl__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(3)
% 5.12/5.40 thf(fact_6114_dbl__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(3)
% 5.12/5.40 thf(fact_6115_dbl__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(3)
% 5.12/5.40 thf(fact_6116_dbl__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_simps(3)
% 5.12/5.40 thf(fact_6117_signed__take__bit__Suc__minus__bit0,axiom,
% 5.12/5.40 ! [N: nat,K: num] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.40 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc_minus_bit0
% 5.12/5.40 thf(fact_6118_signed__take__bit__0,axiom,
% 5.12/5.40 ! [A: code_integer] :
% 5.12/5.40 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_0
% 5.12/5.40 thf(fact_6119_signed__take__bit__0,axiom,
% 5.12/5.40 ! [A: int] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.12/5.40 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_0
% 5.12/5.40 thf(fact_6120_signed__take__bit__minus,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.12/5.40 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_minus
% 5.12/5.40 thf(fact_6121_signed__take__bit__diff,axiom,
% 5.12/5.40 ! [N: nat,K: int,L: int] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.12/5.40 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_diff
% 5.12/5.40 thf(fact_6122_list__eq__iff__nth__eq,axiom,
% 5.12/5.40 ( ( ^ [Y4: list_VEBT_VEBT,Z: list_VEBT_VEBT] : ( Y4 = Z ) )
% 5.12/5.40 = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.12/5.40 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.12/5.40 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.12/5.40 => ( ( nth_VEBT_VEBT @ Xs3 @ I2 )
% 5.12/5.40 = ( nth_VEBT_VEBT @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_eq_iff_nth_eq
% 5.12/5.40 thf(fact_6123_list__eq__iff__nth__eq,axiom,
% 5.12/5.40 ( ( ^ [Y4: list_o,Z: list_o] : ( Y4 = Z ) )
% 5.12/5.40 = ( ^ [Xs3: list_o,Ys3: list_o] :
% 5.12/5.40 ( ( ( size_size_list_o @ Xs3 )
% 5.12/5.40 = ( size_size_list_o @ Ys3 ) )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs3 ) )
% 5.12/5.40 => ( ( nth_o @ Xs3 @ I2 )
% 5.12/5.40 = ( nth_o @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_eq_iff_nth_eq
% 5.12/5.40 thf(fact_6124_list__eq__iff__nth__eq,axiom,
% 5.12/5.40 ( ( ^ [Y4: list_nat,Z: list_nat] : ( Y4 = Z ) )
% 5.12/5.40 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 5.12/5.40 ( ( ( size_size_list_nat @ Xs3 )
% 5.12/5.40 = ( size_size_list_nat @ Ys3 ) )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs3 ) )
% 5.12/5.40 => ( ( nth_nat @ Xs3 @ I2 )
% 5.12/5.40 = ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_eq_iff_nth_eq
% 5.12/5.40 thf(fact_6125_list__eq__iff__nth__eq,axiom,
% 5.12/5.40 ( ( ^ [Y4: list_int,Z: list_int] : ( Y4 = Z ) )
% 5.12/5.40 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 5.12/5.40 ( ( ( size_size_list_int @ Xs3 )
% 5.12/5.40 = ( size_size_list_int @ Ys3 ) )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs3 ) )
% 5.12/5.40 => ( ( nth_int @ Xs3 @ I2 )
% 5.12/5.40 = ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_eq_iff_nth_eq
% 5.12/5.40 thf(fact_6126_Skolem__list__nth,axiom,
% 5.12/5.40 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.12/5.40 ( ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ? [X7: vEBT_VEBT] : ( P @ I2 @ X7 ) ) )
% 5.12/5.40 = ( ? [Xs3: list_VEBT_VEBT] :
% 5.12/5.40 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.12/5.40 = K )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ( P @ I2 @ ( nth_VEBT_VEBT @ Xs3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Skolem_list_nth
% 5.12/5.40 thf(fact_6127_Skolem__list__nth,axiom,
% 5.12/5.40 ! [K: nat,P: nat > $o > $o] :
% 5.12/5.40 ( ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ? [X7: $o] : ( P @ I2 @ X7 ) ) )
% 5.12/5.40 = ( ? [Xs3: list_o] :
% 5.12/5.40 ( ( ( size_size_list_o @ Xs3 )
% 5.12/5.40 = K )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ( P @ I2 @ ( nth_o @ Xs3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Skolem_list_nth
% 5.12/5.40 thf(fact_6128_Skolem__list__nth,axiom,
% 5.12/5.40 ! [K: nat,P: nat > nat > $o] :
% 5.12/5.40 ( ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ? [X7: nat] : ( P @ I2 @ X7 ) ) )
% 5.12/5.40 = ( ? [Xs3: list_nat] :
% 5.12/5.40 ( ( ( size_size_list_nat @ Xs3 )
% 5.12/5.40 = K )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ( P @ I2 @ ( nth_nat @ Xs3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Skolem_list_nth
% 5.12/5.40 thf(fact_6129_Skolem__list__nth,axiom,
% 5.12/5.40 ! [K: nat,P: nat > int > $o] :
% 5.12/5.40 ( ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ? [X7: int] : ( P @ I2 @ X7 ) ) )
% 5.12/5.40 = ( ? [Xs3: list_int] :
% 5.12/5.40 ( ( ( size_size_list_int @ Xs3 )
% 5.12/5.40 = K )
% 5.12/5.40 & ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ K )
% 5.12/5.40 => ( P @ I2 @ ( nth_int @ Xs3 @ I2 ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Skolem_list_nth
% 5.12/5.40 thf(fact_6130_nth__equalityI,axiom,
% 5.12/5.40 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.12/5.40 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.12/5.40 = ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.12/5.40 => ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 5.12/5.40 = ( nth_VEBT_VEBT @ Ys2 @ I3 ) ) )
% 5.12/5.40 => ( Xs = Ys2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_equalityI
% 5.12/5.40 thf(fact_6131_nth__equalityI,axiom,
% 5.12/5.40 ! [Xs: list_o,Ys2: list_o] :
% 5.12/5.40 ( ( ( size_size_list_o @ Xs )
% 5.12/5.40 = ( size_size_list_o @ Ys2 ) )
% 5.12/5.40 => ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( ( nth_o @ Xs @ I3 )
% 5.12/5.40 = ( nth_o @ Ys2 @ I3 ) ) )
% 5.12/5.40 => ( Xs = Ys2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_equalityI
% 5.12/5.40 thf(fact_6132_nth__equalityI,axiom,
% 5.12/5.40 ! [Xs: list_nat,Ys2: list_nat] :
% 5.12/5.40 ( ( ( size_size_list_nat @ Xs )
% 5.12/5.40 = ( size_size_list_nat @ Ys2 ) )
% 5.12/5.40 => ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( ( nth_nat @ Xs @ I3 )
% 5.12/5.40 = ( nth_nat @ Ys2 @ I3 ) ) )
% 5.12/5.40 => ( Xs = Ys2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_equalityI
% 5.12/5.40 thf(fact_6133_nth__equalityI,axiom,
% 5.12/5.40 ! [Xs: list_int,Ys2: list_int] :
% 5.12/5.40 ( ( ( size_size_list_int @ Xs )
% 5.12/5.40 = ( size_size_list_int @ Ys2 ) )
% 5.12/5.40 => ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( ( nth_int @ Xs @ I3 )
% 5.12/5.40 = ( nth_int @ Ys2 @ I3 ) ) )
% 5.12/5.40 => ( Xs = Ys2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_equalityI
% 5.12/5.40 thf(fact_6134_dbl__def,axiom,
% 5.12/5.40 ( neg_numeral_dbl_real
% 5.12/5.40 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_def
% 5.12/5.40 thf(fact_6135_dbl__def,axiom,
% 5.12/5.40 ( neg_numeral_dbl_rat
% 5.12/5.40 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_def
% 5.12/5.40 thf(fact_6136_dbl__def,axiom,
% 5.12/5.40 ( neg_numeral_dbl_int
% 5.12/5.40 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_def
% 5.12/5.40 thf(fact_6137_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_complex] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.12/5.40 => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6138_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_real] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.12/5.40 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6139_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_set_nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.12/5.40 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6140_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6141_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6142_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6143_nth__mem,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_int] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_mem
% 5.12/5.40 thf(fact_6144_list__ball__nth,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( ! [X3: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_ball_nth
% 5.12/5.40 thf(fact_6145_list__ball__nth,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_o,P: $o > $o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( ! [X3: $o] :
% 5.12/5.40 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_ball_nth
% 5.12/5.40 thf(fact_6146_list__ball__nth,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( ! [X3: nat] :
% 5.12/5.40 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_ball_nth
% 5.12/5.40 thf(fact_6147_list__ball__nth,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_int,P: int > $o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( ! [X3: int] :
% 5.12/5.40 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.12/5.40 => ( P @ X3 ) )
% 5.12/5.40 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % list_ball_nth
% 5.12/5.40 thf(fact_6148_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: complex,Xs: list_complex] :
% 5.12/5.40 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.12/5.40 & ( ( nth_complex @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6149_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: real,Xs: list_real] :
% 5.12/5.40 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 5.12/5.40 & ( ( nth_real @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6150_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: set_nat,Xs: list_set_nat] :
% 5.12/5.40 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.12/5.40 & ( ( nth_set_nat @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6151_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 & ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6152_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: $o,Xs: list_o] :
% 5.12/5.40 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 & ( ( nth_o @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6153_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: nat,Xs: list_nat] :
% 5.12/5.40 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 & ( ( nth_nat @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6154_in__set__conv__nth,axiom,
% 5.12/5.40 ! [X: int,Xs: list_int] :
% 5.12/5.40 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.12/5.40 = ( ? [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 & ( ( nth_int @ Xs @ I2 )
% 5.12/5.40 = X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_set_conv_nth
% 5.12/5.40 thf(fact_6155_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_complex,P: complex > $o,X: complex] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_complex @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6156_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_real,P: real > $o,X: real] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_real @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6157_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_set_nat @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6158_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6159_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_o,P: $o > $o,X: $o] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_o @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6160_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_nat,P: nat > $o,X: nat] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_nat @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6161_all__nth__imp__all__set,axiom,
% 5.12/5.40 ! [Xs: list_int,P: int > $o,X: int] :
% 5.12/5.40 ( ! [I3: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_int @ Xs @ I3 ) ) )
% 5.12/5.40 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.12/5.40 => ( P @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_nth_imp_all_set
% 5.12/5.40 thf(fact_6162_all__set__conv__all__nth,axiom,
% 5.12/5.40 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.12/5.40 ( ( ! [X2: vEBT_VEBT] :
% 5.12/5.40 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.40 => ( P @ X2 ) ) )
% 5.12/5.40 = ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_set_conv_all_nth
% 5.12/5.40 thf(fact_6163_all__set__conv__all__nth,axiom,
% 5.12/5.40 ! [Xs: list_o,P: $o > $o] :
% 5.12/5.40 ( ( ! [X2: $o] :
% 5.12/5.40 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.12/5.40 => ( P @ X2 ) ) )
% 5.12/5.40 = ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_o @ Xs @ I2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_set_conv_all_nth
% 5.12/5.40 thf(fact_6164_all__set__conv__all__nth,axiom,
% 5.12/5.40 ! [Xs: list_nat,P: nat > $o] :
% 5.12/5.40 ( ( ! [X2: nat] :
% 5.12/5.40 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.12/5.40 => ( P @ X2 ) ) )
% 5.12/5.40 = ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_set_conv_all_nth
% 5.12/5.40 thf(fact_6165_all__set__conv__all__nth,axiom,
% 5.12/5.40 ! [Xs: list_int,P: int > $o] :
% 5.12/5.40 ( ( ! [X2: int] :
% 5.12/5.40 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.12/5.40 => ( P @ X2 ) ) )
% 5.12/5.40 = ( ! [I2: nat] :
% 5.12/5.40 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( P @ ( nth_int @ Xs @ I2 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % all_set_conv_all_nth
% 5.12/5.40 thf(fact_6166_round__mono,axiom,
% 5.12/5.40 ! [X: rat,Y: rat] :
% 5.12/5.40 ( ( ord_less_eq_rat @ X @ Y )
% 5.12/5.40 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_mono
% 5.12/5.40 thf(fact_6167_floor__le__round,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim8280529875227126926d_real @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_le_round
% 5.12/5.40 thf(fact_6168_floor__le__round,axiom,
% 5.12/5.40 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim7778729529865785530nd_rat @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % floor_le_round
% 5.12/5.40 thf(fact_6169_ceiling__ge__round,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % ceiling_ge_round
% 5.12/5.40 thf(fact_6170_nth__rotate1,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.12/5.40 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs ) @ N )
% 5.12/5.40 = ( nth_VEBT_VEBT @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_rotate1
% 5.12/5.40 thf(fact_6171_nth__rotate1,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_o] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.12/5.40 => ( ( nth_o @ ( rotate1_o @ Xs ) @ N )
% 5.12/5.40 = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_rotate1
% 5.12/5.40 thf(fact_6172_nth__rotate1,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.12/5.40 => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N )
% 5.12/5.40 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_rotate1
% 5.12/5.40 thf(fact_6173_nth__rotate1,axiom,
% 5.12/5.40 ! [N: nat,Xs: list_int] :
% 5.12/5.40 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.12/5.40 => ( ( nth_int @ ( rotate1_int @ Xs ) @ N )
% 5.12/5.40 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % nth_rotate1
% 5.12/5.40 thf(fact_6174_signed__take__bit__int__less__exp,axiom,
% 5.12/5.40 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_less_exp
% 5.12/5.40 thf(fact_6175_round__diff__minimal,axiom,
% 5.12/5.40 ! [Z2: real,M2: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z2 ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ ( ring_1_of_int_real @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_diff_minimal
% 5.12/5.40 thf(fact_6176_round__diff__minimal,axiom,
% 5.12/5.40 ! [Z2: rat,M2: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z2 ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z2 @ ( ring_1_of_int_rat @ M2 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_diff_minimal
% 5.12/5.40 thf(fact_6177_signed__take__bit__int__less__self__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.12/5.40 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_less_self_iff
% 5.12/5.40 thf(fact_6178_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.12/5.40 ! [K: int,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.12/5.40 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_greater_eq_self_iff
% 5.12/5.40 thf(fact_6179_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.12/5.40 ! [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 ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_greater_eq_minus_exp
% 5.12/5.40 thf(fact_6180_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.12/5.40 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_less_eq_self_iff
% 5.12/5.40 thf(fact_6181_signed__take__bit__int__greater__self__iff,axiom,
% 5.12/5.40 ! [K: int,N: nat] :
% 5.12/5.40 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.12/5.40 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_greater_self_iff
% 5.12/5.40 thf(fact_6182_signed__take__bit__int__less__eq,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.12/5.40 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_less_eq
% 5.12/5.40 thf(fact_6183_signed__take__bit__int__eq__self__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.12/5.40 = K )
% 5.12/5.40 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.12/5.40 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_eq_self_iff
% 5.12/5.40 thf(fact_6184_signed__take__bit__int__eq__self,axiom,
% 5.12/5.40 ! [N: nat,K: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.12/5.40 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.40 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.12/5.40 = K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_eq_self
% 5.12/5.40 thf(fact_6185_signed__take__bit__int__greater__eq,axiom,
% 5.12/5.40 ! [K: int,N: nat] :
% 5.12/5.40 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.40 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_int_greater_eq
% 5.12/5.40 thf(fact_6186_round__def,axiom,
% 5.12/5.40 ( archim8280529875227126926d_real
% 5.12/5.40 = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_def
% 5.12/5.40 thf(fact_6187_round__def,axiom,
% 5.12/5.40 ( archim7778729529865785530nd_rat
% 5.12/5.40 = ( ^ [X2: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_def
% 5.12/5.40 thf(fact_6188_signed__take__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: code_integer] :
% 5.12/5.40 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.12/5.40 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc
% 5.12/5.40 thf(fact_6189_signed__take__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,A: int] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.12/5.40 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc
% 5.12/5.40 thf(fact_6190_of__int__round__le,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_le
% 5.12/5.40 thf(fact_6191_of__int__round__le,axiom,
% 5.12/5.40 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_le
% 5.12/5.40 thf(fact_6192_of__int__round__ge,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_ge
% 5.12/5.40 thf(fact_6193_of__int__round__ge,axiom,
% 5.12/5.40 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_ge
% 5.12/5.40 thf(fact_6194_of__int__round__gt,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_gt
% 5.12/5.40 thf(fact_6195_of__int__round__gt,axiom,
% 5.12/5.40 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_gt
% 5.12/5.40 thf(fact_6196_of__int__round__abs__le,axiom,
% 5.12/5.40 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_abs_le
% 5.12/5.40 thf(fact_6197_of__int__round__abs__le,axiom,
% 5.12/5.40 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % of_int_round_abs_le
% 5.12/5.40 thf(fact_6198_round__unique_H,axiom,
% 5.12/5.40 ! [X: real,N: int] :
% 5.12/5.40 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( archim8280529875227126926d_real @ X )
% 5.12/5.40 = N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_unique'
% 5.12/5.40 thf(fact_6199_round__unique_H,axiom,
% 5.12/5.40 ! [X: rat,N: int] :
% 5.12/5.40 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ( archim7778729529865785530nd_rat @ X )
% 5.12/5.40 = N ) ) ).
% 5.12/5.40
% 5.12/5.40 % round_unique'
% 5.12/5.40 thf(fact_6200_in__children__def,axiom,
% 5.12/5.40 ( vEBT_V5917875025757280293ildren
% 5.12/5.40 = ( ^ [N4: nat,TreeList3: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X2 @ N4 ) ) @ ( vEBT_VEBT_low @ X2 @ N4 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % in_children_def
% 5.12/5.40 thf(fact_6201_log__base__10__eq1,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.40 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.40 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % log_base_10_eq1
% 5.12/5.40 thf(fact_6202_central__binomial__lower__bound,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( 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 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % central_binomial_lower_bound
% 5.12/5.40 thf(fact_6203_signed__take__bit__Suc__minus__bit1,axiom,
% 5.12/5.40 ! [N: nat,K: num] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.40 = ( 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 ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc_minus_bit1
% 5.12/5.40 thf(fact_6204_concat__bit__Suc,axiom,
% 5.12/5.40 ! [N: nat,K: int,L: int] :
% 5.12/5.40 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.12/5.40 = ( 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 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % concat_bit_Suc
% 5.12/5.40 thf(fact_6205_arctan__inverse,axiom,
% 5.12/5.40 ! [X: real] :
% 5.12/5.40 ( ( X != zero_zero_real )
% 5.12/5.40 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.12/5.40 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % arctan_inverse
% 5.12/5.40 thf(fact_6206_verit__eq__simplify_I9_J,axiom,
% 5.12/5.40 ! [X32: num,Y32: num] :
% 5.12/5.40 ( ( ( bit1 @ X32 )
% 5.12/5.40 = ( bit1 @ Y32 ) )
% 5.12/5.40 = ( X32 = Y32 ) ) ).
% 5.12/5.40
% 5.12/5.40 % verit_eq_simplify(9)
% 5.12/5.40 thf(fact_6207_binomial__Suc__n,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( binomial @ ( suc @ N ) @ N )
% 5.12/5.40 = ( suc @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_Suc_n
% 5.12/5.40 thf(fact_6208_binomial__n__n,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( binomial @ N @ N )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_n_n
% 5.12/5.40 thf(fact_6209_concat__bit__0,axiom,
% 5.12/5.40 ! [K: int,L: int] :
% 5.12/5.40 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.12/5.40 = L ) ).
% 5.12/5.40
% 5.12/5.40 % concat_bit_0
% 5.12/5.40 thf(fact_6210_binomial__1,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.40 = N ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_1
% 5.12/5.40 thf(fact_6211_binomial__0__Suc,axiom,
% 5.12/5.40 ! [K: nat] :
% 5.12/5.40 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.12/5.40 = zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_0_Suc
% 5.12/5.40 thf(fact_6212_binomial__eq__0__iff,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( ( binomial @ N @ K )
% 5.12/5.40 = zero_zero_nat )
% 5.12/5.40 = ( ord_less_nat @ N @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_eq_0_iff
% 5.12/5.40 thf(fact_6213_binomial__Suc__Suc,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.12/5.40 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_Suc_Suc
% 5.12/5.40 thf(fact_6214_binomial__n__0,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( binomial @ N @ zero_zero_nat )
% 5.12/5.40 = one_one_nat ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_n_0
% 5.12/5.40 thf(fact_6215_concat__bit__nonnegative__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int,L: int] :
% 5.12/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.12/5.40 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.12/5.40
% 5.12/5.40 % concat_bit_nonnegative_iff
% 5.12/5.40 thf(fact_6216_concat__bit__negative__iff,axiom,
% 5.12/5.40 ! [N: nat,K: int,L: int] :
% 5.12/5.40 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.12/5.40 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % concat_bit_negative_iff
% 5.12/5.40 thf(fact_6217_dbl__inc__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(5)
% 5.12/5.40 thf(fact_6218_dbl__inc__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(5)
% 5.12/5.40 thf(fact_6219_dbl__inc__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(5)
% 5.12/5.40 thf(fact_6220_dbl__inc__simps_I5_J,axiom,
% 5.12/5.40 ! [K: num] :
% 5.12/5.40 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(5)
% 5.12/5.40 thf(fact_6221_zdiv__numeral__Bit1,axiom,
% 5.12/5.40 ! [V: num,W: num] :
% 5.12/5.40 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.12/5.40 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zdiv_numeral_Bit1
% 5.12/5.40 thf(fact_6222_zero__less__binomial__iff,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_less_binomial_iff
% 5.12/5.40 thf(fact_6223_dbl__inc__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.12/5.40 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(3)
% 5.12/5.40 thf(fact_6224_dbl__inc__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.12/5.40 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(3)
% 5.12/5.40 thf(fact_6225_dbl__inc__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.12/5.40 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(3)
% 5.12/5.40 thf(fact_6226_dbl__inc__simps_I3_J,axiom,
% 5.12/5.40 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.12/5.40 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_inc_simps(3)
% 5.12/5.40 thf(fact_6227_div__Suc__eq__div__add3,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.12/5.40 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % div_Suc_eq_div_add3
% 5.12/5.40 thf(fact_6228_Suc__div__eq__add3__div__numeral,axiom,
% 5.12/5.40 ! [M2: nat,V: num] :
% 5.12/5.40 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.12/5.40 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_div_eq_add3_div_numeral
% 5.12/5.40 thf(fact_6229_mod__Suc__eq__mod__add3,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.12/5.40 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % mod_Suc_eq_mod_add3
% 5.12/5.40 thf(fact_6230_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.12/5.40 ! [M2: nat,V: num] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.12/5.40 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_mod_eq_add3_mod_numeral
% 5.12/5.40 thf(fact_6231_dbl__dec__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_dec_simps(4)
% 5.12/5.40 thf(fact_6232_dbl__dec__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_dec_simps(4)
% 5.12/5.40 thf(fact_6233_dbl__dec__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_dec_simps(4)
% 5.12/5.40 thf(fact_6234_dbl__dec__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_dec_simps(4)
% 5.12/5.40 thf(fact_6235_dbl__dec__simps_I4_J,axiom,
% 5.12/5.40 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % dbl_dec_simps(4)
% 5.12/5.40 thf(fact_6236_zmod__numeral__Bit1,axiom,
% 5.12/5.40 ! [V: num,W: num] :
% 5.12/5.40 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.12/5.40 = ( 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 ) ) ).
% 5.12/5.40
% 5.12/5.40 % zmod_numeral_Bit1
% 5.12/5.40 thf(fact_6237_signed__take__bit__Suc__bit1,axiom,
% 5.12/5.40 ! [N: nat,K: num] :
% 5.12/5.40 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % signed_take_bit_Suc_bit1
% 5.12/5.40 thf(fact_6238_choose__one,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( binomial @ N @ one_one_nat )
% 5.12/5.40 = N ) ).
% 5.12/5.40
% 5.12/5.40 % choose_one
% 5.12/5.40 thf(fact_6239_verit__eq__simplify_I14_J,axiom,
% 5.12/5.40 ! [X23: num,X32: num] :
% 5.12/5.40 ( ( bit0 @ X23 )
% 5.12/5.40 != ( bit1 @ X32 ) ) ).
% 5.12/5.40
% 5.12/5.40 % verit_eq_simplify(14)
% 5.12/5.40 thf(fact_6240_verit__eq__simplify_I12_J,axiom,
% 5.12/5.40 ! [X32: num] :
% 5.12/5.40 ( one
% 5.12/5.40 != ( bit1 @ X32 ) ) ).
% 5.12/5.40
% 5.12/5.40 % verit_eq_simplify(12)
% 5.12/5.40 thf(fact_6241_pi__neq__zero,axiom,
% 5.12/5.40 pi != zero_zero_real ).
% 5.12/5.40
% 5.12/5.40 % pi_neq_zero
% 5.12/5.40 thf(fact_6242_binomial__eq__0,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_nat @ N @ K )
% 5.12/5.40 => ( ( binomial @ N @ K )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_eq_0
% 5.12/5.40 thf(fact_6243_Suc__times__binomial,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.12/5.40 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_times_binomial
% 5.12/5.40 thf(fact_6244_Suc__times__binomial__eq,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_times_binomial_eq
% 5.12/5.40 thf(fact_6245_binomial__symmetric,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( binomial @ N @ K )
% 5.12/5.40 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_symmetric
% 5.12/5.40 thf(fact_6246_binomial__gbinomial,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_gbinomial
% 5.12/5.40 thf(fact_6247_binomial__gbinomial,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_gbinomial
% 5.12/5.40 thf(fact_6248_binomial__gbinomial,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_gbinomial
% 5.12/5.40 thf(fact_6249_num_Oexhaust,axiom,
% 5.12/5.40 ! [Y: num] :
% 5.12/5.40 ( ( Y != one )
% 5.12/5.40 => ( ! [X24: num] :
% 5.12/5.40 ( Y
% 5.12/5.40 != ( bit0 @ X24 ) )
% 5.12/5.40 => ~ ! [X33: num] :
% 5.12/5.40 ( Y
% 5.12/5.40 != ( bit1 @ X33 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % num.exhaust
% 5.12/5.40 thf(fact_6250_pi__not__less__zero,axiom,
% 5.12/5.40 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % pi_not_less_zero
% 5.12/5.40 thf(fact_6251_pi__gt__zero,axiom,
% 5.12/5.40 ord_less_real @ zero_zero_real @ pi ).
% 5.12/5.40
% 5.12/5.40 % pi_gt_zero
% 5.12/5.40 thf(fact_6252_pi__ge__zero,axiom,
% 5.12/5.40 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.12/5.40
% 5.12/5.40 % pi_ge_zero
% 5.12/5.40 thf(fact_6253_inc_Osimps_I2_J,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( inc @ ( bit0 @ X ) )
% 5.12/5.40 = ( bit1 @ X ) ) ).
% 5.12/5.40
% 5.12/5.40 % inc.simps(2)
% 5.12/5.40 thf(fact_6254_inc_Osimps_I3_J,axiom,
% 5.12/5.40 ! [X: num] :
% 5.12/5.40 ( ( inc @ ( bit1 @ X ) )
% 5.12/5.40 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % inc.simps(3)
% 5.12/5.40 thf(fact_6255_zero__less__binomial,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % zero_less_binomial
% 5.12/5.40 thf(fact_6256_Suc__times__binomial__add,axiom,
% 5.12/5.40 ! [A: nat,B: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.12/5.40 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_times_binomial_add
% 5.12/5.40 thf(fact_6257_choose__mult,axiom,
% 5.12/5.40 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ M2 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.40 => ( ( times_times_nat @ ( binomial @ N @ M2 ) @ ( binomial @ M2 @ K ) )
% 5.12/5.40 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % choose_mult
% 5.12/5.40 thf(fact_6258_binomial__Suc__Suc__eq__times,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.12/5.40 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_Suc_Suc_eq_times
% 5.12/5.40 thf(fact_6259_binomial__absorb__comp,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_absorb_comp
% 5.12/5.40 thf(fact_6260_numeral__Bit1,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.12/5.40 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1
% 5.12/5.40 thf(fact_6261_numeral__Bit1,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.12/5.40 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1
% 5.12/5.40 thf(fact_6262_numeral__Bit1,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.12/5.40 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1
% 5.12/5.40 thf(fact_6263_numeral__Bit1,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.12/5.40 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1
% 5.12/5.40 thf(fact_6264_numeral__Bit1,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.12/5.40 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1
% 5.12/5.40 thf(fact_6265_eval__nat__numeral_I3_J,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.12/5.40 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % eval_nat_numeral(3)
% 5.12/5.40 thf(fact_6266_power__minus__Bit1,axiom,
% 5.12/5.40 ! [X: int,K: num] :
% 5.12/5.40 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit1
% 5.12/5.40 thf(fact_6267_power__minus__Bit1,axiom,
% 5.12/5.40 ! [X: real,K: num] :
% 5.12/5.40 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit1
% 5.12/5.40 thf(fact_6268_power__minus__Bit1,axiom,
% 5.12/5.40 ! [X: complex,K: num] :
% 5.12/5.40 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit1
% 5.12/5.40 thf(fact_6269_power__minus__Bit1,axiom,
% 5.12/5.40 ! [X: code_integer,K: num] :
% 5.12/5.40 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit1
% 5.12/5.40 thf(fact_6270_power__minus__Bit1,axiom,
% 5.12/5.40 ! [X: rat,K: num] :
% 5.12/5.40 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.40 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % power_minus_Bit1
% 5.12/5.40 thf(fact_6271_binomial__absorption,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.12/5.40 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_absorption
% 5.12/5.40 thf(fact_6272_numeral__Bit1__div__2,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1_div_2
% 5.12/5.40 thf(fact_6273_numeral__Bit1__div__2,axiom,
% 5.12/5.40 ! [N: num] :
% 5.12/5.40 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.40 = ( numeral_numeral_int @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_Bit1_div_2
% 5.12/5.40 thf(fact_6274_binomial__fact__lemma,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_fact_lemma
% 5.12/5.40 thf(fact_6275_cong__exp__iff__simps_I3_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 != zero_zero_int ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(3)
% 5.12/5.40 thf(fact_6276_cong__exp__iff__simps_I3_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 != zero_zero_nat ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(3)
% 5.12/5.40 thf(fact_6277_cong__exp__iff__simps_I3_J,axiom,
% 5.12/5.40 ! [N: num,Q5: num] :
% 5.12/5.40 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 != zero_z3403309356797280102nteger ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(3)
% 5.12/5.40 thf(fact_6278_numeral__3__eq__3,axiom,
% 5.12/5.40 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.12/5.40 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % numeral_3_eq_3
% 5.12/5.40 thf(fact_6279_machin__Euler,axiom,
% 5.12/5.40 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.12/5.40 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % machin_Euler
% 5.12/5.40 thf(fact_6280_Suc3__eq__add__3,axiom,
% 5.12/5.40 ! [N: nat] :
% 5.12/5.40 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.12/5.40 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc3_eq_add_3
% 5.12/5.40 thf(fact_6281_machin,axiom,
% 5.12/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.40 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % machin
% 5.12/5.40 thf(fact_6282_pi__less__4,axiom,
% 5.12/5.40 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pi_less_4
% 5.12/5.40 thf(fact_6283_pi__ge__two,axiom,
% 5.12/5.40 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.12/5.40
% 5.12/5.40 % pi_ge_two
% 5.12/5.40 thf(fact_6284_pi__half__neq__two,axiom,
% 5.12/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.40 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % pi_half_neq_two
% 5.12/5.40 thf(fact_6285_binomial__ge__n__over__k__pow__k,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_ge_n_over_k_pow_k
% 5.12/5.40 thf(fact_6286_binomial__ge__n__over__k__pow__k,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_ge_n_over_k_pow_k
% 5.12/5.40 thf(fact_6287_binomial__mono,axiom,
% 5.12/5.40 ! [K: nat,K6: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ K6 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.12/5.40 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_mono
% 5.12/5.40 thf(fact_6288_binomial__maximum_H,axiom,
% 5.12/5.40 ! [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 ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_maximum'
% 5.12/5.40 thf(fact_6289_binomial__maximum,axiom,
% 5.12/5.40 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_maximum
% 5.12/5.40 thf(fact_6290_binomial__antimono,axiom,
% 5.12/5.40 ! [K: nat,K6: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ K6 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.12/5.40 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.12/5.40 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_antimono
% 5.12/5.40 thf(fact_6291_choose__reduce__nat,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.40 => ( ( binomial @ N @ K )
% 5.12/5.40 = ( 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 ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % choose_reduce_nat
% 5.12/5.40 thf(fact_6292_times__binomial__minus1__eq,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.40 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % times_binomial_minus1_eq
% 5.12/5.40 thf(fact_6293_num_Osize_I6_J,axiom,
% 5.12/5.40 ! [X32: num] :
% 5.12/5.40 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.12/5.40 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % num.size(6)
% 5.12/5.40 thf(fact_6294_binomial__altdef__nat,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( binomial @ N @ K )
% 5.12/5.40 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_altdef_nat
% 5.12/5.40 thf(fact_6295_cong__exp__iff__simps_I11_J,axiom,
% 5.12/5.40 ! [M2: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q5 ) )
% 5.12/5.40 = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(11)
% 5.12/5.40 thf(fact_6296_cong__exp__iff__simps_I11_J,axiom,
% 5.12/5.40 ! [M2: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q5 ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(11)
% 5.12/5.40 thf(fact_6297_cong__exp__iff__simps_I11_J,axiom,
% 5.12/5.40 ! [M2: num,Q5: num] :
% 5.12/5.40 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ Q5 ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(11)
% 5.12/5.40 thf(fact_6298_cong__exp__iff__simps_I7_J,axiom,
% 5.12/5.40 ! [Q5: num,N: num] :
% 5.12/5.40 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q5 ) )
% 5.12/5.40 = zero_zero_int ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(7)
% 5.12/5.40 thf(fact_6299_cong__exp__iff__simps_I7_J,axiom,
% 5.12/5.40 ! [Q5: num,N: num] :
% 5.12/5.40 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q5 ) )
% 5.12/5.40 = zero_zero_nat ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(7)
% 5.12/5.40 thf(fact_6300_cong__exp__iff__simps_I7_J,axiom,
% 5.12/5.40 ! [Q5: num,N: num] :
% 5.12/5.40 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) )
% 5.12/5.40 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q5 ) ) ) )
% 5.12/5.40 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q5 ) )
% 5.12/5.40 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.40
% 5.12/5.40 % cong_exp_iff_simps(7)
% 5.12/5.40 thf(fact_6301_Suc__div__eq__add3__div,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 5.12/5.40 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_div_eq_add3_div
% 5.12/5.40 thf(fact_6302_Suc__mod__eq__add3__mod,axiom,
% 5.12/5.40 ! [M2: nat,N: nat] :
% 5.12/5.40 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 5.12/5.40 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 5.12/5.40
% 5.12/5.40 % Suc_mod_eq_add3_mod
% 5.12/5.40 thf(fact_6303_pi__half__neq__zero,axiom,
% 5.12/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.40 != zero_zero_real ) ).
% 5.12/5.40
% 5.12/5.40 % pi_half_neq_zero
% 5.12/5.40 thf(fact_6304_pi__half__less__two,axiom,
% 5.12/5.40 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % pi_half_less_two
% 5.12/5.40 thf(fact_6305_pi__half__le__two,axiom,
% 5.12/5.40 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % pi_half_le_two
% 5.12/5.40 thf(fact_6306_exp__le,axiom,
% 5.12/5.40 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.12/5.40
% 5.12/5.40 % exp_le
% 5.12/5.40 thf(fact_6307_binomial__strict__mono,axiom,
% 5.12/5.40 ! [K: nat,K6: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ K @ K6 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.12/5.40 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_strict_mono
% 5.12/5.40 thf(fact_6308_binomial__strict__antimono,axiom,
% 5.12/5.40 ! [K: nat,K6: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ K @ K6 )
% 5.12/5.40 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.12/5.40 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.12/5.40 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_strict_antimono
% 5.12/5.40 thf(fact_6309_binomial__less__binomial__Suc,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.40 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_less_binomial_Suc
% 5.12/5.40 thf(fact_6310_binomial__addition__formula,axiom,
% 5.12/5.40 ! [N: nat,K: nat] :
% 5.12/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.40 => ( ( binomial @ N @ ( suc @ K ) )
% 5.12/5.40 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_addition_formula
% 5.12/5.40 thf(fact_6311_binomial__fact,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_fact
% 5.12/5.40 thf(fact_6312_binomial__fact,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_fact
% 5.12/5.40 thf(fact_6313_binomial__fact,axiom,
% 5.12/5.40 ! [K: nat,N: nat] :
% 5.12/5.40 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.40 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.12/5.40 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.12/5.40
% 5.12/5.40 % binomial_fact
% 5.12/5.40 thf(fact_6314_fact__binomial,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_binomial
% 5.12/5.41 thf(fact_6315_fact__binomial,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.12/5.41 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_binomial
% 5.12/5.41 thf(fact_6316_fact__binomial,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.12/5.41 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_binomial
% 5.12/5.41 thf(fact_6317_mod__exhaust__less__4,axiom,
% 5.12/5.41 ! [M2: nat] :
% 5.12/5.41 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_nat )
% 5.12/5.41 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_exhaust_less_4
% 5.12/5.41 thf(fact_6318_pi__half__gt__zero,axiom,
% 5.12/5.41 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pi_half_gt_zero
% 5.12/5.41 thf(fact_6319_pi__half__ge__zero,axiom,
% 5.12/5.41 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pi_half_ge_zero
% 5.12/5.41 thf(fact_6320_m2pi__less__pi,axiom,
% 5.12/5.41 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.12/5.41
% 5.12/5.41 % m2pi_less_pi
% 5.12/5.41 thf(fact_6321_arctan__ubound,axiom,
% 5.12/5.41 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % arctan_ubound
% 5.12/5.41 thf(fact_6322_arctan__one,axiom,
% 5.12/5.41 ( ( arctan @ one_one_real )
% 5.12/5.41 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % arctan_one
% 5.12/5.41 thf(fact_6323_choose__two,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_two
% 5.12/5.41 thf(fact_6324_minus__pi__half__less__zero,axiom,
% 5.12/5.41 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.12/5.41
% 5.12/5.41 % minus_pi_half_less_zero
% 5.12/5.41 thf(fact_6325_arctan__lbound,axiom,
% 5.12/5.41 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % arctan_lbound
% 5.12/5.41 thf(fact_6326_arctan__bounded,axiom,
% 5.12/5.41 ! [Y: real] :
% 5.12/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.12/5.41 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % arctan_bounded
% 5.12/5.41 thf(fact_6327_log__base__10__eq2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 = ( times_times_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % log_base_10_eq2
% 5.12/5.41 thf(fact_6328_binomial__code,axiom,
% 5.12/5.41 ( binomial
% 5.12/5.41 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % binomial_code
% 5.12/5.41 thf(fact_6329_sin__cos__npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( 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 ) ) ) )
% 5.12/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_npi
% 5.12/5.41 thf(fact_6330_signed__take__bit__numeral__minus__bit1,axiom,
% 5.12/5.41 ! [L: num,K: num] :
% 5.12/5.41 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.41 = ( 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 ) ) ).
% 5.12/5.41
% 5.12/5.41 % signed_take_bit_numeral_minus_bit1
% 5.12/5.41 thf(fact_6331_cos__pi__eq__zero,axiom,
% 5.12/5.41 ! [M2: nat] :
% 5.12/5.41 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_pi_eq_zero
% 5.12/5.41 thf(fact_6332_signed__take__bit__numeral__bit1,axiom,
% 5.12/5.41 ! [L: num,K: num] :
% 5.12/5.41 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.12/5.41 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % signed_take_bit_numeral_bit1
% 5.12/5.41 thf(fact_6333_cot__less__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.41 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_less_zero
% 5.12/5.41 thf(fact_6334_sin__zero,axiom,
% 5.12/5.41 ( ( sin_real @ zero_zero_real )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero
% 5.12/5.41 thf(fact_6335_cos__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.41 = ( cos_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_minus
% 5.12/5.41 thf(fact_6336_cos__minus,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( cos_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.41 = ( cos_complex @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_minus
% 5.12/5.41 thf(fact_6337_sin__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_minus
% 5.12/5.41 thf(fact_6338_sin__minus,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( sin_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( sin_complex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_minus
% 5.12/5.41 thf(fact_6339_cot__zero,axiom,
% 5.12/5.41 ( ( cot_real @ zero_zero_real )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cot_zero
% 5.12/5.41 thf(fact_6340_cot__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cot_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( cot_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_minus
% 5.12/5.41 thf(fact_6341_cot__minus,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( cot_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( cot_complex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_minus
% 5.12/5.41 thf(fact_6342_cos__zero,axiom,
% 5.12/5.41 ( ( cos_complex @ zero_zero_complex )
% 5.12/5.41 = one_one_complex ) ).
% 5.12/5.41
% 5.12/5.41 % cos_zero
% 5.12/5.41 thf(fact_6343_cos__zero,axiom,
% 5.12/5.41 ( ( cos_real @ zero_zero_real )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_zero
% 5.12/5.41 thf(fact_6344_pred__numeral__simps_I1_J,axiom,
% 5.12/5.41 ( ( pred_numeral @ one )
% 5.12/5.41 = zero_zero_nat ) ).
% 5.12/5.41
% 5.12/5.41 % pred_numeral_simps(1)
% 5.12/5.41 thf(fact_6345_sin__pi,axiom,
% 5.12/5.41 ( ( sin_real @ pi )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_pi
% 5.12/5.41 thf(fact_6346_Suc__eq__numeral,axiom,
% 5.12/5.41 ! [N: nat,K: num] :
% 5.12/5.41 ( ( ( suc @ N )
% 5.12/5.41 = ( numeral_numeral_nat @ K ) )
% 5.12/5.41 = ( N
% 5.12/5.41 = ( pred_numeral @ K ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Suc_eq_numeral
% 5.12/5.41 thf(fact_6347_eq__numeral__Suc,axiom,
% 5.12/5.41 ! [K: num,N: nat] :
% 5.12/5.41 ( ( ( numeral_numeral_nat @ K )
% 5.12/5.41 = ( suc @ N ) )
% 5.12/5.41 = ( ( pred_numeral @ K )
% 5.12/5.41 = N ) ) ).
% 5.12/5.41
% 5.12/5.41 % eq_numeral_Suc
% 5.12/5.41 thf(fact_6348_sin__pi__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 5.12/5.41 = ( sin_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_pi_minus
% 5.12/5.41 thf(fact_6349_pred__numeral__inc,axiom,
% 5.12/5.41 ! [K: num] :
% 5.12/5.41 ( ( pred_numeral @ ( inc @ K ) )
% 5.12/5.41 = ( numeral_numeral_nat @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % pred_numeral_inc
% 5.12/5.41 thf(fact_6350_cot__pi,axiom,
% 5.12/5.41 ( ( cot_real @ pi )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cot_pi
% 5.12/5.41 thf(fact_6351_sin__of__real__pi,axiom,
% 5.12/5.41 ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real_pi
% 5.12/5.41 thf(fact_6352_sin__of__real__pi,axiom,
% 5.12/5.41 ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.12/5.41 = zero_zero_complex ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real_pi
% 5.12/5.41 thf(fact_6353_pred__numeral__simps_I3_J,axiom,
% 5.12/5.41 ! [K: num] :
% 5.12/5.41 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.12/5.41 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pred_numeral_simps(3)
% 5.12/5.41 thf(fact_6354_less__numeral__Suc,axiom,
% 5.12/5.41 ! [K: num,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.12/5.41 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % less_numeral_Suc
% 5.12/5.41 thf(fact_6355_less__Suc__numeral,axiom,
% 5.12/5.41 ! [N: nat,K: num] :
% 5.12/5.41 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.41 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % less_Suc_numeral
% 5.12/5.41 thf(fact_6356_le__Suc__numeral,axiom,
% 5.12/5.41 ! [N: nat,K: num] :
% 5.12/5.41 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.41 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % le_Suc_numeral
% 5.12/5.41 thf(fact_6357_le__numeral__Suc,axiom,
% 5.12/5.41 ! [K: num,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.12/5.41 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % le_numeral_Suc
% 5.12/5.41 thf(fact_6358_diff__Suc__numeral,axiom,
% 5.12/5.41 ! [N: nat,K: num] :
% 5.12/5.41 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.41 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % diff_Suc_numeral
% 5.12/5.41 thf(fact_6359_diff__numeral__Suc,axiom,
% 5.12/5.41 ! [K: num,N: nat] :
% 5.12/5.41 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.12/5.41 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % diff_numeral_Suc
% 5.12/5.41 thf(fact_6360_cos__pi,axiom,
% 5.12/5.41 ( ( cos_real @ pi )
% 5.12/5.41 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_pi
% 5.12/5.41 thf(fact_6361_cos__periodic__pi2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_periodic_pi2
% 5.12/5.41 thf(fact_6362_cos__periodic__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_periodic_pi
% 5.12/5.41 thf(fact_6363_sin__periodic__pi2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_periodic_pi2
% 5.12/5.41 thf(fact_6364_sin__periodic__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_periodic_pi
% 5.12/5.41 thf(fact_6365_cos__minus__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_minus_pi
% 5.12/5.41 thf(fact_6366_cos__pi__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_pi_minus
% 5.12/5.41 thf(fact_6367_sin__minus__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_minus_pi
% 5.12/5.41 thf(fact_6368_sin__cos__squared__add3,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.12/5.41 = one_one_complex ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add3
% 5.12/5.41 thf(fact_6369_sin__cos__squared__add3,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add3
% 5.12/5.41 thf(fact_6370_cos__of__real__pi,axiom,
% 5.12/5.41 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real_pi
% 5.12/5.41 thf(fact_6371_cos__of__real__pi,axiom,
% 5.12/5.41 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real_pi
% 5.12/5.41 thf(fact_6372_sin__npi2,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_npi2
% 5.12/5.41 thf(fact_6373_sin__npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_npi
% 5.12/5.41 thf(fact_6374_sin__npi__int,axiom,
% 5.12/5.41 ! [N: int] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_npi_int
% 5.12/5.41 thf(fact_6375_cot__npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cot_npi
% 5.12/5.41 thf(fact_6376_cos__pi__half,axiom,
% 5.12/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_pi_half
% 5.12/5.41 thf(fact_6377_sin__two__pi,axiom,
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_two_pi
% 5.12/5.41 thf(fact_6378_sin__pi__half,axiom,
% 5.12/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_pi_half
% 5.12/5.41 thf(fact_6379_cos__two__pi,axiom,
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_two_pi
% 5.12/5.41 thf(fact_6380_cos__periodic,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.41 = ( cos_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_periodic
% 5.12/5.41 thf(fact_6381_sin__periodic,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.41 = ( sin_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_periodic
% 5.12/5.41 thf(fact_6382_cos__2pi__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.12/5.41 = ( cos_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_2pi_minus
% 5.12/5.41 thf(fact_6383_cos__npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.12/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_npi
% 5.12/5.41 thf(fact_6384_cos__npi2,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_npi2
% 5.12/5.41 thf(fact_6385_cot__periodic,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.41 = ( cot_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_periodic
% 5.12/5.41 thf(fact_6386_sin__cos__squared__add,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add
% 5.12/5.41 thf(fact_6387_sin__cos__squared__add,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_complex ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add
% 5.12/5.41 thf(fact_6388_sin__cos__squared__add2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add2
% 5.12/5.41 thf(fact_6389_sin__cos__squared__add2,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_complex ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_squared_add2
% 5.12/5.41 thf(fact_6390_cos__of__real__pi__half,axiom,
% 5.12/5.41 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real_pi_half
% 5.12/5.41 thf(fact_6391_cos__of__real__pi__half,axiom,
% 5.12/5.41 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = zero_zero_complex ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real_pi_half
% 5.12/5.41 thf(fact_6392_sin__of__real__pi__half,axiom,
% 5.12/5.41 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real_pi_half
% 5.12/5.41 thf(fact_6393_sin__of__real__pi__half,axiom,
% 5.12/5.41 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_complex ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real_pi_half
% 5.12/5.41 thf(fact_6394_sin__2npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_2npi
% 5.12/5.41 thf(fact_6395_cos__2npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_2npi
% 5.12/5.41 thf(fact_6396_sin__2pi__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_2pi_minus
% 5.12/5.41 thf(fact_6397_sin__int__2pin,axiom,
% 5.12/5.41 ! [N: int] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_int_2pin
% 5.12/5.41 thf(fact_6398_cos__int__2pin,axiom,
% 5.12/5.41 ! [N: int] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_int_2pin
% 5.12/5.41 thf(fact_6399_signed__take__bit__numeral__minus__bit0,axiom,
% 5.12/5.41 ! [L: num,K: num] :
% 5.12/5.41 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.41 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % signed_take_bit_numeral_minus_bit0
% 5.12/5.41 thf(fact_6400_cos__3over2__pi,axiom,
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_3over2_pi
% 5.12/5.41 thf(fact_6401_sin__3over2__pi,axiom,
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.12/5.41 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_3over2_pi
% 5.12/5.41 thf(fact_6402_cos__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( real_V1803761363581548252l_real @ X ) )
% 5.12/5.41 = ( real_V1803761363581548252l_real @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real
% 5.12/5.41 thf(fact_6403_cos__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_complex @ ( real_V4546457046886955230omplex @ X ) )
% 5.12/5.41 = ( real_V4546457046886955230omplex @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_of_real
% 5.12/5.41 thf(fact_6404_cot__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( real_V1803761363581548252l_real @ ( cot_real @ X ) )
% 5.12/5.41 = ( cot_real @ ( real_V1803761363581548252l_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_of_real
% 5.12/5.41 thf(fact_6405_cot__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( real_V4546457046886955230omplex @ ( cot_real @ X ) )
% 5.12/5.41 = ( cot_complex @ ( real_V4546457046886955230omplex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_of_real
% 5.12/5.41 thf(fact_6406_sin__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( real_V1803761363581548252l_real @ X ) )
% 5.12/5.41 = ( real_V1803761363581548252l_real @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real
% 5.12/5.41 thf(fact_6407_sin__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_complex @ ( real_V4546457046886955230omplex @ X ) )
% 5.12/5.41 = ( real_V4546457046886955230omplex @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_of_real
% 5.12/5.41 thf(fact_6408_cot__def,axiom,
% 5.12/5.41 ( cot_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X2 ) @ ( sin_complex @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_def
% 5.12/5.41 thf(fact_6409_cot__def,axiom,
% 5.12/5.41 ( cot_real
% 5.12/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_def
% 5.12/5.41 thf(fact_6410_cos__one__sin__zero,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( ( cos_complex @ X )
% 5.12/5.41 = one_one_complex )
% 5.12/5.41 => ( ( sin_complex @ X )
% 5.12/5.41 = zero_zero_complex ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_one_sin_zero
% 5.12/5.41 thf(fact_6411_cos__one__sin__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( cos_real @ X )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_one_sin_zero
% 5.12/5.41 thf(fact_6412_polar__Ex,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ? [R3: real,A4: real] :
% 5.12/5.41 ( ( X
% 5.12/5.41 = ( times_times_real @ R3 @ ( cos_real @ A4 ) ) )
% 5.12/5.41 & ( Y
% 5.12/5.41 = ( times_times_real @ R3 @ ( sin_real @ A4 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % polar_Ex
% 5.12/5.41 thf(fact_6413_sin__add,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.41 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_add
% 5.12/5.41 thf(fact_6414_sin__diff,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.41 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_diff
% 5.12/5.41 thf(fact_6415_cos__diff,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.41 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_diff
% 5.12/5.41 thf(fact_6416_cos__add,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.41 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_add
% 5.12/5.41 thf(fact_6417_sin__zero__norm__cos__one,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.12/5.41 = one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_norm_cos_one
% 5.12/5.41 thf(fact_6418_sin__zero__norm__cos__one,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( ( sin_complex @ X )
% 5.12/5.41 = zero_zero_complex )
% 5.12/5.41 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.12/5.41 = one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_norm_cos_one
% 5.12/5.41 thf(fact_6419_sin__zero__abs__cos__one,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.12/5.41 = one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_abs_cos_one
% 5.12/5.41 thf(fact_6420_sin__double,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_double
% 5.12/5.41 thf(fact_6421_sin__double,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_double
% 5.12/5.41 thf(fact_6422_sincos__principal__value,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ? [Y3: real] :
% 5.12/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.12/5.41 & ( ord_less_eq_real @ Y3 @ pi )
% 5.12/5.41 & ( ( sin_real @ Y3 )
% 5.12/5.41 = ( sin_real @ X ) )
% 5.12/5.41 & ( ( cos_real @ Y3 )
% 5.12/5.41 = ( cos_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sincos_principal_value
% 5.12/5.41 thf(fact_6423_sin__x__le__x,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_x_le_x
% 5.12/5.41 thf(fact_6424_sin__le__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_le_one
% 5.12/5.41 thf(fact_6425_cos__le__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_le_one
% 5.12/5.41 thf(fact_6426_abs__sin__x__le__abs__x,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % abs_sin_x_le_abs_x
% 5.12/5.41 thf(fact_6427_cos__arctan__not__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( arctan @ X ) )
% 5.12/5.41 != zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_arctan_not_zero
% 5.12/5.41 thf(fact_6428_numeral__eq__Suc,axiom,
% 5.12/5.41 ( numeral_numeral_nat
% 5.12/5.41 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % numeral_eq_Suc
% 5.12/5.41 thf(fact_6429_cos__int__times__real,axiom,
% 5.12/5.41 ! [M2: int,X: real] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.12/5.41 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_int_times_real
% 5.12/5.41 thf(fact_6430_cos__int__times__real,axiom,
% 5.12/5.41 ! [M2: int,X: real] :
% 5.12/5.41 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M2 ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.12/5.41 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_int_times_real
% 5.12/5.41 thf(fact_6431_sin__cos__le1,axiom,
% 5.12/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_le1
% 5.12/5.41 thf(fact_6432_sin__int__times__real,axiom,
% 5.12/5.41 ! [M2: int,X: real] :
% 5.12/5.41 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.12/5.41 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_int_times_real
% 5.12/5.41 thf(fact_6433_sin__int__times__real,axiom,
% 5.12/5.41 ! [M2: int,X: real] :
% 5.12/5.41 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M2 ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.12/5.41 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M2 ) @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_int_times_real
% 5.12/5.41 thf(fact_6434_cos__squared__eq,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_squared_eq
% 5.12/5.41 thf(fact_6435_cos__squared__eq,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_squared_eq
% 5.12/5.41 thf(fact_6436_sin__squared__eq,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_squared_eq
% 5.12/5.41 thf(fact_6437_sin__squared__eq,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_squared_eq
% 5.12/5.41 thf(fact_6438_sin__gt__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ pi )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_gt_zero
% 5.12/5.41 thf(fact_6439_sin__x__ge__neg__x,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_x_ge_neg_x
% 5.12/5.41 thf(fact_6440_sin__ge__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_ge_zero
% 5.12/5.41 thf(fact_6441_sin__ge__minus__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_ge_minus_one
% 5.12/5.41 thf(fact_6442_cos__inj__pi,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.12/5.41 => ( ( ( cos_real @ X )
% 5.12/5.41 = ( cos_real @ Y ) )
% 5.12/5.41 => ( X = Y ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_inj_pi
% 5.12/5.41 thf(fact_6443_cos__mono__le__eq,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.12/5.41 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.12/5.41 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_mono_le_eq
% 5.12/5.41 thf(fact_6444_cos__monotone__0__pi__le,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_monotone_0_pi_le
% 5.12/5.41 thf(fact_6445_sin__times__pi__eq__0,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_times_pi_eq_0
% 5.12/5.41 thf(fact_6446_cos__ge__minus__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_ge_minus_one
% 5.12/5.41 thf(fact_6447_abs__sin__le__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % abs_sin_le_one
% 5.12/5.41 thf(fact_6448_abs__cos__le__one,axiom,
% 5.12/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % abs_cos_le_one
% 5.12/5.41 thf(fact_6449_cos__diff__cos,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z2 ) )
% 5.12/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z2 @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_diff_cos
% 5.12/5.41 thf(fact_6450_cos__diff__cos,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z2 ) )
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z2 @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_diff_cos
% 5.12/5.41 thf(fact_6451_sin__diff__sin,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z2 ) )
% 5.12/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_diff_sin
% 5.12/5.41 thf(fact_6452_sin__diff__sin,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z2 ) )
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_diff_sin
% 5.12/5.41 thf(fact_6453_sin__plus__sin,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z2 ) )
% 5.12/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_plus_sin
% 5.12/5.41 thf(fact_6454_sin__plus__sin,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z2 ) )
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_plus_sin
% 5.12/5.41 thf(fact_6455_cos__times__sin,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z2 ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z2 ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_times_sin
% 5.12/5.41 thf(fact_6456_cos__times__sin,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z2 ) )
% 5.12/5.41 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z2 ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_times_sin
% 5.12/5.41 thf(fact_6457_sin__times__cos,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z2 ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z2 ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_times_cos
% 5.12/5.41 thf(fact_6458_sin__times__cos,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z2 ) )
% 5.12/5.41 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z2 ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_times_cos
% 5.12/5.41 thf(fact_6459_sin__times__sin,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z2 ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z2 ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_times_sin
% 5.12/5.41 thf(fact_6460_sin__times__sin,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z2 ) )
% 5.12/5.41 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z2 ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_times_sin
% 5.12/5.41 thf(fact_6461_cos__double,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double
% 5.12/5.41 thf(fact_6462_cos__double,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double
% 5.12/5.41 thf(fact_6463_sin__cos__eq,axiom,
% 5.12/5.41 ( sin_real
% 5.12/5.41 = ( ^ [X2: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_eq
% 5.12/5.41 thf(fact_6464_sin__cos__eq,axiom,
% 5.12/5.41 ( sin_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_cos_eq
% 5.12/5.41 thf(fact_6465_cos__sin__eq,axiom,
% 5.12/5.41 ( cos_real
% 5.12/5.41 = ( ^ [X2: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_sin_eq
% 5.12/5.41 thf(fact_6466_cos__sin__eq,axiom,
% 5.12/5.41 ( cos_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_sin_eq
% 5.12/5.41 thf(fact_6467_pred__numeral__def,axiom,
% 5.12/5.41 ( pred_numeral
% 5.12/5.41 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pred_numeral_def
% 5.12/5.41 thf(fact_6468_cos__double__sin,axiom,
% 5.12/5.41 ! [W: complex] :
% 5.12/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.12/5.41 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double_sin
% 5.12/5.41 thf(fact_6469_cos__double__sin,axiom,
% 5.12/5.41 ! [W: real] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.12/5.41 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double_sin
% 5.12/5.41 thf(fact_6470_minus__sin__cos__eq,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 5.12/5.41 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_sin_cos_eq
% 5.12/5.41 thf(fact_6471_minus__sin__cos__eq,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 5.12/5.41 = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_sin_cos_eq
% 5.12/5.41 thf(fact_6472_cos__two__neq__zero,axiom,
% 5.12/5.41 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.41 != zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % cos_two_neq_zero
% 5.12/5.41 thf(fact_6473_cos__monotone__0__pi,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ord_less_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_monotone_0_pi
% 5.12/5.41 thf(fact_6474_cos__mono__less__eq,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.12/5.41 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.12/5.41 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_mono_less_eq
% 5.12/5.41 thf(fact_6475_sin__eq__0__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ pi )
% 5.12/5.41 => ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 => ( X = zero_zero_real ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_eq_0_pi
% 5.12/5.41 thf(fact_6476_sin__zero__pi__iff,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 5.12/5.41 => ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( X = zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_pi_iff
% 5.12/5.41 thf(fact_6477_cos__monotone__minus__pi__0_H,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.41 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_monotone_minus_pi_0'
% 5.12/5.41 thf(fact_6478_sin__zero__iff__int2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( ? [I2: int] :
% 5.12/5.41 ( X
% 5.12/5.41 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_iff_int2
% 5.12/5.41 thf(fact_6479_sincos__total__pi,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ? [T3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.41 & ( ord_less_eq_real @ T3 @ pi )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( cos_real @ T3 ) )
% 5.12/5.41 & ( Y
% 5.12/5.41 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sincos_total_pi
% 5.12/5.41 thf(fact_6480_sin__expansion__lemma,axiom,
% 5.12/5.41 ! [X: real,M2: nat] :
% 5.12/5.41 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.41 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_expansion_lemma
% 5.12/5.41 thf(fact_6481_cos__expansion__lemma,axiom,
% 5.12/5.41 ! [X: real,M2: nat] :
% 5.12/5.41 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_expansion_lemma
% 5.12/5.41 thf(fact_6482_sin__gt__zero__02,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_gt_zero_02
% 5.12/5.41 thf(fact_6483_cos__two__less__zero,axiom,
% 5.12/5.41 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.12/5.41
% 5.12/5.41 % cos_two_less_zero
% 5.12/5.41 thf(fact_6484_cos__two__le__zero,axiom,
% 5.12/5.41 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.12/5.41
% 5.12/5.41 % cos_two_le_zero
% 5.12/5.41 thf(fact_6485_cos__is__zero,axiom,
% 5.12/5.41 ? [X3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.12/5.41 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.41 & ( ( cos_real @ X3 )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 & ! [Y5: real] :
% 5.12/5.41 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.12/5.41 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.41 & ( ( cos_real @ Y5 )
% 5.12/5.41 = zero_zero_real ) )
% 5.12/5.41 => ( Y5 = X3 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_is_zero
% 5.12/5.41 thf(fact_6486_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.12/5.41 ( set_fo2584398358068434914at_nat
% 5.12/5.41 = ( ^ [F2: nat > nat > nat,A3: nat,B2: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B2 @ A3 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F2 @ A3 @ Acc ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fold_atLeastAtMost_nat.simps
% 5.12/5.41 thf(fact_6487_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.12/5.41 ! [X: nat > nat > nat,Xa: nat,Xb3: nat,Xc: nat,Y: nat] :
% 5.12/5.41 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb3 @ Xc )
% 5.12/5.41 = Y )
% 5.12/5.41 => ( ( ( ord_less_nat @ Xb3 @ Xa )
% 5.12/5.41 => ( Y = Xc ) )
% 5.12/5.41 & ( ~ ( ord_less_nat @ Xb3 @ Xa )
% 5.12/5.41 => ( Y
% 5.12/5.41 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb3 @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fold_atLeastAtMost_nat.elims
% 5.12/5.41 thf(fact_6488_cos__monotone__minus__pi__0,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.12/5.41 => ( ( ord_less_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.41 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_monotone_minus_pi_0
% 5.12/5.41 thf(fact_6489_cos__total,axiom,
% 5.12/5.41 ! [Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.41 => ? [X3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.12/5.41 & ( ord_less_eq_real @ X3 @ pi )
% 5.12/5.41 & ( ( cos_real @ X3 )
% 5.12/5.41 = Y )
% 5.12/5.41 & ! [Y5: real] :
% 5.12/5.41 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.12/5.41 & ( ord_less_eq_real @ Y5 @ pi )
% 5.12/5.41 & ( ( cos_real @ Y5 )
% 5.12/5.41 = Y ) )
% 5.12/5.41 => ( Y5 = X3 ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_total
% 5.12/5.41 thf(fact_6490_sincos__total__pi__half,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.41 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ? [T3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.41 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( cos_real @ T3 ) )
% 5.12/5.41 & ( Y
% 5.12/5.41 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sincos_total_pi_half
% 5.12/5.41 thf(fact_6491_sincos__total__2pi__le,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ? [T3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.41 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( cos_real @ T3 ) )
% 5.12/5.41 & ( Y
% 5.12/5.41 = ( sin_real @ T3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sincos_total_2pi_le
% 5.12/5.41 thf(fact_6492_sincos__total__2pi,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ~ ! [T3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.41 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 => ( ( X
% 5.12/5.41 = ( cos_real @ T3 ) )
% 5.12/5.41 => ( Y
% 5.12/5.41 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sincos_total_2pi
% 5.12/5.41 thf(fact_6493_sin__integer__2pi,axiom,
% 5.12/5.41 ! [N: real] :
% 5.12/5.41 ( ( member_real @ N @ ring_1_Ints_real )
% 5.12/5.41 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.12/5.41 = zero_zero_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_integer_2pi
% 5.12/5.41 thf(fact_6494_cos__integer__2pi,axiom,
% 5.12/5.41 ! [N: real] :
% 5.12/5.41 ( ( member_real @ N @ ring_1_Ints_real )
% 5.12/5.41 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.12/5.41 = one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_integer_2pi
% 5.12/5.41 thf(fact_6495_sin__pi__divide__n__ge__0,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( N != zero_zero_nat )
% 5.12/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_pi_divide_n_ge_0
% 5.12/5.41 thf(fact_6496_cos__plus__cos,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z2 ) )
% 5.12/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_plus_cos
% 5.12/5.41 thf(fact_6497_cos__plus__cos,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z2 ) )
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_plus_cos
% 5.12/5.41 thf(fact_6498_cos__times__cos,axiom,
% 5.12/5.41 ! [W: complex,Z2: complex] :
% 5.12/5.41 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z2 ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z2 ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z2 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_times_cos
% 5.12/5.41 thf(fact_6499_cos__times__cos,axiom,
% 5.12/5.41 ! [W: real,Z2: real] :
% 5.12/5.41 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z2 ) )
% 5.12/5.41 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z2 ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_times_cos
% 5.12/5.41 thf(fact_6500_sin__gt__zero2,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_gt_zero2
% 5.12/5.41 thf(fact_6501_sin__lt__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ pi @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_lt_zero
% 5.12/5.41 thf(fact_6502_cos__double__less__one,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.41 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double_less_one
% 5.12/5.41 thf(fact_6503_sin__30,axiom,
% 5.12/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.12/5.41 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_30
% 5.12/5.41 thf(fact_6504_cos__gt__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_gt_zero
% 5.12/5.41 thf(fact_6505_sin__monotone__2pi__le,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_monotone_2pi_le
% 5.12/5.41 thf(fact_6506_sin__mono__le__eq,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.12/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_mono_le_eq
% 5.12/5.41 thf(fact_6507_sin__inj__pi,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ( sin_real @ X )
% 5.12/5.41 = ( sin_real @ Y ) )
% 5.12/5.41 => ( X = Y ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_inj_pi
% 5.12/5.41 thf(fact_6508_cos__60,axiom,
% 5.12/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.12/5.41 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_60
% 5.12/5.41 thf(fact_6509_cos__one__2pi__int,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( cos_real @ X )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 = ( ? [X2: int] :
% 5.12/5.41 ( X
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_one_2pi_int
% 5.12/5.41 thf(fact_6510_cos__double__cos,axiom,
% 5.12/5.41 ! [W: complex] :
% 5.12/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.12/5.41 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double_cos
% 5.12/5.41 thf(fact_6511_cos__double__cos,axiom,
% 5.12/5.41 ! [W: real] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.12/5.41 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_double_cos
% 5.12/5.41 thf(fact_6512_cos__treble__cos,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.12/5.41 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_treble_cos
% 5.12/5.41 thf(fact_6513_cos__treble__cos,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.12/5.41 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_treble_cos
% 5.12/5.41 thf(fact_6514_sin__le__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ pi @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_le_zero
% 5.12/5.41 thf(fact_6515_sin__less__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.41 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_less_zero
% 5.12/5.41 thf(fact_6516_sin__mono__less__eq,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.12/5.41 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_mono_less_eq
% 5.12/5.41 thf(fact_6517_sin__monotone__2pi,axiom,
% 5.12/5.41 ! [Y: real,X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.41 => ( ( ord_less_real @ Y @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_monotone_2pi
% 5.12/5.41 thf(fact_6518_sin__total,axiom,
% 5.12/5.41 ! [Y: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.41 => ? [X3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.12/5.41 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 & ( ( sin_real @ X3 )
% 5.12/5.41 = Y )
% 5.12/5.41 & ! [Y5: real] :
% 5.12/5.41 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.12/5.41 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 & ( ( sin_real @ Y5 )
% 5.12/5.41 = Y ) )
% 5.12/5.41 => ( Y5 = X3 ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_total
% 5.12/5.41 thf(fact_6519_cos__gt__zero__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_gt_zero_pi
% 5.12/5.41 thf(fact_6520_cos__ge__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_ge_zero
% 5.12/5.41 thf(fact_6521_cos__one__2pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( cos_real @ X )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 = ( ? [X2: nat] :
% 5.12/5.41 ( X
% 5.12/5.41 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.12/5.41 | ? [X2: nat] :
% 5.12/5.41 ( X
% 5.12/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_one_2pi
% 5.12/5.41 thf(fact_6522_sin__pi__divide__n__gt__0,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_pi_divide_n_gt_0
% 5.12/5.41 thf(fact_6523_cot__gt__zero,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_gt_zero
% 5.12/5.41 thf(fact_6524_fact__code,axiom,
% 5.12/5.41 ( semiri5044797733671781792omplex
% 5.12/5.41 = ( ^ [N4: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_code
% 5.12/5.41 thf(fact_6525_fact__code,axiom,
% 5.12/5.41 ( semiri773545260158071498ct_rat
% 5.12/5.41 = ( ^ [N4: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_code
% 5.12/5.41 thf(fact_6526_fact__code,axiom,
% 5.12/5.41 ( semiri1406184849735516958ct_int
% 5.12/5.41 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_code
% 5.12/5.41 thf(fact_6527_fact__code,axiom,
% 5.12/5.41 ( semiri1408675320244567234ct_nat
% 5.12/5.41 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_code
% 5.12/5.41 thf(fact_6528_fact__code,axiom,
% 5.12/5.41 ( semiri2265585572941072030t_real
% 5.12/5.41 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % fact_code
% 5.12/5.41 thf(fact_6529_tan__double,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( ( cos_complex @ X )
% 5.12/5.41 != zero_zero_complex )
% 5.12/5.41 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 != zero_zero_complex )
% 5.12/5.41 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_double
% 5.12/5.41 thf(fact_6530_tan__double,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( cos_real @ X )
% 5.12/5.41 != zero_zero_real )
% 5.12/5.41 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 != zero_zero_real )
% 5.12/5.41 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.41 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_double
% 5.12/5.41 thf(fact_6531_complex__unimodular__polar,axiom,
% 5.12/5.41 ! [Z2: complex] :
% 5.12/5.41 ( ( ( real_V1022390504157884413omplex @ Z2 )
% 5.12/5.41 = one_one_real )
% 5.12/5.41 => ~ ! [T3: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.41 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.41 => ( Z2
% 5.12/5.41 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % complex_unimodular_polar
% 5.12/5.41 thf(fact_6532_sin__zero__iff,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( ? [N4: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.41 | ? [N4: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_iff
% 5.12/5.41 thf(fact_6533_cos__zero__iff,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ( cos_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( ? [N4: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.41 | ? [N4: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_zero_iff
% 5.12/5.41 thf(fact_6534_sin__zero__lemma,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ( sin_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 => ? [N2: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % sin_zero_lemma
% 5.12/5.41 thf(fact_6535_cos__zero__lemma,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.41 => ( ( ( cos_real @ X )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 => ? [N2: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.12/5.41 & ( X
% 5.12/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cos_zero_lemma
% 5.12/5.41 thf(fact_6536_dvd__0__right,axiom,
% 5.12/5.41 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_right
% 5.12/5.41 thf(fact_6537_dvd__0__right,axiom,
% 5.12/5.41 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_right
% 5.12/5.41 thf(fact_6538_dvd__0__right,axiom,
% 5.12/5.41 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_right
% 5.12/5.41 thf(fact_6539_dvd__0__right,axiom,
% 5.12/5.41 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_right
% 5.12/5.41 thf(fact_6540_dvd__0__right,axiom,
% 5.12/5.41 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_right
% 5.12/5.41 thf(fact_6541_dvd__0__left__iff,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.12/5.41 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left_iff
% 5.12/5.41 thf(fact_6542_dvd__0__left__iff,axiom,
% 5.12/5.41 ! [A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.12/5.41 = ( A = zero_zero_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left_iff
% 5.12/5.41 thf(fact_6543_dvd__0__left__iff,axiom,
% 5.12/5.41 ! [A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.12/5.41 = ( A = zero_zero_rat ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left_iff
% 5.12/5.41 thf(fact_6544_dvd__0__left__iff,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.12/5.41 = ( A = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left_iff
% 5.12/5.41 thf(fact_6545_dvd__0__left__iff,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.12/5.41 = ( A = zero_zero_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left_iff
% 5.12/5.41 thf(fact_6546_dvd__add__triv__right__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_right_iff
% 5.12/5.41 thf(fact_6547_dvd__add__triv__right__iff,axiom,
% 5.12/5.41 ! [A: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_right_iff
% 5.12/5.41 thf(fact_6548_dvd__add__triv__right__iff,axiom,
% 5.12/5.41 ! [A: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_right_iff
% 5.12/5.41 thf(fact_6549_dvd__add__triv__right__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_right_iff
% 5.12/5.41 thf(fact_6550_dvd__add__triv__right__iff,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_right_iff
% 5.12/5.41 thf(fact_6551_dvd__add__triv__left__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_left_iff
% 5.12/5.41 thf(fact_6552_dvd__add__triv__left__iff,axiom,
% 5.12/5.41 ! [A: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_left_iff
% 5.12/5.41 thf(fact_6553_dvd__add__triv__left__iff,axiom,
% 5.12/5.41 ! [A: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_left_iff
% 5.12/5.41 thf(fact_6554_dvd__add__triv__left__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_left_iff
% 5.12/5.41 thf(fact_6555_dvd__add__triv__left__iff,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_triv_left_iff
% 5.12/5.41 thf(fact_6556_div__dvd__div,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_div
% 5.12/5.41 thf(fact_6557_div__dvd__div,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_div
% 5.12/5.41 thf(fact_6558_div__dvd__div,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_div
% 5.12/5.41 thf(fact_6559_minus__dvd__iff,axiom,
% 5.12/5.41 ! [X: int,Y: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.12/5.41 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_dvd_iff
% 5.12/5.41 thf(fact_6560_minus__dvd__iff,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 5.12/5.41 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_dvd_iff
% 5.12/5.41 thf(fact_6561_minus__dvd__iff,axiom,
% 5.12/5.41 ! [X: complex,Y: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 5.12/5.41 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_dvd_iff
% 5.12/5.41 thf(fact_6562_minus__dvd__iff,axiom,
% 5.12/5.41 ! [X: code_integer,Y: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_dvd_iff
% 5.12/5.41 thf(fact_6563_minus__dvd__iff,axiom,
% 5.12/5.41 ! [X: rat,Y: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 5.12/5.41 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % minus_dvd_iff
% 5.12/5.41 thf(fact_6564_dvd__minus__iff,axiom,
% 5.12/5.41 ! [X: int,Y: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.12/5.41 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_iff
% 5.12/5.41 thf(fact_6565_dvd__minus__iff,axiom,
% 5.12/5.41 ! [X: real,Y: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 5.12/5.41 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_iff
% 5.12/5.41 thf(fact_6566_dvd__minus__iff,axiom,
% 5.12/5.41 ! [X: complex,Y: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 5.12/5.41 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_iff
% 5.12/5.41 thf(fact_6567_dvd__minus__iff,axiom,
% 5.12/5.41 ! [X: code_integer,Y: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_iff
% 5.12/5.41 thf(fact_6568_dvd__minus__iff,axiom,
% 5.12/5.41 ! [X: rat,Y: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 5.12/5.41 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_iff
% 5.12/5.41 thf(fact_6569_dvd__abs__iff,axiom,
% 5.12/5.41 ! [M2: int,K: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ M2 @ ( abs_abs_int @ K ) )
% 5.12/5.41 = ( dvd_dvd_int @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_abs_iff
% 5.12/5.41 thf(fact_6570_dvd__abs__iff,axiom,
% 5.12/5.41 ! [M2: real,K: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ M2 @ ( abs_abs_real @ K ) )
% 5.12/5.41 = ( dvd_dvd_real @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_abs_iff
% 5.12/5.41 thf(fact_6571_dvd__abs__iff,axiom,
% 5.12/5.41 ! [M2: code_integer,K: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ M2 @ ( abs_abs_Code_integer @ K ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_abs_iff
% 5.12/5.41 thf(fact_6572_dvd__abs__iff,axiom,
% 5.12/5.41 ! [M2: rat,K: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ M2 @ ( abs_abs_rat @ K ) )
% 5.12/5.41 = ( dvd_dvd_rat @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_abs_iff
% 5.12/5.41 thf(fact_6573_abs__dvd__iff,axiom,
% 5.12/5.41 ! [M2: int,K: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( abs_abs_int @ M2 ) @ K )
% 5.12/5.41 = ( dvd_dvd_int @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % abs_dvd_iff
% 5.12/5.41 thf(fact_6574_abs__dvd__iff,axiom,
% 5.12/5.41 ! [M2: real,K: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( abs_abs_real @ M2 ) @ K )
% 5.12/5.41 = ( dvd_dvd_real @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % abs_dvd_iff
% 5.12/5.41 thf(fact_6575_abs__dvd__iff,axiom,
% 5.12/5.41 ! [M2: code_integer,K: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M2 ) @ K )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % abs_dvd_iff
% 5.12/5.41 thf(fact_6576_abs__dvd__iff,axiom,
% 5.12/5.41 ! [M2: rat,K: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M2 ) @ K )
% 5.12/5.41 = ( dvd_dvd_rat @ M2 @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % abs_dvd_iff
% 5.12/5.41 thf(fact_6577_tan__pi,axiom,
% 5.12/5.41 ( ( tan_real @ pi )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % tan_pi
% 5.12/5.41 thf(fact_6578_tan__zero,axiom,
% 5.12/5.41 ( ( tan_real @ zero_zero_real )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % tan_zero
% 5.12/5.41 thf(fact_6579_nat__dvd__1__iff__1,axiom,
% 5.12/5.41 ! [M2: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 5.12/5.41 = ( M2 = one_one_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % nat_dvd_1_iff_1
% 5.12/5.41 thf(fact_6580_tan__minus,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( tan_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( tan_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_minus
% 5.12/5.41 thf(fact_6581_tan__minus,axiom,
% 5.12/5.41 ! [X: complex] :
% 5.12/5.41 ( ( tan_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( tan_complex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_minus
% 5.12/5.41 thf(fact_6582_tan__periodic__pi,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.12/5.41 = ( tan_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_periodic_pi
% 5.12/5.41 thf(fact_6583_dvd__times__right__cancel__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_right_cancel_iff
% 5.12/5.41 thf(fact_6584_dvd__times__right__cancel__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_right_cancel_iff
% 5.12/5.41 thf(fact_6585_dvd__times__right__cancel__iff,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.12/5.41 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_right_cancel_iff
% 5.12/5.41 thf(fact_6586_dvd__times__left__cancel__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_left_cancel_iff
% 5.12/5.41 thf(fact_6587_dvd__times__left__cancel__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.12/5.41 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_left_cancel_iff
% 5.12/5.41 thf(fact_6588_dvd__times__left__cancel__iff,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_times_left_cancel_iff
% 5.12/5.41 thf(fact_6589_dvd__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.41 = ( ( C = zero_z3403309356797280102nteger )
% 5.12/5.41 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_right
% 5.12/5.41 thf(fact_6590_dvd__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: real,C: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.12/5.41 = ( ( C = zero_zero_real )
% 5.12/5.41 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_right
% 5.12/5.41 thf(fact_6591_dvd__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: rat,C: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.12/5.41 = ( ( C = zero_zero_rat )
% 5.12/5.41 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_right
% 5.12/5.41 thf(fact_6592_dvd__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.12/5.41 = ( ( C = zero_zero_int )
% 5.12/5.41 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_right
% 5.12/5.41 thf(fact_6593_dvd__mult__cancel__left,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.12/5.41 = ( ( C = zero_z3403309356797280102nteger )
% 5.12/5.41 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_left
% 5.12/5.41 thf(fact_6594_dvd__mult__cancel__left,axiom,
% 5.12/5.41 ! [C: real,A: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.12/5.41 = ( ( C = zero_zero_real )
% 5.12/5.41 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_left
% 5.12/5.41 thf(fact_6595_dvd__mult__cancel__left,axiom,
% 5.12/5.41 ! [C: rat,A: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.12/5.41 = ( ( C = zero_zero_rat )
% 5.12/5.41 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_left
% 5.12/5.41 thf(fact_6596_dvd__mult__cancel__left,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.41 = ( ( C = zero_zero_int )
% 5.12/5.41 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel_left
% 5.12/5.41 thf(fact_6597_unit__prod,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_prod
% 5.12/5.41 thf(fact_6598_unit__prod,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_prod
% 5.12/5.41 thf(fact_6599_unit__prod,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_prod
% 5.12/5.41 thf(fact_6600_dvd__add__times__triv__right__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_right_iff
% 5.12/5.41 thf(fact_6601_dvd__add__times__triv__right__iff,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_right_iff
% 5.12/5.41 thf(fact_6602_dvd__add__times__triv__right__iff,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_right_iff
% 5.12/5.41 thf(fact_6603_dvd__add__times__triv__right__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_right_iff
% 5.12/5.41 thf(fact_6604_dvd__add__times__triv__right__iff,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_right_iff
% 5.12/5.41 thf(fact_6605_dvd__add__times__triv__left__iff,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_left_iff
% 5.12/5.41 thf(fact_6606_dvd__add__times__triv__left__iff,axiom,
% 5.12/5.41 ! [A: real,C: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_left_iff
% 5.12/5.41 thf(fact_6607_dvd__add__times__triv__left__iff,axiom,
% 5.12/5.41 ! [A: rat,C: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_left_iff
% 5.12/5.41 thf(fact_6608_dvd__add__times__triv__left__iff,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_left_iff
% 5.12/5.41 thf(fact_6609_dvd__add__times__triv__left__iff,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_times_triv_left_iff
% 5.12/5.41 thf(fact_6610_dvd__div__mult__self,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult_self
% 5.12/5.41 thf(fact_6611_dvd__div__mult__self,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult_self
% 5.12/5.41 thf(fact_6612_dvd__div__mult__self,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult_self
% 5.12/5.41 thf(fact_6613_dvd__mult__div__cancel,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_div_cancel
% 5.12/5.41 thf(fact_6614_dvd__mult__div__cancel,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_div_cancel
% 5.12/5.41 thf(fact_6615_dvd__mult__div__cancel,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_div_cancel
% 5.12/5.41 thf(fact_6616_unit__div__1__div__1,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_div_1
% 5.12/5.41 thf(fact_6617_unit__div__1__div__1,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_div_1
% 5.12/5.41 thf(fact_6618_unit__div__1__div__1,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_div_1
% 5.12/5.41 thf(fact_6619_unit__div__1__unit,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_unit
% 5.12/5.41 thf(fact_6620_unit__div__1__unit,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_unit
% 5.12/5.41 thf(fact_6621_unit__div__1__unit,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_1_unit
% 5.12/5.41 thf(fact_6622_unit__div,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div
% 5.12/5.41 thf(fact_6623_unit__div,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div
% 5.12/5.41 thf(fact_6624_unit__div,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div
% 5.12/5.41 thf(fact_6625_div__add,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.12/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_add
% 5.12/5.41 thf(fact_6626_div__add,axiom,
% 5.12/5.41 ! [C: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_add
% 5.12/5.41 thf(fact_6627_div__add,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_add
% 5.12/5.41 thf(fact_6628_div__diff,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.12/5.41 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_diff
% 5.12/5.41 thf(fact_6629_div__diff,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.12/5.41 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_diff
% 5.12/5.41 thf(fact_6630_dvd__imp__mod__0,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( modulo_modulo_int @ B @ A )
% 5.12/5.41 = zero_zero_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_imp_mod_0
% 5.12/5.41 thf(fact_6631_dvd__imp__mod__0,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( modulo_modulo_nat @ B @ A )
% 5.12/5.41 = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_imp_mod_0
% 5.12/5.41 thf(fact_6632_dvd__imp__mod__0,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.12/5.41 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_imp_mod_0
% 5.12/5.41 thf(fact_6633_dvd__imp__mod__0,axiom,
% 5.12/5.41 ! [A: code_natural,B: code_natural] :
% 5.12/5.41 ( ( dvd_dvd_Code_natural @ A @ B )
% 5.12/5.41 => ( ( modulo8411746178871703098atural @ B @ A )
% 5.12/5.41 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_imp_mod_0
% 5.12/5.41 thf(fact_6634_dvd__1__iff__1,axiom,
% 5.12/5.41 ! [M2: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.12/5.41 = ( M2
% 5.12/5.41 = ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_1_iff_1
% 5.12/5.41 thf(fact_6635_dvd__1__left,axiom,
% 5.12/5.41 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_1_left
% 5.12/5.41 thf(fact_6636_nat__mult__dvd__cancel__disj,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.41 = ( ( K = zero_zero_nat )
% 5.12/5.41 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % nat_mult_dvd_cancel_disj
% 5.12/5.41 thf(fact_6637_unit__mult__div__div,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_div_div
% 5.12/5.41 thf(fact_6638_unit__mult__div__div,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.12/5.41 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_div_div
% 5.12/5.41 thf(fact_6639_unit__mult__div__div,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.12/5.41 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_div_div
% 5.12/5.41 thf(fact_6640_unit__div__mult__self,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_self
% 5.12/5.41 thf(fact_6641_unit__div__mult__self,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_self
% 5.12/5.41 thf(fact_6642_unit__div__mult__self,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.12/5.41 = B ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_self
% 5.12/5.41 thf(fact_6643_pow__divides__pow__iff,axiom,
% 5.12/5.41 ! [N: nat,A: int,B: int] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pow_divides_pow_iff
% 5.12/5.41 thf(fact_6644_pow__divides__pow__iff,axiom,
% 5.12/5.41 ! [N: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pow_divides_pow_iff
% 5.12/5.41 thf(fact_6645_tan__npi,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.12/5.41 = zero_zero_real ) ).
% 5.12/5.41
% 5.12/5.41 % tan_npi
% 5.12/5.41 thf(fact_6646_tan__periodic__n,axiom,
% 5.12/5.41 ! [X: real,N: num] :
% 5.12/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.12/5.41 = ( tan_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_periodic_n
% 5.12/5.41 thf(fact_6647_tan__periodic__nat,axiom,
% 5.12/5.41 ! [X: real,N: nat] :
% 5.12/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.12/5.41 = ( tan_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_periodic_nat
% 5.12/5.41 thf(fact_6648_tan__periodic__int,axiom,
% 5.12/5.41 ! [X: real,I: int] :
% 5.12/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.12/5.41 = ( tan_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_periodic_int
% 5.12/5.41 thf(fact_6649_even__Suc__Suc__iff,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_Suc_Suc_iff
% 5.12/5.41 thf(fact_6650_even__Suc,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_Suc
% 5.12/5.41 thf(fact_6651_norm__cos__sin,axiom,
% 5.12/5.41 ! [T: real] :
% 5.12/5.41 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.12/5.41 = one_one_real ) ).
% 5.12/5.41
% 5.12/5.41 % norm_cos_sin
% 5.12/5.41 thf(fact_6652_even__plus__one__iff,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_plus_one_iff
% 5.12/5.41 thf(fact_6653_even__plus__one__iff,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_plus_one_iff
% 5.12/5.41 thf(fact_6654_even__plus__one__iff,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_plus_one_iff
% 5.12/5.41 thf(fact_6655_even__diff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_diff
% 5.12/5.41 thf(fact_6656_even__diff,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_diff
% 5.12/5.41 thf(fact_6657_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.41 ! [N: nat,A: int] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.12/5.41 = ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Parity.ring_1_class.power_minus_even
% 5.12/5.41 thf(fact_6658_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.41 ! [N: nat,A: real] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.12/5.41 = ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Parity.ring_1_class.power_minus_even
% 5.12/5.41 thf(fact_6659_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.41 ! [N: nat,A: complex] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.12/5.41 = ( power_power_complex @ A @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Parity.ring_1_class.power_minus_even
% 5.12/5.41 thf(fact_6660_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.41 ! [N: nat,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.12/5.41 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Parity.ring_1_class.power_minus_even
% 5.12/5.41 thf(fact_6661_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.12/5.41 ! [N: nat,A: rat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.12/5.41 = ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Parity.ring_1_class.power_minus_even
% 5.12/5.41 thf(fact_6662_power__minus__odd,axiom,
% 5.12/5.41 ! [N: nat,A: int] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.12/5.41 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_minus_odd
% 5.12/5.41 thf(fact_6663_power__minus__odd,axiom,
% 5.12/5.41 ! [N: nat,A: real] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.12/5.41 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_minus_odd
% 5.12/5.41 thf(fact_6664_power__minus__odd,axiom,
% 5.12/5.41 ! [N: nat,A: complex] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_minus_odd
% 5.12/5.41 thf(fact_6665_power__minus__odd,axiom,
% 5.12/5.41 ! [N: nat,A: code_integer] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.12/5.41 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_minus_odd
% 5.12/5.41 thf(fact_6666_power__minus__odd,axiom,
% 5.12/5.41 ! [N: nat,A: rat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.12/5.41 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_minus_odd
% 5.12/5.41 thf(fact_6667_odd__Suc__div__two,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_Suc_div_two
% 5.12/5.41 thf(fact_6668_even__Suc__div__two,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_Suc_div_two
% 5.12/5.41 thf(fact_6669_tan__periodic,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.41 = ( tan_real @ X ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_periodic
% 5.12/5.41 thf(fact_6670_even__succ__div__2,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_2
% 5.12/5.41 thf(fact_6671_even__succ__div__2,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_2
% 5.12/5.41 thf(fact_6672_even__succ__div__2,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_2
% 5.12/5.41 thf(fact_6673_even__succ__div__two,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_two
% 5.12/5.41 thf(fact_6674_even__succ__div__two,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_two
% 5.12/5.41 thf(fact_6675_even__succ__div__two,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_two
% 5.12/5.41 thf(fact_6676_odd__succ__div__two,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_succ_div_two
% 5.12/5.41 thf(fact_6677_odd__succ__div__two,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_succ_div_two
% 5.12/5.41 thf(fact_6678_odd__succ__div__two,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_succ_div_two
% 5.12/5.41 thf(fact_6679_zero__le__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: real,W: num] :
% 5.12/5.41 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_le_power_eq_numeral
% 5.12/5.41 thf(fact_6680_zero__le__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: rat,W: num] :
% 5.12/5.41 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_le_power_eq_numeral
% 5.12/5.41 thf(fact_6681_zero__le__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: int,W: num] :
% 5.12/5.41 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_le_power_eq_numeral
% 5.12/5.41 thf(fact_6682_even__power,axiom,
% 5.12/5.41 ! [A: code_integer,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_power
% 5.12/5.41 thf(fact_6683_even__power,axiom,
% 5.12/5.41 ! [A: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_power
% 5.12/5.41 thf(fact_6684_even__power,axiom,
% 5.12/5.41 ! [A: int,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_power
% 5.12/5.41 thf(fact_6685_power__less__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: real,W: num] :
% 5.12/5.41 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq_numeral
% 5.12/5.41 thf(fact_6686_power__less__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: rat,W: num] :
% 5.12/5.41 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq_numeral
% 5.12/5.41 thf(fact_6687_power__less__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: int,W: num] :
% 5.12/5.41 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq_numeral
% 5.12/5.41 thf(fact_6688_power__less__zero__eq,axiom,
% 5.12/5.41 ! [A: real,N: nat] :
% 5.12/5.41 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq
% 5.12/5.41 thf(fact_6689_power__less__zero__eq,axiom,
% 5.12/5.41 ! [A: rat,N: nat] :
% 5.12/5.41 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq
% 5.12/5.41 thf(fact_6690_power__less__zero__eq,axiom,
% 5.12/5.41 ! [A: int,N: nat] :
% 5.12/5.41 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_less_zero_eq
% 5.12/5.41 thf(fact_6691_neg__one__odd__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.12/5.41 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_odd_power
% 5.12/5.41 thf(fact_6692_neg__one__odd__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.12/5.41 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_odd_power
% 5.12/5.41 thf(fact_6693_neg__one__odd__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_odd_power
% 5.12/5.41 thf(fact_6694_neg__one__odd__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.12/5.41 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_odd_power
% 5.12/5.41 thf(fact_6695_neg__one__odd__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.12/5.41 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_odd_power
% 5.12/5.41 thf(fact_6696_neg__one__even__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.12/5.41 = one_one_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_even_power
% 5.12/5.41 thf(fact_6697_neg__one__even__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.12/5.41 = one_one_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_even_power
% 5.12/5.41 thf(fact_6698_neg__one__even__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.12/5.41 = one_one_complex ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_even_power
% 5.12/5.41 thf(fact_6699_neg__one__even__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.12/5.41 = one_one_Code_integer ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_even_power
% 5.12/5.41 thf(fact_6700_neg__one__even__power,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.12/5.41 = one_one_rat ) ) ).
% 5.12/5.41
% 5.12/5.41 % neg_one_even_power
% 5.12/5.41 thf(fact_6701_even__of__nat,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_of_nat
% 5.12/5.41 thf(fact_6702_even__of__nat,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_of_nat
% 5.12/5.41 thf(fact_6703_even__of__nat,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_of_nat
% 5.12/5.41 thf(fact_6704_odd__Suc__minus__one,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.12/5.41 = N ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_Suc_minus_one
% 5.12/5.41 thf(fact_6705_even__diff__nat,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.41 = ( ( ord_less_nat @ M2 @ N )
% 5.12/5.41 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_diff_nat
% 5.12/5.41 thf(fact_6706_odd__two__times__div__two__succ,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_two_times_div_two_succ
% 5.12/5.41 thf(fact_6707_odd__two__times__div__two__succ,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_two_times_div_two_succ
% 5.12/5.41 thf(fact_6708_odd__two__times__div__two__succ,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.12/5.41 = A ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_two_times_div_two_succ
% 5.12/5.41 thf(fact_6709_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.12/5.41 = ( N = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % semiring_parity_class.even_mask_iff
% 5.12/5.41 thf(fact_6710_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.12/5.41 = ( N = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % semiring_parity_class.even_mask_iff
% 5.12/5.41 thf(fact_6711_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.12/5.41 = ( N = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % semiring_parity_class.even_mask_iff
% 5.12/5.41 thf(fact_6712_zero__less__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: real,W: num] :
% 5.12/5.41 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( ( numeral_numeral_nat @ W )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A != zero_zero_real ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_less_power_eq_numeral
% 5.12/5.41 thf(fact_6713_zero__less__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: rat,W: num] :
% 5.12/5.41 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( ( numeral_numeral_nat @ W )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A != zero_zero_rat ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_less_power_eq_numeral
% 5.12/5.41 thf(fact_6714_zero__less__power__eq__numeral,axiom,
% 5.12/5.41 ! [A: int,W: num] :
% 5.12/5.41 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.12/5.41 = ( ( ( numeral_numeral_nat @ W )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A != zero_zero_int ) )
% 5.12/5.41 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % zero_less_power_eq_numeral
% 5.12/5.41 thf(fact_6715_odd__two__times__div__two__nat,axiom,
% 5.12/5.41 ! [N: nat] :
% 5.12/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.41 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % odd_two_times_div_two_nat
% 5.12/5.41 thf(fact_6716_power__le__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: real,W: num] :
% 5.12/5.41 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.12/5.41 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_le_zero_eq_numeral
% 5.12/5.41 thf(fact_6717_power__le__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: rat,W: num] :
% 5.12/5.41 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.12/5.41 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_le_zero_eq_numeral
% 5.12/5.41 thf(fact_6718_power__le__zero__eq__numeral,axiom,
% 5.12/5.41 ! [A: int,W: num] :
% 5.12/5.41 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.12/5.41 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.12/5.41 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.12/5.41 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_le_zero_eq_numeral
% 5.12/5.41 thf(fact_6719_even__succ__div__exp,axiom,
% 5.12/5.41 ! [A: code_integer,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_exp
% 5.12/5.41 thf(fact_6720_even__succ__div__exp,axiom,
% 5.12/5.41 ! [A: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_exp
% 5.12/5.41 thf(fact_6721_even__succ__div__exp,axiom,
% 5.12/5.41 ! [A: int,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_div_exp
% 5.12/5.41 thf(fact_6722_even__succ__mod__exp,axiom,
% 5.12/5.41 ! [A: int,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_mod_exp
% 5.12/5.41 thf(fact_6723_even__succ__mod__exp,axiom,
% 5.12/5.41 ! [A: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_mod_exp
% 5.12/5.41 thf(fact_6724_even__succ__mod__exp,axiom,
% 5.12/5.41 ! [A: code_integer,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_mod_exp
% 5.12/5.41 thf(fact_6725_even__succ__mod__exp,axiom,
% 5.12/5.41 ! [A: code_natural,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.41 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_succ_mod_exp
% 5.12/5.41 thf(fact_6726_dvd__trans,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ C )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_trans
% 5.12/5.41 thf(fact_6727_dvd__trans,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ C )
% 5.12/5.41 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_trans
% 5.12/5.41 thf(fact_6728_dvd__trans,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_trans
% 5.12/5.41 thf(fact_6729_dvd__refl,axiom,
% 5.12/5.41 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_refl
% 5.12/5.41 thf(fact_6730_dvd__refl,axiom,
% 5.12/5.41 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_refl
% 5.12/5.41 thf(fact_6731_dvd__refl,axiom,
% 5.12/5.41 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_refl
% 5.12/5.41 thf(fact_6732_dvd__antisym,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ M2 @ N )
% 5.12/5.41 => ( ( dvd_dvd_nat @ N @ M2 )
% 5.12/5.41 => ( M2 = N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_antisym
% 5.12/5.41 thf(fact_6733_of__nat__dvd__iff,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % of_nat_dvd_iff
% 5.12/5.41 thf(fact_6734_of__nat__dvd__iff,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % of_nat_dvd_iff
% 5.12/5.41 thf(fact_6735_of__nat__dvd__iff,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ N ) ) ).
% 5.12/5.41
% 5.12/5.41 % of_nat_dvd_iff
% 5.12/5.41 thf(fact_6736_tan__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( real_V1803761363581548252l_real @ ( tan_real @ X ) )
% 5.12/5.41 = ( tan_real @ ( real_V1803761363581548252l_real @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_of_real
% 5.12/5.41 thf(fact_6737_tan__of__real,axiom,
% 5.12/5.41 ! [X: real] :
% 5.12/5.41 ( ( real_V4546457046886955230omplex @ ( tan_real @ X ) )
% 5.12/5.41 = ( tan_complex @ ( real_V4546457046886955230omplex @ X ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_of_real
% 5.12/5.41 thf(fact_6738_dvd__0__left,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.12/5.41 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left
% 5.12/5.41 thf(fact_6739_dvd__0__left,axiom,
% 5.12/5.41 ! [A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.12/5.41 => ( A = zero_zero_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left
% 5.12/5.41 thf(fact_6740_dvd__0__left,axiom,
% 5.12/5.41 ! [A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.12/5.41 => ( A = zero_zero_rat ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left
% 5.12/5.41 thf(fact_6741_dvd__0__left,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.12/5.41 => ( A = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left
% 5.12/5.41 thf(fact_6742_dvd__0__left,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.12/5.41 => ( A = zero_zero_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_0_left
% 5.12/5.41 thf(fact_6743_dvd__field__iff,axiom,
% 5.12/5.41 ( dvd_dvd_real
% 5.12/5.41 = ( ^ [A3: real,B2: real] :
% 5.12/5.41 ( ( A3 = zero_zero_real )
% 5.12/5.41 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_field_iff
% 5.12/5.41 thf(fact_6744_dvd__field__iff,axiom,
% 5.12/5.41 ( dvd_dvd_rat
% 5.12/5.41 = ( ^ [A3: rat,B2: rat] :
% 5.12/5.41 ( ( A3 = zero_zero_rat )
% 5.12/5.41 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_field_iff
% 5.12/5.41 thf(fact_6745_dvd__triv__right,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_right
% 5.12/5.41 thf(fact_6746_dvd__triv__right,axiom,
% 5.12/5.41 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_right
% 5.12/5.41 thf(fact_6747_dvd__triv__right,axiom,
% 5.12/5.41 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_right
% 5.12/5.41 thf(fact_6748_dvd__triv__right,axiom,
% 5.12/5.41 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_right
% 5.12/5.41 thf(fact_6749_dvd__triv__right,axiom,
% 5.12/5.41 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_right
% 5.12/5.41 thf(fact_6750_dvd__mult__right,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_right
% 5.12/5.41 thf(fact_6751_dvd__mult__right,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_right
% 5.12/5.41 thf(fact_6752_dvd__mult__right,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_right
% 5.12/5.41 thf(fact_6753_dvd__mult__right,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_right
% 5.12/5.41 thf(fact_6754_dvd__mult__right,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_right
% 5.12/5.41 thf(fact_6755_mult__dvd__mono,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_dvd_mono
% 5.12/5.41 thf(fact_6756_mult__dvd__mono,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_real @ C @ D )
% 5.12/5.41 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_dvd_mono
% 5.12/5.41 thf(fact_6757_mult__dvd__mono,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_rat @ C @ D )
% 5.12/5.41 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_dvd_mono
% 5.12/5.41 thf(fact_6758_mult__dvd__mono,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ D )
% 5.12/5.41 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_dvd_mono
% 5.12/5.41 thf(fact_6759_mult__dvd__mono,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ D )
% 5.12/5.41 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_dvd_mono
% 5.12/5.41 thf(fact_6760_dvd__triv__left,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_left
% 5.12/5.41 thf(fact_6761_dvd__triv__left,axiom,
% 5.12/5.41 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_left
% 5.12/5.41 thf(fact_6762_dvd__triv__left,axiom,
% 5.12/5.41 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_left
% 5.12/5.41 thf(fact_6763_dvd__triv__left,axiom,
% 5.12/5.41 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_left
% 5.12/5.41 thf(fact_6764_dvd__triv__left,axiom,
% 5.12/5.41 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_triv_left
% 5.12/5.41 thf(fact_6765_dvd__mult__left,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_left
% 5.12/5.41 thf(fact_6766_dvd__mult__left,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_left
% 5.12/5.41 thf(fact_6767_dvd__mult__left,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_left
% 5.12/5.41 thf(fact_6768_dvd__mult__left,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_left
% 5.12/5.41 thf(fact_6769_dvd__mult__left,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.41 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_left
% 5.12/5.41 thf(fact_6770_dvd__mult2,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult2
% 5.12/5.41 thf(fact_6771_dvd__mult2,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ B )
% 5.12/5.41 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult2
% 5.12/5.41 thf(fact_6772_dvd__mult2,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ B )
% 5.12/5.41 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult2
% 5.12/5.41 thf(fact_6773_dvd__mult2,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult2
% 5.12/5.41 thf(fact_6774_dvd__mult2,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult2
% 5.12/5.41 thf(fact_6775_dvd__mult,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult
% 5.12/5.41 thf(fact_6776_dvd__mult,axiom,
% 5.12/5.41 ! [A: real,C: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ C )
% 5.12/5.41 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult
% 5.12/5.41 thf(fact_6777_dvd__mult,axiom,
% 5.12/5.41 ! [A: rat,C: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ C )
% 5.12/5.41 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult
% 5.12/5.41 thf(fact_6778_dvd__mult,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ C )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult
% 5.12/5.41 thf(fact_6779_dvd__mult,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ C )
% 5.12/5.41 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult
% 5.12/5.41 thf(fact_6780_dvd__def,axiom,
% 5.12/5.41 ( dvd_dvd_Code_integer
% 5.12/5.41 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.12/5.41 ? [K3: code_integer] :
% 5.12/5.41 ( A3
% 5.12/5.41 = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_def
% 5.12/5.41 thf(fact_6781_dvd__def,axiom,
% 5.12/5.41 ( dvd_dvd_real
% 5.12/5.41 = ( ^ [B2: real,A3: real] :
% 5.12/5.41 ? [K3: real] :
% 5.12/5.41 ( A3
% 5.12/5.41 = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_def
% 5.12/5.41 thf(fact_6782_dvd__def,axiom,
% 5.12/5.41 ( dvd_dvd_rat
% 5.12/5.41 = ( ^ [B2: rat,A3: rat] :
% 5.12/5.41 ? [K3: rat] :
% 5.12/5.41 ( A3
% 5.12/5.41 = ( times_times_rat @ B2 @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_def
% 5.12/5.41 thf(fact_6783_dvd__def,axiom,
% 5.12/5.41 ( dvd_dvd_nat
% 5.12/5.41 = ( ^ [B2: nat,A3: nat] :
% 5.12/5.41 ? [K3: nat] :
% 5.12/5.41 ( A3
% 5.12/5.41 = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_def
% 5.12/5.41 thf(fact_6784_dvd__def,axiom,
% 5.12/5.41 ( dvd_dvd_int
% 5.12/5.41 = ( ^ [B2: int,A3: int] :
% 5.12/5.41 ? [K3: int] :
% 5.12/5.41 ( A3
% 5.12/5.41 = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_def
% 5.12/5.41 thf(fact_6785_dvdI,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.12/5.41 ( ( A
% 5.12/5.41 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdI
% 5.12/5.41 thf(fact_6786_dvdI,axiom,
% 5.12/5.41 ! [A: real,B: real,K: real] :
% 5.12/5.41 ( ( A
% 5.12/5.41 = ( times_times_real @ B @ K ) )
% 5.12/5.41 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdI
% 5.12/5.41 thf(fact_6787_dvdI,axiom,
% 5.12/5.41 ! [A: rat,B: rat,K: rat] :
% 5.12/5.41 ( ( A
% 5.12/5.41 = ( times_times_rat @ B @ K ) )
% 5.12/5.41 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdI
% 5.12/5.41 thf(fact_6788_dvdI,axiom,
% 5.12/5.41 ! [A: nat,B: nat,K: nat] :
% 5.12/5.41 ( ( A
% 5.12/5.41 = ( times_times_nat @ B @ K ) )
% 5.12/5.41 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdI
% 5.12/5.41 thf(fact_6789_dvdI,axiom,
% 5.12/5.41 ! [A: int,B: int,K: int] :
% 5.12/5.41 ( ( A
% 5.12/5.41 = ( times_times_int @ B @ K ) )
% 5.12/5.41 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdI
% 5.12/5.41 thf(fact_6790_dvdE,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ~ ! [K2: code_integer] :
% 5.12/5.41 ( A
% 5.12/5.41 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdE
% 5.12/5.41 thf(fact_6791_dvdE,axiom,
% 5.12/5.41 ! [B: real,A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ B @ A )
% 5.12/5.41 => ~ ! [K2: real] :
% 5.12/5.41 ( A
% 5.12/5.41 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdE
% 5.12/5.41 thf(fact_6792_dvdE,axiom,
% 5.12/5.41 ! [B: rat,A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ B @ A )
% 5.12/5.41 => ~ ! [K2: rat] :
% 5.12/5.41 ( A
% 5.12/5.41 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdE
% 5.12/5.41 thf(fact_6793_dvdE,axiom,
% 5.12/5.41 ! [B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ~ ! [K2: nat] :
% 5.12/5.41 ( A
% 5.12/5.41 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdE
% 5.12/5.41 thf(fact_6794_dvdE,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ~ ! [K2: int] :
% 5.12/5.41 ( A
% 5.12/5.41 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvdE
% 5.12/5.41 thf(fact_6795_one__dvd,axiom,
% 5.12/5.41 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6796_one__dvd,axiom,
% 5.12/5.41 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6797_one__dvd,axiom,
% 5.12/5.41 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6798_one__dvd,axiom,
% 5.12/5.41 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6799_one__dvd,axiom,
% 5.12/5.41 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6800_one__dvd,axiom,
% 5.12/5.41 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.12/5.41
% 5.12/5.41 % one_dvd
% 5.12/5.41 thf(fact_6801_unit__imp__dvd,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_dvd
% 5.12/5.41 thf(fact_6802_unit__imp__dvd,axiom,
% 5.12/5.41 ! [B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_dvd
% 5.12/5.41 thf(fact_6803_unit__imp__dvd,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_dvd
% 5.12/5.41 thf(fact_6804_dvd__unit__imp__unit,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_unit_imp_unit
% 5.12/5.41 thf(fact_6805_dvd__unit__imp__unit,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_unit_imp_unit
% 5.12/5.41 thf(fact_6806_dvd__unit__imp__unit,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_unit_imp_unit
% 5.12/5.41 thf(fact_6807_dvd__add__right__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_right_iff
% 5.12/5.41 thf(fact_6808_dvd__add__right__iff,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_right_iff
% 5.12/5.41 thf(fact_6809_dvd__add__right__iff,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_right_iff
% 5.12/5.41 thf(fact_6810_dvd__add__right__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_right_iff
% 5.12/5.41 thf(fact_6811_dvd__add__right__iff,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_right_iff
% 5.12/5.41 thf(fact_6812_dvd__add__left__iff,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_left_iff
% 5.12/5.41 thf(fact_6813_dvd__add__left__iff,axiom,
% 5.12/5.41 ! [A: real,C: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_left_iff
% 5.12/5.41 thf(fact_6814_dvd__add__left__iff,axiom,
% 5.12/5.41 ! [A: rat,C: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_left_iff
% 5.12/5.41 thf(fact_6815_dvd__add__left__iff,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_left_iff
% 5.12/5.41 thf(fact_6816_dvd__add__left__iff,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ C )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add_left_iff
% 5.12/5.41 thf(fact_6817_dvd__add,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add
% 5.12/5.41 thf(fact_6818_dvd__add,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_real @ A @ C )
% 5.12/5.41 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add
% 5.12/5.41 thf(fact_6819_dvd__add,axiom,
% 5.12/5.41 ! [A: rat,B: rat,C: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_rat @ A @ C )
% 5.12/5.41 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add
% 5.12/5.41 thf(fact_6820_dvd__add,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ C )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add
% 5.12/5.41 thf(fact_6821_dvd__add,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ C )
% 5.12/5.41 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_add
% 5.12/5.41 thf(fact_6822_dvd__diff,axiom,
% 5.12/5.41 ! [X: code_integer,Y: code_integer,Z2: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ X @ Z2 )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff
% 5.12/5.41 thf(fact_6823_dvd__diff,axiom,
% 5.12/5.41 ! [X: rat,Y: rat,Z2: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ X @ Y )
% 5.12/5.41 => ( ( dvd_dvd_rat @ X @ Z2 )
% 5.12/5.41 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff
% 5.12/5.41 thf(fact_6824_dvd__diff,axiom,
% 5.12/5.41 ! [X: int,Y: int,Z2: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ X @ Y )
% 5.12/5.41 => ( ( dvd_dvd_int @ X @ Z2 )
% 5.12/5.41 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff
% 5.12/5.41 thf(fact_6825_dvd__diff__commute,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff_commute
% 5.12/5.41 thf(fact_6826_dvd__diff__commute,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff_commute
% 5.12/5.41 thf(fact_6827_div__div__div__same,axiom,
% 5.12/5.41 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_div_same
% 5.12/5.41 thf(fact_6828_div__div__div__same,axiom,
% 5.12/5.41 ! [D: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ D @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.12/5.41 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_div_same
% 5.12/5.41 thf(fact_6829_div__div__div__same,axiom,
% 5.12/5.41 ! [D: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ D @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.12/5.41 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_div_same
% 5.12/5.41 thf(fact_6830_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.12/5.41 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6831_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: complex,C: complex,B: complex] :
% 5.12/5.41 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.12/5.41 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_complex @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_complex @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6832_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: real,C: real,B: real] :
% 5.12/5.41 ( ( ( divide_divide_real @ A @ C )
% 5.12/5.41 = ( divide_divide_real @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_real @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_real @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6833_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: rat,C: rat,B: rat] :
% 5.12/5.41 ( ( ( divide_divide_rat @ A @ C )
% 5.12/5.41 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_rat @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_rat @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6834_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat] :
% 5.12/5.41 ( ( ( divide_divide_nat @ A @ C )
% 5.12/5.41 = ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6835_dvd__div__eq__cancel,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( ( divide_divide_int @ A @ C )
% 5.12/5.41 = ( divide_divide_int @ B @ C ) )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_cancel
% 5.12/5.41 thf(fact_6836_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.12/5.41 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6837_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: complex,A: complex,B: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_complex @ C @ B )
% 5.12/5.41 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.12/5.41 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6838_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: real,A: real,B: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_real @ C @ B )
% 5.12/5.41 => ( ( ( divide_divide_real @ A @ C )
% 5.12/5.41 = ( divide_divide_real @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6839_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: rat,A: rat,B: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_rat @ C @ B )
% 5.12/5.41 => ( ( ( divide_divide_rat @ A @ C )
% 5.12/5.41 = ( divide_divide_rat @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6840_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( ( divide_divide_nat @ A @ C )
% 5.12/5.41 = ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6841_dvd__div__eq__iff,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( ( divide_divide_int @ A @ C )
% 5.12/5.41 = ( divide_divide_int @ B @ C ) )
% 5.12/5.41 = ( A = B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_iff
% 5.12/5.41 thf(fact_6842_gcd__nat_Oextremum,axiom,
% 5.12/5.41 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.12/5.41
% 5.12/5.41 % gcd_nat.extremum
% 5.12/5.41 thf(fact_6843_gcd__nat_Oextremum__strict,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.12/5.41 & ( zero_zero_nat != A ) ) ).
% 5.12/5.41
% 5.12/5.41 % gcd_nat.extremum_strict
% 5.12/5.41 thf(fact_6844_gcd__nat_Oextremum__unique,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.12/5.41 = ( A = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % gcd_nat.extremum_unique
% 5.12/5.41 thf(fact_6845_gcd__nat_Onot__eq__extremum,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 5.12/5.41 & ( A != zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % gcd_nat.not_eq_extremum
% 5.12/5.41 thf(fact_6846_gcd__nat_Oextremum__uniqueI,axiom,
% 5.12/5.41 ! [A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.12/5.41 => ( A = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % gcd_nat.extremum_uniqueI
% 5.12/5.41 thf(fact_6847_complex__minus,axiom,
% 5.12/5.41 ! [A: real,B: real] :
% 5.12/5.41 ( ( uminus1482373934393186551omplex @ ( complex2 @ A @ B ) )
% 5.12/5.41 = ( complex2 @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % complex_minus
% 5.12/5.41 thf(fact_6848_dvd__if__abs__eq,axiom,
% 5.12/5.41 ! [L: int,K: int] :
% 5.12/5.41 ( ( ( abs_abs_int @ L )
% 5.12/5.41 = ( abs_abs_int @ K ) )
% 5.12/5.41 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_if_abs_eq
% 5.12/5.41 thf(fact_6849_dvd__if__abs__eq,axiom,
% 5.12/5.41 ! [L: real,K: real] :
% 5.12/5.41 ( ( ( abs_abs_real @ L )
% 5.12/5.41 = ( abs_abs_real @ K ) )
% 5.12/5.41 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_if_abs_eq
% 5.12/5.41 thf(fact_6850_dvd__if__abs__eq,axiom,
% 5.12/5.41 ! [L: code_integer,K: code_integer] :
% 5.12/5.41 ( ( ( abs_abs_Code_integer @ L )
% 5.12/5.41 = ( abs_abs_Code_integer @ K ) )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_if_abs_eq
% 5.12/5.41 thf(fact_6851_dvd__if__abs__eq,axiom,
% 5.12/5.41 ! [L: rat,K: rat] :
% 5.12/5.41 ( ( ( abs_abs_rat @ L )
% 5.12/5.41 = ( abs_abs_rat @ K ) )
% 5.12/5.41 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_if_abs_eq
% 5.12/5.41 thf(fact_6852_dvd__mod__imp__dvd,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_imp_dvd
% 5.12/5.41 thf(fact_6853_dvd__mod__imp__dvd,axiom,
% 5.12/5.41 ! [C: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_imp_dvd
% 5.12/5.41 thf(fact_6854_dvd__mod__imp__dvd,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_imp_dvd
% 5.12/5.41 thf(fact_6855_dvd__mod__imp__dvd,axiom,
% 5.12/5.41 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.12/5.41 ( ( dvd_dvd_Code_natural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.41 => ( ( dvd_dvd_Code_natural @ C @ B )
% 5.12/5.41 => ( dvd_dvd_Code_natural @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_imp_dvd
% 5.12/5.41 thf(fact_6856_dvd__mod__iff,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_iff
% 5.12/5.41 thf(fact_6857_dvd__mod__iff,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_iff
% 5.12/5.41 thf(fact_6858_dvd__mod__iff,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_iff
% 5.12/5.41 thf(fact_6859_dvd__mod__iff,axiom,
% 5.12/5.41 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.12/5.41 ( ( dvd_dvd_Code_natural @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_natural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_natural @ C @ A ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mod_iff
% 5.12/5.41 thf(fact_6860_dvd__diff__nat,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ K @ M2 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diff_nat
% 5.12/5.41 thf(fact_6861_complex__diff,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.41 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.12/5.41 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % complex_diff
% 5.12/5.41 thf(fact_6862_tan__arctan,axiom,
% 5.12/5.41 ! [Y: real] :
% 5.12/5.41 ( ( tan_real @ ( arctan @ Y ) )
% 5.12/5.41 = Y ) ).
% 5.12/5.41
% 5.12/5.41 % tan_arctan
% 5.12/5.41 thf(fact_6863_not__is__unit__0,axiom,
% 5.12/5.41 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.12/5.41
% 5.12/5.41 % not_is_unit_0
% 5.12/5.41 thf(fact_6864_not__is__unit__0,axiom,
% 5.12/5.41 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.12/5.41
% 5.12/5.41 % not_is_unit_0
% 5.12/5.41 thf(fact_6865_not__is__unit__0,axiom,
% 5.12/5.41 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.12/5.41
% 5.12/5.41 % not_is_unit_0
% 5.12/5.41 thf(fact_6866_minf_I10_J,axiom,
% 5.12/5.41 ! [D: code_integer,S: code_integer] :
% 5.12/5.41 ? [Z4: code_integer] :
% 5.12/5.41 ! [X4: code_integer] :
% 5.12/5.41 ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(10)
% 5.12/5.41 thf(fact_6867_minf_I10_J,axiom,
% 5.12/5.41 ! [D: real,S: real] :
% 5.12/5.41 ? [Z4: real] :
% 5.12/5.41 ! [X4: real] :
% 5.12/5.41 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(10)
% 5.12/5.41 thf(fact_6868_minf_I10_J,axiom,
% 5.12/5.41 ! [D: rat,S: rat] :
% 5.12/5.41 ? [Z4: rat] :
% 5.12/5.41 ! [X4: rat] :
% 5.12/5.41 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(10)
% 5.12/5.41 thf(fact_6869_minf_I10_J,axiom,
% 5.12/5.41 ! [D: nat,S: nat] :
% 5.12/5.41 ? [Z4: nat] :
% 5.12/5.41 ! [X4: nat] :
% 5.12/5.41 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(10)
% 5.12/5.41 thf(fact_6870_minf_I10_J,axiom,
% 5.12/5.41 ! [D: int,S: int] :
% 5.12/5.41 ? [Z4: int] :
% 5.12/5.41 ! [X4: int] :
% 5.12/5.41 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(10)
% 5.12/5.41 thf(fact_6871_minf_I9_J,axiom,
% 5.12/5.41 ! [D: code_integer,S: code_integer] :
% 5.12/5.41 ? [Z4: code_integer] :
% 5.12/5.41 ! [X4: code_integer] :
% 5.12/5.41 ( ( ord_le6747313008572928689nteger @ X4 @ Z4 )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(9)
% 5.12/5.41 thf(fact_6872_minf_I9_J,axiom,
% 5.12/5.41 ! [D: real,S: real] :
% 5.12/5.41 ? [Z4: real] :
% 5.12/5.41 ! [X4: real] :
% 5.12/5.41 ( ( ord_less_real @ X4 @ Z4 )
% 5.12/5.41 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(9)
% 5.12/5.41 thf(fact_6873_minf_I9_J,axiom,
% 5.12/5.41 ! [D: rat,S: rat] :
% 5.12/5.41 ? [Z4: rat] :
% 5.12/5.41 ! [X4: rat] :
% 5.12/5.41 ( ( ord_less_rat @ X4 @ Z4 )
% 5.12/5.41 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(9)
% 5.12/5.41 thf(fact_6874_minf_I9_J,axiom,
% 5.12/5.41 ! [D: nat,S: nat] :
% 5.12/5.41 ? [Z4: nat] :
% 5.12/5.41 ! [X4: nat] :
% 5.12/5.41 ( ( ord_less_nat @ X4 @ Z4 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(9)
% 5.12/5.41 thf(fact_6875_minf_I9_J,axiom,
% 5.12/5.41 ! [D: int,S: int] :
% 5.12/5.41 ? [Z4: int] :
% 5.12/5.41 ! [X4: int] :
% 5.12/5.41 ( ( ord_less_int @ X4 @ Z4 )
% 5.12/5.41 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % minf(9)
% 5.12/5.41 thf(fact_6876_pinf_I10_J,axiom,
% 5.12/5.41 ! [D: code_integer,S: code_integer] :
% 5.12/5.41 ? [Z4: code_integer] :
% 5.12/5.41 ! [X4: code_integer] :
% 5.12/5.41 ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(10)
% 5.12/5.41 thf(fact_6877_pinf_I10_J,axiom,
% 5.12/5.41 ! [D: real,S: real] :
% 5.12/5.41 ? [Z4: real] :
% 5.12/5.41 ! [X4: real] :
% 5.12/5.41 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(10)
% 5.12/5.41 thf(fact_6878_pinf_I10_J,axiom,
% 5.12/5.41 ! [D: rat,S: rat] :
% 5.12/5.41 ? [Z4: rat] :
% 5.12/5.41 ! [X4: rat] :
% 5.12/5.41 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(10)
% 5.12/5.41 thf(fact_6879_pinf_I10_J,axiom,
% 5.12/5.41 ! [D: nat,S: nat] :
% 5.12/5.41 ? [Z4: nat] :
% 5.12/5.41 ! [X4: nat] :
% 5.12/5.41 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(10)
% 5.12/5.41 thf(fact_6880_pinf_I10_J,axiom,
% 5.12/5.41 ! [D: int,S: int] :
% 5.12/5.41 ? [Z4: int] :
% 5.12/5.41 ! [X4: int] :
% 5.12/5.41 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.41 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(10)
% 5.12/5.41 thf(fact_6881_pinf_I9_J,axiom,
% 5.12/5.41 ! [D: code_integer,S: code_integer] :
% 5.12/5.41 ? [Z4: code_integer] :
% 5.12/5.41 ! [X4: code_integer] :
% 5.12/5.41 ( ( ord_le6747313008572928689nteger @ Z4 @ X4 )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(9)
% 5.12/5.41 thf(fact_6882_pinf_I9_J,axiom,
% 5.12/5.41 ! [D: real,S: real] :
% 5.12/5.41 ? [Z4: real] :
% 5.12/5.41 ! [X4: real] :
% 5.12/5.41 ( ( ord_less_real @ Z4 @ X4 )
% 5.12/5.41 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(9)
% 5.12/5.41 thf(fact_6883_pinf_I9_J,axiom,
% 5.12/5.41 ! [D: rat,S: rat] :
% 5.12/5.41 ? [Z4: rat] :
% 5.12/5.41 ! [X4: rat] :
% 5.12/5.41 ( ( ord_less_rat @ Z4 @ X4 )
% 5.12/5.41 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(9)
% 5.12/5.41 thf(fact_6884_pinf_I9_J,axiom,
% 5.12/5.41 ! [D: nat,S: nat] :
% 5.12/5.41 ? [Z4: nat] :
% 5.12/5.41 ! [X4: nat] :
% 5.12/5.41 ( ( ord_less_nat @ Z4 @ X4 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(9)
% 5.12/5.41 thf(fact_6885_pinf_I9_J,axiom,
% 5.12/5.41 ! [D: int,S: int] :
% 5.12/5.41 ? [Z4: int] :
% 5.12/5.41 ! [X4: int] :
% 5.12/5.41 ( ( ord_less_int @ Z4 @ X4 )
% 5.12/5.41 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 5.12/5.41 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % pinf(9)
% 5.12/5.41 thf(fact_6886_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.12/5.41 = zero_z3403309356797280102nteger )
% 5.12/5.41 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6887_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: complex,A: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ B @ A )
% 5.12/5.41 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.12/5.41 = zero_zero_complex )
% 5.12/5.41 = ( A = zero_zero_complex ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6888_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: real,A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ B @ A )
% 5.12/5.41 => ( ( ( divide_divide_real @ A @ B )
% 5.12/5.41 = zero_zero_real )
% 5.12/5.41 = ( A = zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6889_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: rat,A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ B @ A )
% 5.12/5.41 => ( ( ( divide_divide_rat @ A @ B )
% 5.12/5.41 = zero_zero_rat )
% 5.12/5.41 = ( A = zero_zero_rat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6890_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( ( divide_divide_nat @ A @ B )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 = ( A = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6891_dvd__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( ( divide_divide_int @ A @ B )
% 5.12/5.41 = zero_zero_int )
% 5.12/5.41 = ( A = zero_zero_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_0_iff
% 5.12/5.41 thf(fact_6892_is__unit__mult__iff,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.12/5.41 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_mult_iff
% 5.12/5.41 thf(fact_6893_is__unit__mult__iff,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.12/5.41 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_mult_iff
% 5.12/5.41 thf(fact_6894_is__unit__mult__iff,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.12/5.41 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_mult_iff
% 5.12/5.41 thf(fact_6895_dvd__mult__unit__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff
% 5.12/5.41 thf(fact_6896_dvd__mult__unit__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff
% 5.12/5.41 thf(fact_6897_dvd__mult__unit__iff,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff
% 5.12/5.41 thf(fact_6898_mult__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff
% 5.12/5.41 thf(fact_6899_mult__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff
% 5.12/5.41 thf(fact_6900_mult__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff
% 5.12/5.41 thf(fact_6901_dvd__mult__unit__iff_H,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff'
% 5.12/5.41 thf(fact_6902_dvd__mult__unit__iff_H,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff'
% 5.12/5.41 thf(fact_6903_dvd__mult__unit__iff_H,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_unit_iff'
% 5.12/5.41 thf(fact_6904_mult__unit__dvd__iff_H,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff'
% 5.12/5.41 thf(fact_6905_mult__unit__dvd__iff_H,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff'
% 5.12/5.41 thf(fact_6906_mult__unit__dvd__iff_H,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mult_unit_dvd_iff'
% 5.12/5.41 thf(fact_6907_unit__mult__left__cancel,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.12/5.41 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_left_cancel
% 5.12/5.41 thf(fact_6908_unit__mult__left__cancel,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( ( times_times_nat @ A @ B )
% 5.12/5.41 = ( times_times_nat @ A @ C ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_left_cancel
% 5.12/5.41 thf(fact_6909_unit__mult__left__cancel,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( ( times_times_int @ A @ B )
% 5.12/5.41 = ( times_times_int @ A @ C ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_left_cancel
% 5.12/5.41 thf(fact_6910_unit__mult__right__cancel,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.12/5.41 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_right_cancel
% 5.12/5.41 thf(fact_6911_unit__mult__right__cancel,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( ( times_times_nat @ B @ A )
% 5.12/5.41 = ( times_times_nat @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_right_cancel
% 5.12/5.41 thf(fact_6912_unit__mult__right__cancel,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( ( times_times_int @ B @ A )
% 5.12/5.41 = ( times_times_int @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_mult_right_cancel
% 5.12/5.41 thf(fact_6913_dvd__div__mult,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult
% 5.12/5.41 thf(fact_6914_dvd__div__mult,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult
% 5.12/5.41 thf(fact_6915_dvd__div__mult,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.12/5.41 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult
% 5.12/5.41 thf(fact_6916_div__mult__swap,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_swap
% 5.12/5.41 thf(fact_6917_div__mult__swap,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_swap
% 5.12/5.41 thf(fact_6918_div__mult__swap,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.12/5.41 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_swap
% 5.12/5.41 thf(fact_6919_div__div__eq__right,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_eq_right
% 5.12/5.41 thf(fact_6920_div__div__eq__right,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_eq_right
% 5.12/5.41 thf(fact_6921_div__div__eq__right,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.12/5.41 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_div_eq_right
% 5.12/5.41 thf(fact_6922_dvd__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult2_eq
% 5.12/5.41 thf(fact_6923_dvd__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: nat,C: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.41 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult2_eq
% 5.12/5.41 thf(fact_6924_dvd__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: int,C: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.41 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_mult2_eq
% 5.12/5.41 thf(fact_6925_dvd__mult__imp__div,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_imp_div
% 5.12/5.41 thf(fact_6926_dvd__mult__imp__div,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.12/5.41 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_imp_div
% 5.12/5.41 thf(fact_6927_dvd__mult__imp__div,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.12/5.41 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_imp_div
% 5.12/5.41 thf(fact_6928_div__mult__div__if__dvd,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_div_if_dvd
% 5.12/5.41 thf(fact_6929_div__mult__div__if__dvd,axiom,
% 5.12/5.41 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_nat @ D @ C )
% 5.12/5.41 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_div_if_dvd
% 5.12/5.41 thf(fact_6930_div__mult__div__if__dvd,axiom,
% 5.12/5.41 ! [B: int,A: int,D: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ D @ C )
% 5.12/5.41 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.12/5.41 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_div_if_dvd
% 5.12/5.41 thf(fact_6931_dvd__div__unit__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_unit_iff
% 5.12/5.41 thf(fact_6932_dvd__div__unit__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_unit_iff
% 5.12/5.41 thf(fact_6933_dvd__div__unit__iff,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_unit_iff
% 5.12/5.41 thf(fact_6934_div__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_unit_dvd_iff
% 5.12/5.41 thf(fact_6935_div__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_unit_dvd_iff
% 5.12/5.41 thf(fact_6936_div__unit__dvd__iff,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_unit_dvd_iff
% 5.12/5.41 thf(fact_6937_unit__div__cancel,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.12/5.41 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_cancel
% 5.12/5.41 thf(fact_6938_unit__div__cancel,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ( ( ( divide_divide_nat @ B @ A )
% 5.12/5.41 = ( divide_divide_nat @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_cancel
% 5.12/5.41 thf(fact_6939_unit__div__cancel,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ( ( ( divide_divide_int @ B @ A )
% 5.12/5.41 = ( divide_divide_int @ C @ A ) )
% 5.12/5.41 = ( B = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_cancel
% 5.12/5.41 thf(fact_6940_div__plus__div__distrib__dvd__left,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.12/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_left
% 5.12/5.41 thf(fact_6941_div__plus__div__distrib__dvd__left,axiom,
% 5.12/5.41 ! [C: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_left
% 5.12/5.41 thf(fact_6942_div__plus__div__distrib__dvd__left,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_left
% 5.12/5.41 thf(fact_6943_div__plus__div__distrib__dvd__right,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.12/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_right
% 5.12/5.41 thf(fact_6944_div__plus__div__distrib__dvd__right,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_right
% 5.12/5.41 thf(fact_6945_div__plus__div__distrib__dvd__right,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.12/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_plus_div_distrib_dvd_right
% 5.12/5.41 thf(fact_6946_Complex__eq__1,axiom,
% 5.12/5.41 ! [A: real,B: real] :
% 5.12/5.41 ( ( ( complex2 @ A @ B )
% 5.12/5.41 = one_one_complex )
% 5.12/5.41 = ( ( A = one_one_real )
% 5.12/5.41 & ( B = zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Complex_eq_1
% 5.12/5.41 thf(fact_6947_one__complex_Ocode,axiom,
% 5.12/5.41 ( one_one_complex
% 5.12/5.41 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.12/5.41
% 5.12/5.41 % one_complex.code
% 5.12/5.41 thf(fact_6948_dvd__neg__div,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.12/5.41 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_neg_div
% 5.12/5.41 thf(fact_6949_dvd__neg__div,axiom,
% 5.12/5.41 ! [B: real,A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ B @ A )
% 5.12/5.41 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.12/5.41 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_neg_div
% 5.12/5.41 thf(fact_6950_dvd__neg__div,axiom,
% 5.12/5.41 ! [B: complex,A: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ B @ A )
% 5.12/5.41 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_neg_div
% 5.12/5.41 thf(fact_6951_dvd__neg__div,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.12/5.41 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_neg_div
% 5.12/5.41 thf(fact_6952_dvd__neg__div,axiom,
% 5.12/5.41 ! [B: rat,A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ B @ A )
% 5.12/5.41 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.12/5.41 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_neg_div
% 5.12/5.41 thf(fact_6953_dvd__div__neg,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.12/5.41 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_neg
% 5.12/5.41 thf(fact_6954_dvd__div__neg,axiom,
% 5.12/5.41 ! [B: real,A: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ B @ A )
% 5.12/5.41 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.12/5.41 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_neg
% 5.12/5.41 thf(fact_6955_dvd__div__neg,axiom,
% 5.12/5.41 ! [B: complex,A: complex] :
% 5.12/5.41 ( ( dvd_dvd_complex @ B @ A )
% 5.12/5.41 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_neg
% 5.12/5.41 thf(fact_6956_dvd__div__neg,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.12/5.41 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_neg
% 5.12/5.41 thf(fact_6957_dvd__div__neg,axiom,
% 5.12/5.41 ! [B: rat,A: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ B @ A )
% 5.12/5.41 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.12/5.41 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_neg
% 5.12/5.41 thf(fact_6958_div__power,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_power
% 5.12/5.41 thf(fact_6959_div__power,axiom,
% 5.12/5.41 ! [B: nat,A: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.12/5.41 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_power
% 5.12/5.41 thf(fact_6960_div__power,axiom,
% 5.12/5.41 ! [B: int,A: int,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.12/5.41 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_power
% 5.12/5.41 thf(fact_6961_mod__0__imp__dvd,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.41 = zero_zero_int )
% 5.12/5.41 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_0_imp_dvd
% 5.12/5.41 thf(fact_6962_mod__0__imp__dvd,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( ( modulo_modulo_nat @ A @ B )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_0_imp_dvd
% 5.12/5.41 thf(fact_6963_mod__0__imp__dvd,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.12/5.41 = zero_z3403309356797280102nteger )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_0_imp_dvd
% 5.12/5.41 thf(fact_6964_mod__0__imp__dvd,axiom,
% 5.12/5.41 ! [A: code_natural,B: code_natural] :
% 5.12/5.41 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.12/5.41 = zero_z2226904508553997617atural )
% 5.12/5.41 => ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_0_imp_dvd
% 5.12/5.41 thf(fact_6965_dvd__eq__mod__eq__0,axiom,
% 5.12/5.41 ( dvd_dvd_int
% 5.12/5.41 = ( ^ [A3: int,B2: int] :
% 5.12/5.41 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.12/5.41 = zero_zero_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_eq_mod_eq_0
% 5.12/5.41 thf(fact_6966_dvd__eq__mod__eq__0,axiom,
% 5.12/5.41 ( dvd_dvd_nat
% 5.12/5.41 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.41 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.12/5.41 = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_eq_mod_eq_0
% 5.12/5.41 thf(fact_6967_dvd__eq__mod__eq__0,axiom,
% 5.12/5.41 ( dvd_dvd_Code_integer
% 5.12/5.41 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.12/5.41 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.12/5.41 = zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_eq_mod_eq_0
% 5.12/5.41 thf(fact_6968_dvd__eq__mod__eq__0,axiom,
% 5.12/5.41 ( dvd_dvd_Code_natural
% 5.12/5.41 = ( ^ [A3: code_natural,B2: code_natural] :
% 5.12/5.41 ( ( modulo8411746178871703098atural @ B2 @ A3 )
% 5.12/5.41 = zero_z2226904508553997617atural ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_eq_mod_eq_0
% 5.12/5.41 thf(fact_6969_mod__eq__0__iff__dvd,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( ( modulo_modulo_int @ A @ B )
% 5.12/5.41 = zero_zero_int )
% 5.12/5.41 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_0_iff_dvd
% 5.12/5.41 thf(fact_6970_mod__eq__0__iff__dvd,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( ( modulo_modulo_nat @ A @ B )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_0_iff_dvd
% 5.12/5.41 thf(fact_6971_mod__eq__0__iff__dvd,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.12/5.41 = zero_z3403309356797280102nteger )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_0_iff_dvd
% 5.12/5.41 thf(fact_6972_mod__eq__0__iff__dvd,axiom,
% 5.12/5.41 ! [A: code_natural,B: code_natural] :
% 5.12/5.41 ( ( ( modulo8411746178871703098atural @ A @ B )
% 5.12/5.41 = zero_z2226904508553997617atural )
% 5.12/5.41 = ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_0_iff_dvd
% 5.12/5.41 thf(fact_6973_dvd__minus__mod,axiom,
% 5.12/5.41 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_mod
% 5.12/5.41 thf(fact_6974_dvd__minus__mod,axiom,
% 5.12/5.41 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_mod
% 5.12/5.41 thf(fact_6975_dvd__minus__mod,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_mod
% 5.12/5.41 thf(fact_6976_dvd__minus__mod,axiom,
% 5.12/5.41 ! [B: code_natural,A: code_natural] : ( dvd_dvd_Code_natural @ B @ ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_mod
% 5.12/5.41 thf(fact_6977_mod__eq__dvd__iff,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int] :
% 5.12/5.41 ( ( ( modulo_modulo_int @ A @ C )
% 5.12/5.41 = ( modulo_modulo_int @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_dvd_iff
% 5.12/5.41 thf(fact_6978_mod__eq__dvd__iff,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.12/5.41 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.12/5.41 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_dvd_iff
% 5.12/5.41 thf(fact_6979_nat__dvd__not__less,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.41 => ( ( ord_less_nat @ M2 @ N )
% 5.12/5.41 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % nat_dvd_not_less
% 5.12/5.41 thf(fact_6980_dvd__pos__nat,axiom,
% 5.12/5.41 ! [N: nat,M2: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ( dvd_dvd_nat @ M2 @ N )
% 5.12/5.41 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_pos_nat
% 5.12/5.41 thf(fact_6981_dvd__minus__self,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 5.12/5.41 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.41 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_self
% 5.12/5.41 thf(fact_6982_less__eq__dvd__minus,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.41 => ( ( dvd_dvd_nat @ M2 @ N )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % less_eq_dvd_minus
% 5.12/5.41 thf(fact_6983_dvd__diffD1,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.41 => ( ( dvd_dvd_nat @ K @ M2 )
% 5.12/5.41 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.41 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diffD1
% 5.12/5.41 thf(fact_6984_dvd__diffD,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 5.12/5.41 => ( ( dvd_dvd_nat @ K @ N )
% 5.12/5.41 => ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.41 => ( dvd_dvd_nat @ K @ M2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_diffD
% 5.12/5.41 thf(fact_6985_bezout1__nat,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ? [D5: nat,X3: nat,Y3: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ D5 @ A )
% 5.12/5.41 & ( dvd_dvd_nat @ D5 @ B )
% 5.12/5.41 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.12/5.41 = D5 )
% 5.12/5.41 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.12/5.41 = D5 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % bezout1_nat
% 5.12/5.41 thf(fact_6986_cot__altdef,axiom,
% 5.12/5.41 ( cot_real
% 5.12/5.41 = ( ^ [X2: real] : ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_altdef
% 5.12/5.41 thf(fact_6987_cot__altdef,axiom,
% 5.12/5.41 ( cot_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( invers8013647133539491842omplex @ ( tan_complex @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % cot_altdef
% 5.12/5.41 thf(fact_6988_tan__altdef,axiom,
% 5.12/5.41 ( tan_real
% 5.12/5.41 = ( ^ [X2: real] : ( inverse_inverse_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_altdef
% 5.12/5.41 thf(fact_6989_tan__altdef,axiom,
% 5.12/5.41 ( tan_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( invers8013647133539491842omplex @ ( cot_complex @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_altdef
% 5.12/5.41 thf(fact_6990_unit__dvdE,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ! [C2: code_integer] :
% 5.12/5.41 ( B
% 5.12/5.41 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_dvdE
% 5.12/5.41 thf(fact_6991_unit__dvdE,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ~ ( ( A != zero_zero_nat )
% 5.12/5.41 => ! [C2: nat] :
% 5.12/5.41 ( B
% 5.12/5.41 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_dvdE
% 5.12/5.41 thf(fact_6992_unit__dvdE,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ~ ( ( A != zero_zero_int )
% 5.12/5.41 => ! [C2: int] :
% 5.12/5.41 ( B
% 5.12/5.41 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_dvdE
% 5.12/5.41 thf(fact_6993_unity__coeff__ex,axiom,
% 5.12/5.41 ! [P: code_integer > $o,L: code_integer] :
% 5.12/5.41 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X2 ) ) )
% 5.12/5.41 = ( ? [X2: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.12/5.41 & ( P @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unity_coeff_ex
% 5.12/5.41 thf(fact_6994_unity__coeff__ex,axiom,
% 5.12/5.41 ! [P: real > $o,L: real] :
% 5.12/5.41 ( ( ? [X2: real] : ( P @ ( times_times_real @ L @ X2 ) ) )
% 5.12/5.41 = ( ? [X2: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.12/5.41 & ( P @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unity_coeff_ex
% 5.12/5.41 thf(fact_6995_unity__coeff__ex,axiom,
% 5.12/5.41 ! [P: rat > $o,L: rat] :
% 5.12/5.41 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 5.12/5.41 = ( ? [X2: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.12/5.41 & ( P @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unity_coeff_ex
% 5.12/5.41 thf(fact_6996_unity__coeff__ex,axiom,
% 5.12/5.41 ! [P: nat > $o,L: nat] :
% 5.12/5.41 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 5.12/5.41 = ( ? [X2: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.12/5.41 & ( P @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unity_coeff_ex
% 5.12/5.41 thf(fact_6997_unity__coeff__ex,axiom,
% 5.12/5.41 ! [P: int > $o,L: int] :
% 5.12/5.41 ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 5.12/5.41 = ( ? [X2: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.12/5.41 & ( P @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unity_coeff_ex
% 5.12/5.41 thf(fact_6998_dvd__div__div__eq__mult,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( C != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.12/5.41 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.12/5.41 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.12/5.41 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_div_eq_mult
% 5.12/5.41 thf(fact_6999_dvd__div__div__eq__mult,axiom,
% 5.12/5.41 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( C != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ D )
% 5.12/5.41 => ( ( ( divide_divide_nat @ B @ A )
% 5.12/5.41 = ( divide_divide_nat @ D @ C ) )
% 5.12/5.41 = ( ( times_times_nat @ B @ C )
% 5.12/5.41 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_div_eq_mult
% 5.12/5.41 thf(fact_7000_dvd__div__div__eq__mult,axiom,
% 5.12/5.41 ! [A: int,C: int,B: int,D: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( C != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ D )
% 5.12/5.41 => ( ( ( divide_divide_int @ B @ A )
% 5.12/5.41 = ( divide_divide_int @ D @ C ) )
% 5.12/5.41 = ( ( times_times_int @ B @ C )
% 5.12/5.41 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_div_eq_mult
% 5.12/5.41 thf(fact_7001_dvd__div__iff__mult,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( C != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_iff_mult
% 5.12/5.41 thf(fact_7002_dvd__div__iff__mult,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( C != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_iff_mult
% 5.12/5.41 thf(fact_7003_dvd__div__iff__mult,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( C != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.12/5.41 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_iff_mult
% 5.12/5.41 thf(fact_7004_div__dvd__iff__mult,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( B != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_iff_mult
% 5.12/5.41 thf(fact_7005_div__dvd__iff__mult,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( B != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_iff_mult
% 5.12/5.41 thf(fact_7006_div__dvd__iff__mult,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( B != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.12/5.41 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_dvd_iff_mult
% 5.12/5.41 thf(fact_7007_dvd__div__eq__mult,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.12/5.41 = C )
% 5.12/5.41 = ( B
% 5.12/5.41 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_mult
% 5.12/5.41 thf(fact_7008_dvd__div__eq__mult,axiom,
% 5.12/5.41 ! [A: nat,B: nat,C: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.41 => ( ( ( divide_divide_nat @ B @ A )
% 5.12/5.41 = C )
% 5.12/5.41 = ( B
% 5.12/5.41 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_mult
% 5.12/5.41 thf(fact_7009_dvd__div__eq__mult,axiom,
% 5.12/5.41 ! [A: int,B: int,C: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ A @ B )
% 5.12/5.41 => ( ( ( divide_divide_int @ B @ A )
% 5.12/5.41 = C )
% 5.12/5.41 = ( B
% 5.12/5.41 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_div_eq_mult
% 5.12/5.41 thf(fact_7010_unit__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.12/5.41 = zero_z3403309356797280102nteger )
% 5.12/5.41 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_eq_0_iff
% 5.12/5.41 thf(fact_7011_unit__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( ( divide_divide_nat @ A @ B )
% 5.12/5.41 = zero_zero_nat )
% 5.12/5.41 = ( A = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_eq_0_iff
% 5.12/5.41 thf(fact_7012_unit__div__eq__0__iff,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( ( divide_divide_int @ A @ B )
% 5.12/5.41 = zero_zero_int )
% 5.12/5.41 = ( A = zero_zero_int ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_eq_0_iff
% 5.12/5.41 thf(fact_7013_inf__period_I3_J,axiom,
% 5.12/5.41 ! [D: code_integer,D6: code_integer,T: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ D @ D6 )
% 5.12/5.41 => ! [X4: code_integer,K4: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(3)
% 5.12/5.41 thf(fact_7014_inf__period_I3_J,axiom,
% 5.12/5.41 ! [D: real,D6: real,T: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ D @ D6 )
% 5.12/5.41 => ! [X4: real,K4: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) )
% 5.12/5.41 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(3)
% 5.12/5.41 thf(fact_7015_inf__period_I3_J,axiom,
% 5.12/5.41 ! [D: rat,D6: rat,T: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ D @ D6 )
% 5.12/5.41 => ! [X4: rat,K4: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) )
% 5.12/5.41 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(3)
% 5.12/5.41 thf(fact_7016_inf__period_I3_J,axiom,
% 5.12/5.41 ! [D: int,D6: int,T: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.41 => ! [X4: int,K4: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.12/5.41 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(3)
% 5.12/5.41 thf(fact_7017_inf__period_I4_J,axiom,
% 5.12/5.41 ! [D: code_integer,D6: code_integer,T: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ D @ D6 )
% 5.12/5.41 => ! [X4: code_integer,K4: code_integer] :
% 5.12/5.41 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(4)
% 5.12/5.41 thf(fact_7018_inf__period_I4_J,axiom,
% 5.12/5.41 ! [D: real,D6: real,T: real] :
% 5.12/5.41 ( ( dvd_dvd_real @ D @ D6 )
% 5.12/5.41 => ! [X4: real,K4: real] :
% 5.12/5.41 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(4)
% 5.12/5.41 thf(fact_7019_inf__period_I4_J,axiom,
% 5.12/5.41 ! [D: rat,D6: rat,T: rat] :
% 5.12/5.41 ( ( dvd_dvd_rat @ D @ D6 )
% 5.12/5.41 => ! [X4: rat,K4: rat] :
% 5.12/5.41 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(4)
% 5.12/5.41 thf(fact_7020_inf__period_I4_J,axiom,
% 5.12/5.41 ! [D: int,D6: int,T: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.41 => ! [X4: int,K4: int] :
% 5.12/5.41 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D6 ) ) @ T ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % inf_period(4)
% 5.12/5.41 thf(fact_7021_unit__eq__div1,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.12/5.41 = C )
% 5.12/5.41 = ( A
% 5.12/5.41 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div1
% 5.12/5.41 thf(fact_7022_unit__eq__div1,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( ( divide_divide_nat @ A @ B )
% 5.12/5.41 = C )
% 5.12/5.41 = ( A
% 5.12/5.41 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div1
% 5.12/5.41 thf(fact_7023_unit__eq__div1,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( ( divide_divide_int @ A @ B )
% 5.12/5.41 = C )
% 5.12/5.41 = ( A
% 5.12/5.41 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div1
% 5.12/5.41 thf(fact_7024_unit__eq__div2,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( A
% 5.12/5.41 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.12/5.41 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.12/5.41 = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div2
% 5.12/5.41 thf(fact_7025_unit__eq__div2,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( A
% 5.12/5.41 = ( divide_divide_nat @ C @ B ) )
% 5.12/5.41 = ( ( times_times_nat @ A @ B )
% 5.12/5.41 = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div2
% 5.12/5.41 thf(fact_7026_unit__eq__div2,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( A
% 5.12/5.41 = ( divide_divide_int @ C @ B ) )
% 5.12/5.41 = ( ( times_times_int @ A @ B )
% 5.12/5.41 = C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_eq_div2
% 5.12/5.41 thf(fact_7027_div__mult__unit2,axiom,
% 5.12/5.41 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_unit2
% 5.12/5.41 thf(fact_7028_div__mult__unit2,axiom,
% 5.12/5.41 ! [C: nat,B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ A )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.41 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_unit2
% 5.12/5.41 thf(fact_7029_div__mult__unit2,axiom,
% 5.12/5.41 ! [C: int,B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ A )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.41 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div_mult_unit2
% 5.12/5.41 thf(fact_7030_unit__div__commute,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_commute
% 5.12/5.41 thf(fact_7031_unit__div__commute,axiom,
% 5.12/5.41 ! [B: nat,A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_commute
% 5.12/5.41 thf(fact_7032_unit__div__commute,axiom,
% 5.12/5.41 ! [B: int,A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.12/5.41 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_commute
% 5.12/5.41 thf(fact_7033_unit__div__mult__swap,axiom,
% 5.12/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_swap
% 5.12/5.41 thf(fact_7034_unit__div__mult__swap,axiom,
% 5.12/5.41 ! [C: nat,A: nat,B: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.12/5.41 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.12/5.41 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_swap
% 5.12/5.41 thf(fact_7035_unit__div__mult__swap,axiom,
% 5.12/5.41 ! [C: int,A: int,B: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.12/5.41 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.12/5.41 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_div_mult_swap
% 5.12/5.41 thf(fact_7036_is__unit__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult2_eq
% 5.12/5.41 thf(fact_7037_is__unit__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: nat,C: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.12/5.41 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult2_eq
% 5.12/5.41 thf(fact_7038_is__unit__div__mult2__eq,axiom,
% 5.12/5.41 ! [B: int,C: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.12/5.41 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult2_eq
% 5.12/5.41 thf(fact_7039_unit__imp__mod__eq__0,axiom,
% 5.12/5.41 ! [B: int,A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( modulo_modulo_int @ A @ B )
% 5.12/5.41 = zero_zero_int ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_mod_eq_0
% 5.12/5.41 thf(fact_7040_unit__imp__mod__eq__0,axiom,
% 5.12/5.41 ! [B: nat,A: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( modulo_modulo_nat @ A @ B )
% 5.12/5.41 = zero_zero_nat ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_mod_eq_0
% 5.12/5.41 thf(fact_7041_unit__imp__mod__eq__0,axiom,
% 5.12/5.41 ! [B: code_integer,A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.12/5.41 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_mod_eq_0
% 5.12/5.41 thf(fact_7042_unit__imp__mod__eq__0,axiom,
% 5.12/5.41 ! [B: code_natural,A: code_natural] :
% 5.12/5.41 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.12/5.41 => ( ( modulo8411746178871703098atural @ A @ B )
% 5.12/5.41 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.41
% 5.12/5.41 % unit_imp_mod_eq_0
% 5.12/5.41 thf(fact_7043_is__unit__power__iff,axiom,
% 5.12/5.41 ! [A: code_integer,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.12/5.41 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_power_iff
% 5.12/5.41 thf(fact_7044_is__unit__power__iff,axiom,
% 5.12/5.41 ! [A: int,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.12/5.41 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_power_iff
% 5.12/5.41 thf(fact_7045_is__unit__power__iff,axiom,
% 5.12/5.41 ! [A: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.12/5.41 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_power_iff
% 5.12/5.41 thf(fact_7046_Complex__eq__neg__1,axiom,
% 5.12/5.41 ! [A: real,B: real] :
% 5.12/5.41 ( ( ( complex2 @ A @ B )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.12/5.41 = ( ( A
% 5.12/5.41 = ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.41 & ( B = zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Complex_eq_neg_1
% 5.12/5.41 thf(fact_7047_Complex__eq__neg__numeral,axiom,
% 5.12/5.41 ! [A: real,B: real,W: num] :
% 5.12/5.41 ( ( ( complex2 @ A @ B )
% 5.12/5.41 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.41 = ( ( A
% 5.12/5.41 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.12/5.41 & ( B = zero_zero_real ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % Complex_eq_neg_numeral
% 5.12/5.41 thf(fact_7048_dvd__imp__le,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ K @ N )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_imp_le
% 5.12/5.41 thf(fact_7049_dvd__mult__cancel,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.41 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.41 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel
% 5.12/5.41 thf(fact_7050_nat__mult__dvd__cancel1,axiom,
% 5.12/5.41 ! [K: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % nat_mult_dvd_cancel1
% 5.12/5.41 thf(fact_7051_bezout__add__strong__nat,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ? [D5: nat,X3: nat,Y3: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ D5 @ A )
% 5.12/5.41 & ( dvd_dvd_nat @ D5 @ B )
% 5.12/5.41 & ( ( times_times_nat @ A @ X3 )
% 5.12/5.41 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % bezout_add_strong_nat
% 5.12/5.41 thf(fact_7052_mod__greater__zero__iff__not__dvd,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 5.12/5.41 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_greater_zero_iff_not_dvd
% 5.12/5.41 thf(fact_7053_mod__eq__dvd__iff__nat,axiom,
% 5.12/5.41 ! [N: nat,M2: nat,Q5: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.41 => ( ( ( modulo_modulo_nat @ M2 @ Q5 )
% 5.12/5.41 = ( modulo_modulo_nat @ N @ Q5 ) )
% 5.12/5.41 = ( dvd_dvd_nat @ Q5 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_eq_dvd_iff_nat
% 5.12/5.41 thf(fact_7054_real__of__nat__div,axiom,
% 5.12/5.41 ! [D: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ D @ N )
% 5.12/5.41 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.12/5.41 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % real_of_nat_div
% 5.12/5.41 thf(fact_7055_dvd__fact,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 5.12/5.41 => ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.41 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_fact
% 5.12/5.41 thf(fact_7056_tan__def,axiom,
% 5.12/5.41 ( tan_complex
% 5.12/5.41 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_def
% 5.12/5.41 thf(fact_7057_tan__def,axiom,
% 5.12/5.41 ( tan_real
% 5.12/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % tan_def
% 5.12/5.41 thf(fact_7058_even__zero,axiom,
% 5.12/5.41 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.12/5.41
% 5.12/5.41 % even_zero
% 5.12/5.41 thf(fact_7059_even__zero,axiom,
% 5.12/5.41 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.12/5.41
% 5.12/5.41 % even_zero
% 5.12/5.41 thf(fact_7060_even__zero,axiom,
% 5.12/5.41 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.12/5.41
% 5.12/5.41 % even_zero
% 5.12/5.41 thf(fact_7061_is__unitE,axiom,
% 5.12/5.41 ! [A: code_integer,C: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.12/5.41 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ! [B3: code_integer] :
% 5.12/5.41 ( ( B3 != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.12/5.41 = B3 )
% 5.12/5.41 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 5.12/5.41 = A )
% 5.12/5.41 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 5.12/5.41 = one_one_Code_integer )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.12/5.41 != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unitE
% 5.12/5.41 thf(fact_7062_is__unitE,axiom,
% 5.12/5.41 ! [A: nat,C: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.12/5.41 => ~ ( ( A != zero_zero_nat )
% 5.12/5.41 => ! [B3: nat] :
% 5.12/5.41 ( ( B3 != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.12/5.41 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.12/5.41 = B3 )
% 5.12/5.41 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.12/5.41 = A )
% 5.12/5.41 => ( ( ( times_times_nat @ A @ B3 )
% 5.12/5.41 = one_one_nat )
% 5.12/5.41 => ( ( divide_divide_nat @ C @ A )
% 5.12/5.41 != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unitE
% 5.12/5.41 thf(fact_7063_is__unitE,axiom,
% 5.12/5.41 ! [A: int,C: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.12/5.41 => ~ ( ( A != zero_zero_int )
% 5.12/5.41 => ! [B3: int] :
% 5.12/5.41 ( ( B3 != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.12/5.41 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.12/5.41 = B3 )
% 5.12/5.41 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.12/5.41 = A )
% 5.12/5.41 => ( ( ( times_times_int @ A @ B3 )
% 5.12/5.41 = one_one_int )
% 5.12/5.41 => ( ( divide_divide_int @ C @ A )
% 5.12/5.41 != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unitE
% 5.12/5.41 thf(fact_7064_is__unit__div__mult__cancel__left,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_left
% 5.12/5.41 thf(fact_7065_is__unit__div__mult__cancel__left,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.12/5.41 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_left
% 5.12/5.41 thf(fact_7066_is__unit__div__mult__cancel__left,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.12/5.41 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_left
% 5.12/5.41 thf(fact_7067_is__unit__div__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: code_integer,B: code_integer] :
% 5.12/5.41 ( ( A != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.12/5.41 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_right
% 5.12/5.41 thf(fact_7068_is__unit__div__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: nat,B: nat] :
% 5.12/5.41 ( ( A != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.12/5.41 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.12/5.41 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_right
% 5.12/5.41 thf(fact_7069_is__unit__div__mult__cancel__right,axiom,
% 5.12/5.41 ! [A: int,B: int] :
% 5.12/5.41 ( ( A != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.12/5.41 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.12/5.41 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % is_unit_div_mult_cancel_right
% 5.12/5.41 thf(fact_7070_odd__one,axiom,
% 5.12/5.41 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.12/5.41
% 5.12/5.41 % odd_one
% 5.12/5.41 thf(fact_7071_odd__one,axiom,
% 5.12/5.41 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.12/5.41
% 5.12/5.41 % odd_one
% 5.12/5.41 thf(fact_7072_odd__one,axiom,
% 5.12/5.41 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.12/5.41
% 5.12/5.41 % odd_one
% 5.12/5.41 thf(fact_7073_bit__eq__rec,axiom,
% 5.12/5.41 ( ( ^ [Y4: code_integer,Z: code_integer] : ( Y4 = Z ) )
% 5.12/5.41 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.12/5.41 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.12/5.41 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % bit_eq_rec
% 5.12/5.41 thf(fact_7074_bit__eq__rec,axiom,
% 5.12/5.41 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 5.12/5.41 = ( ^ [A3: nat,B2: nat] :
% 5.12/5.41 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.12/5.41 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % bit_eq_rec
% 5.12/5.41 thf(fact_7075_bit__eq__rec,axiom,
% 5.12/5.41 ( ( ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 5.12/5.41 = ( ^ [A3: int,B2: int] :
% 5.12/5.41 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.12/5.41 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.12/5.41 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % bit_eq_rec
% 5.12/5.41 thf(fact_7076_even__minus,axiom,
% 5.12/5.41 ! [A: int] :
% 5.12/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.12/5.41 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_minus
% 5.12/5.41 thf(fact_7077_even__minus,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.41 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.12/5.41
% 5.12/5.41 % even_minus
% 5.12/5.41 thf(fact_7078_dvd__power__iff,axiom,
% 5.12/5.41 ! [X: code_integer,M2: nat,N: nat] :
% 5.12/5.41 ( ( X != zero_z3403309356797280102nteger )
% 5.12/5.41 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.12/5.41 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power_iff
% 5.12/5.41 thf(fact_7079_dvd__power__iff,axiom,
% 5.12/5.41 ! [X: int,M2: nat,N: nat] :
% 5.12/5.41 ( ( X != zero_zero_int )
% 5.12/5.41 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.12/5.41 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power_iff
% 5.12/5.41 thf(fact_7080_dvd__power__iff,axiom,
% 5.12/5.41 ! [X: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( X != zero_zero_nat )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N ) )
% 5.12/5.41 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.12/5.41 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power_iff
% 5.12/5.41 thf(fact_7081_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: code_integer] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_Code_integer ) )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7082_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: rat] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_rat ) )
% 5.12/5.41 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7083_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: int] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_int ) )
% 5.12/5.41 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7084_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: nat] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_nat ) )
% 5.12/5.41 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7085_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: real] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_real ) )
% 5.12/5.41 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7086_dvd__power,axiom,
% 5.12/5.41 ! [N: nat,X: complex] :
% 5.12/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.41 | ( X = one_one_complex ) )
% 5.12/5.41 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_power
% 5.12/5.41 thf(fact_7087_div2__even__ext__nat,axiom,
% 5.12/5.41 ! [X: nat,Y: nat] :
% 5.12/5.41 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.41 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.41 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.12/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.12/5.41 => ( X = Y ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % div2_even_ext_nat
% 5.12/5.41 thf(fact_7088_choose__dvd,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_dvd
% 5.12/5.41 thf(fact_7089_choose__dvd,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_dvd
% 5.12/5.41 thf(fact_7090_choose__dvd,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_dvd
% 5.12/5.41 thf(fact_7091_choose__dvd,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_dvd
% 5.12/5.41 thf(fact_7092_choose__dvd,axiom,
% 5.12/5.41 ! [K: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ K @ N )
% 5.12/5.41 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % choose_dvd
% 5.12/5.41 thf(fact_7093_dvd__mult__cancel1,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 5.12/5.41 = ( N = one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel1
% 5.12/5.41 thf(fact_7094_dvd__mult__cancel2,axiom,
% 5.12/5.41 ! [M2: nat,N: nat] :
% 5.12/5.41 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 5.12/5.41 = ( N = one_one_nat ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_mult_cancel2
% 5.12/5.41 thf(fact_7095_dvd__minus__add,axiom,
% 5.12/5.41 ! [Q5: nat,N: nat,R4: nat,M2: nat] :
% 5.12/5.41 ( ( ord_less_eq_nat @ Q5 @ N )
% 5.12/5.41 => ( ( ord_less_eq_nat @ Q5 @ ( times_times_nat @ R4 @ M2 ) )
% 5.12/5.41 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ Q5 ) )
% 5.12/5.41 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R4 @ M2 ) @ Q5 ) ) ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % dvd_minus_add
% 5.12/5.41 thf(fact_7096_power__dvd__imp__le,axiom,
% 5.12/5.41 ! [I: nat,M2: nat,N: nat] :
% 5.12/5.41 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 5.12/5.41 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.12/5.41 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % power_dvd_imp_le
% 5.12/5.41 thf(fact_7097_mod__nat__eqI,axiom,
% 5.12/5.41 ! [R4: nat,N: nat,M2: nat] :
% 5.12/5.41 ( ( ord_less_nat @ R4 @ N )
% 5.12/5.41 => ( ( ord_less_eq_nat @ R4 @ M2 )
% 5.12/5.41 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R4 ) )
% 5.12/5.41 => ( ( modulo_modulo_nat @ M2 @ N )
% 5.12/5.41 = R4 ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % mod_nat_eqI
% 5.12/5.41 thf(fact_7098_complex__mult,axiom,
% 5.12/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.12/5.41 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.12/5.41 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.12/5.41
% 5.12/5.41 % complex_mult
% 5.12/5.41 thf(fact_7099_even__two__times__div__two,axiom,
% 5.12/5.41 ! [A: code_integer] :
% 5.12/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.41 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_two_times_div_two
% 5.12/5.42 thf(fact_7100_even__two__times__div__two,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_two_times_div_two
% 5.12/5.42 thf(fact_7101_even__two__times__div__two,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_two_times_div_two
% 5.12/5.42 thf(fact_7102_even__iff__mod__2__eq__zero,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_iff_mod_2_eq_zero
% 5.12/5.42 thf(fact_7103_even__iff__mod__2__eq__zero,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_iff_mod_2_eq_zero
% 5.12/5.42 thf(fact_7104_even__iff__mod__2__eq__zero,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_z3403309356797280102nteger ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_iff_mod_2_eq_zero
% 5.12/5.42 thf(fact_7105_even__iff__mod__2__eq__zero,axiom,
% 5.12/5.42 ! [A: code_natural] :
% 5.12/5.42 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_z2226904508553997617atural ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_iff_mod_2_eq_zero
% 5.12/5.42 thf(fact_7106_odd__iff__mod__2__eq__one,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_iff_mod_2_eq_one
% 5.12/5.42 thf(fact_7107_odd__iff__mod__2__eq__one,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_iff_mod_2_eq_one
% 5.12/5.42 thf(fact_7108_odd__iff__mod__2__eq__one,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_Code_integer ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_iff_mod_2_eq_one
% 5.12/5.42 thf(fact_7109_odd__iff__mod__2__eq__one,axiom,
% 5.12/5.42 ! [A: code_natural] :
% 5.12/5.42 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_Code_natural ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_iff_mod_2_eq_one
% 5.12/5.42 thf(fact_7110_uminus__power__if,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.12/5.42 = ( power_power_int @ A @ N ) ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.12/5.42 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_power_if
% 5.12/5.42 thf(fact_7111_uminus__power__if,axiom,
% 5.12/5.42 ! [N: nat,A: real] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.12/5.42 = ( power_power_real @ A @ N ) ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.12/5.42 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_power_if
% 5.12/5.42 thf(fact_7112_uminus__power__if,axiom,
% 5.12/5.42 ! [N: nat,A: complex] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.12/5.42 = ( power_power_complex @ A @ N ) ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_power_if
% 5.12/5.42 thf(fact_7113_uminus__power__if,axiom,
% 5.12/5.42 ! [N: nat,A: code_integer] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.12/5.42 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.12/5.42 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_power_if
% 5.12/5.42 thf(fact_7114_uminus__power__if,axiom,
% 5.12/5.42 ! [N: nat,A: rat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.12/5.42 = ( power_power_rat @ A @ N ) ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.12/5.42 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_power_if
% 5.12/5.42 thf(fact_7115_odd__pos,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_pos
% 5.12/5.42 thf(fact_7116_even__unset__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: code_integer] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 | ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_unset_bit_iff
% 5.12/5.42 thf(fact_7117_even__unset__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 | ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_unset_bit_iff
% 5.12/5.42 thf(fact_7118_even__unset__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 | ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_unset_bit_iff
% 5.12/5.42 thf(fact_7119_even__set__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: code_integer] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 & ( M2 != zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_set_bit_iff
% 5.12/5.42 thf(fact_7120_even__set__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 & ( M2 != zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_set_bit_iff
% 5.12/5.42 thf(fact_7121_even__set__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 & ( M2 != zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_set_bit_iff
% 5.12/5.42 thf(fact_7122_even__flip__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: code_integer] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 != ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_flip_bit_iff
% 5.12/5.42 thf(fact_7123_even__flip__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 != ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_flip_bit_iff
% 5.12/5.42 thf(fact_7124_even__flip__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 != ( M2 = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_flip_bit_iff
% 5.12/5.42 thf(fact_7125_tan__45,axiom,
% 5.12/5.42 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % tan_45
% 5.12/5.42 thf(fact_7126_oddE,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ~ ! [B3: code_integer] :
% 5.12/5.42 ( A
% 5.12/5.42 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % oddE
% 5.12/5.42 thf(fact_7127_oddE,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ~ ! [B3: nat] :
% 5.12/5.42 ( A
% 5.12/5.42 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % oddE
% 5.12/5.42 thf(fact_7128_oddE,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ~ ! [B3: int] :
% 5.12/5.42 ( A
% 5.12/5.42 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % oddE
% 5.12/5.42 thf(fact_7129_parity__cases,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 != zero_zero_int ) )
% 5.12/5.42 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 != one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % parity_cases
% 5.12/5.42 thf(fact_7130_parity__cases,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 != zero_zero_nat ) )
% 5.12/5.42 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 != one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % parity_cases
% 5.12/5.42 thf(fact_7131_parity__cases,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 != zero_z3403309356797280102nteger ) )
% 5.12/5.42 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 != one_one_Code_integer ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % parity_cases
% 5.12/5.42 thf(fact_7132_parity__cases,axiom,
% 5.12/5.42 ! [A: code_natural] :
% 5.12/5.42 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 != zero_z2226904508553997617atural ) )
% 5.12/5.42 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 != one_one_Code_natural ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % parity_cases
% 5.12/5.42 thf(fact_7133_mod2__eq__if,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_int ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mod2_eq_if
% 5.12/5.42 thf(fact_7134_mod2__eq__if,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_nat ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mod2_eq_if
% 5.12/5.42 thf(fact_7135_mod2__eq__if,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_z3403309356797280102nteger ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_Code_integer ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mod2_eq_if
% 5.12/5.42 thf(fact_7136_mod2__eq__if,axiom,
% 5.12/5.42 ! [A: code_natural] :
% 5.12/5.42 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_z2226904508553997617atural ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.12/5.42 = one_one_Code_natural ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mod2_eq_if
% 5.12/5.42 thf(fact_7137_zero__le__even__power,axiom,
% 5.12/5.42 ! [N: nat,A: real] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_even_power
% 5.12/5.42 thf(fact_7138_zero__le__even__power,axiom,
% 5.12/5.42 ! [N: nat,A: rat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_even_power
% 5.12/5.42 thf(fact_7139_zero__le__even__power,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_even_power
% 5.12/5.42 thf(fact_7140_zero__le__odd__power,axiom,
% 5.12/5.42 ! [N: nat,A: real] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.12/5.42 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_odd_power
% 5.12/5.42 thf(fact_7141_zero__le__odd__power,axiom,
% 5.12/5.42 ! [N: nat,A: rat] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.12/5.42 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_odd_power
% 5.12/5.42 thf(fact_7142_zero__le__odd__power,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.12/5.42 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_odd_power
% 5.12/5.42 thf(fact_7143_zero__le__power__eq,axiom,
% 5.12/5.42 ! [A: real,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_power_eq
% 5.12/5.42 thf(fact_7144_zero__le__power__eq,axiom,
% 5.12/5.42 ! [A: rat,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_power_eq
% 5.12/5.42 thf(fact_7145_zero__le__power__eq,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.12/5.42 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_le_power_eq
% 5.12/5.42 thf(fact_7146_minus__one__power__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.12/5.42 = one_one_int ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.12/5.42 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % minus_one_power_iff
% 5.12/5.42 thf(fact_7147_minus__one__power__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.12/5.42 = one_one_real ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.12/5.42 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % minus_one_power_iff
% 5.12/5.42 thf(fact_7148_minus__one__power__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.12/5.42 = one_one_complex ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % minus_one_power_iff
% 5.12/5.42 thf(fact_7149_minus__one__power__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.12/5.42 = one_one_Code_integer ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.12/5.42 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % minus_one_power_iff
% 5.12/5.42 thf(fact_7150_minus__one__power__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.12/5.42 = one_one_rat ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.12/5.42 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % minus_one_power_iff
% 5.12/5.42 thf(fact_7151_central__binomial__odd,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % central_binomial_odd
% 5.12/5.42 thf(fact_7152_tan__gt__zero,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_gt_zero
% 5.12/5.42 thf(fact_7153_lemma__tan__total,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.12/5.42 => ? [X3: real] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.12/5.42 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % lemma_tan_total
% 5.12/5.42 thf(fact_7154_lemma__tan__total1,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ? [X3: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.12/5.42 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( tan_real @ X3 )
% 5.12/5.42 = Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % lemma_tan_total1
% 5.12/5.42 thf(fact_7155_tan__mono__lt__eq,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.12/5.42 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_mono_lt_eq
% 5.12/5.42 thf(fact_7156_tan__monotone_H,axiom,
% 5.12/5.42 ! [Y: real,X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ Y @ X )
% 5.12/5.42 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_monotone'
% 5.12/5.42 thf(fact_7157_tan__monotone,axiom,
% 5.12/5.42 ! [Y: real,X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_monotone
% 5.12/5.42 thf(fact_7158_tan__total,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ? [X3: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.12/5.42 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( tan_real @ X3 )
% 5.12/5.42 = Y )
% 5.12/5.42 & ! [Y5: real] :
% 5.12/5.42 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.12/5.42 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( tan_real @ Y5 )
% 5.12/5.42 = Y ) )
% 5.12/5.42 => ( Y5 = X3 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_total
% 5.12/5.42 thf(fact_7159_tan__minus__45,axiom,
% 5.12/5.42 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.42 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_minus_45
% 5.12/5.42 thf(fact_7160_tan__inverse,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.12/5.42 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_inverse
% 5.12/5.42 thf(fact_7161_tan__cot,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.12/5.42 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_cot
% 5.12/5.42 thf(fact_7162_zero__less__power__eq,axiom,
% 5.12/5.42 ! [A: real,N: nat] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A != zero_zero_real ) )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_power_eq
% 5.12/5.42 thf(fact_7163_zero__less__power__eq,axiom,
% 5.12/5.42 ! [A: rat,N: nat] :
% 5.12/5.42 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A != zero_zero_rat ) )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_power_eq
% 5.12/5.42 thf(fact_7164_zero__less__power__eq,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A != zero_zero_int ) )
% 5.12/5.42 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_power_eq
% 5.12/5.42 thf(fact_7165_add__tan__eq,axiom,
% 5.12/5.42 ! [X: complex,Y: complex] :
% 5.12/5.42 ( ( ( cos_complex @ X )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ Y )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % add_tan_eq
% 5.12/5.42 thf(fact_7166_add__tan__eq,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ Y )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.12/5.42 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % add_tan_eq
% 5.12/5.42 thf(fact_7167_tan__cot_H,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.12/5.42 = ( cot_real @ X ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_cot'
% 5.12/5.42 thf(fact_7168_tan__total__pos,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.42 => ? [X3: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.12/5.42 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( tan_real @ X3 )
% 5.12/5.42 = Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_total_pos
% 5.12/5.42 thf(fact_7169_tan__pos__pi2__le,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_pos_pi2_le
% 5.12/5.42 thf(fact_7170_tan__less__zero,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.42 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_less_zero
% 5.12/5.42 thf(fact_7171_tan__mono__le__eq,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.12/5.42 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_mono_le_eq
% 5.12/5.42 thf(fact_7172_tan__mono__le,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_mono_le
% 5.12/5.42 thf(fact_7173_tan__bound__pi2,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_bound_pi2
% 5.12/5.42 thf(fact_7174_arctan__unique,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ( tan_real @ X )
% 5.12/5.42 = Y )
% 5.12/5.42 => ( ( arctan @ Y )
% 5.12/5.42 = X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arctan_unique
% 5.12/5.42 thf(fact_7175_arctan__tan,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( arctan @ ( tan_real @ X ) )
% 5.12/5.42 = X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arctan_tan
% 5.12/5.42 thf(fact_7176_arctan,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.12/5.42 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( tan_real @ ( arctan @ Y ) )
% 5.12/5.42 = Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % arctan
% 5.12/5.42 thf(fact_7177_even__mask__div__iff_H,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff'
% 5.12/5.42 thf(fact_7178_even__mask__div__iff_H,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff'
% 5.12/5.42 thf(fact_7179_even__mask__div__iff_H,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff'
% 5.12/5.42 thf(fact_7180_power__le__zero__eq,axiom,
% 5.12/5.42 ! [A: real,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.12/5.42 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.42 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % power_le_zero_eq
% 5.12/5.42 thf(fact_7181_power__le__zero__eq,axiom,
% 5.12/5.42 ! [A: rat,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.12/5.42 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.42 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % power_le_zero_eq
% 5.12/5.42 thf(fact_7182_power__le__zero__eq,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.12/5.42 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.42 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.12/5.42 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % power_le_zero_eq
% 5.12/5.42 thf(fact_7183_lemma__tan__add1,axiom,
% 5.12/5.42 ! [X: complex,Y: complex] :
% 5.12/5.42 ( ( ( cos_complex @ X )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ Y )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % lemma_tan_add1
% 5.12/5.42 thf(fact_7184_lemma__tan__add1,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ Y )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) )
% 5.12/5.42 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % lemma_tan_add1
% 5.12/5.42 thf(fact_7185_tan__diff,axiom,
% 5.12/5.42 ! [X: complex,Y: complex] :
% 5.12/5.42 ( ( ( cos_complex @ X )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ Y )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_diff
% 5.12/5.42 thf(fact_7186_tan__diff,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ Y )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( tan_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.42 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_diff
% 5.12/5.42 thf(fact_7187_tan__add,axiom,
% 5.12/5.42 ! [X: complex,Y: complex] :
% 5.12/5.42 ( ( ( cos_complex @ X )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ Y )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_add
% 5.12/5.42 thf(fact_7188_tan__add,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ Y )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( tan_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.42 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_add
% 5.12/5.42 thf(fact_7189_even__mod__4__div__2,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( suc @ zero_zero_nat ) )
% 5.12/5.42 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mod_4_div_2
% 5.12/5.42 thf(fact_7190_complex__inverse,axiom,
% 5.12/5.42 ! [A: real,B: real] :
% 5.12/5.42 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.12/5.42 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % complex_inverse
% 5.12/5.42 thf(fact_7191_tan__total__pi4,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ? [Z4: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z4 )
% 5.12/5.42 & ( ord_less_real @ Z4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 & ( ( tan_real @ Z4 )
% 5.12/5.42 = X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_total_pi4
% 5.12/5.42 thf(fact_7192_even__mask__div__iff,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_z3403309356797280102nteger )
% 5.12/5.42 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff
% 5.12/5.42 thf(fact_7193_even__mask__div__iff,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff
% 5.12/5.42 thf(fact_7194_even__mask__div__iff,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mask_div_iff
% 5.12/5.42 thf(fact_7195_odd__mod__4__div__2,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.12/5.42 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_mod_4_div_2
% 5.12/5.42 thf(fact_7196_Bernoulli__inequality__even,axiom,
% 5.12/5.42 ! [N: nat,X: real] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Bernoulli_inequality_even
% 5.12/5.42 thf(fact_7197_even__mult__exp__div__exp__iff,axiom,
% 5.12/5.42 ! [A: code_integer,M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_z3403309356797280102nteger )
% 5.12/5.42 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.42 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mult_exp_div_exp_iff
% 5.12/5.42 thf(fact_7198_even__mult__exp__div__exp__iff,axiom,
% 5.12/5.42 ! [A: nat,M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.42 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mult_exp_div_exp_iff
% 5.12/5.42 thf(fact_7199_even__mult__exp__div__exp__iff,axiom,
% 5.12/5.42 ! [A: int,M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.42 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.42 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_mult_exp_div_exp_iff
% 5.12/5.42 thf(fact_7200_tan__sec,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 != zero_zero_real )
% 5.12/5.42 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_sec
% 5.12/5.42 thf(fact_7201_tan__sec,axiom,
% 5.12/5.42 ! [X: complex] :
% 5.12/5.42 ( ( ( cos_complex @ X )
% 5.12/5.42 != zero_zero_complex )
% 5.12/5.42 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_sec
% 5.12/5.42 thf(fact_7202_tan__half,axiom,
% 5.12/5.42 ( tan_complex
% 5.12/5.42 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_half
% 5.12/5.42 thf(fact_7203_tan__half,axiom,
% 5.12/5.42 ( tan_real
% 5.12/5.42 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_half
% 5.12/5.42 thf(fact_7204_sin__coeff__def,axiom,
% 5.12/5.42 ( sin_coeff
% 5.12/5.42 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_coeff_def
% 5.12/5.42 thf(fact_7205_cos__coeff__def,axiom,
% 5.12/5.42 ( cos_coeff
% 5.12/5.42 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) @ zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_coeff_def
% 5.12/5.42 thf(fact_7206_sin__tan,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( sin_real @ X )
% 5.12/5.42 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_tan
% 5.12/5.42 thf(fact_7207_cos__tan,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( cos_real @ X )
% 5.12/5.42 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_tan
% 5.12/5.42 thf(fact_7208_cos__npi__int,axiom,
% 5.12/5.42 ! [N: int] :
% 5.12/5.42 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.12/5.42 = one_one_real ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.12/5.42 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_npi_int
% 5.12/5.42 thf(fact_7209_real__sqrt__one,axiom,
% 5.12/5.42 ( ( sqrt @ one_one_real )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_one
% 5.12/5.42 thf(fact_7210_real__sqrt__eq__1__iff,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ( sqrt @ X )
% 5.12/5.42 = one_one_real )
% 5.12/5.42 = ( X = one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_eq_1_iff
% 5.12/5.42 thf(fact_7211_real__sqrt__gt__1__iff,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.12/5.42 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_gt_1_iff
% 5.12/5.42 thf(fact_7212_real__sqrt__lt__1__iff,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.12/5.42 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_lt_1_iff
% 5.12/5.42 thf(fact_7213_real__sqrt__le__1__iff,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.12/5.42 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_le_1_iff
% 5.12/5.42 thf(fact_7214_real__sqrt__ge__1__iff,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.12/5.42 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_ge_1_iff
% 5.12/5.42 thf(fact_7215_int__dvd__int__iff,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.42 = ( dvd_dvd_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % int_dvd_int_iff
% 5.12/5.42 thf(fact_7216_zdvd1__eq,axiom,
% 5.12/5.42 ! [X: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ X @ one_one_int )
% 5.12/5.42 = ( ( abs_abs_int @ X )
% 5.12/5.42 = one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd1_eq
% 5.12/5.42 thf(fact_7217_sin__coeff__0,axiom,
% 5.12/5.42 ( ( sin_coeff @ zero_zero_nat )
% 5.12/5.42 = zero_zero_real ) ).
% 5.12/5.42
% 5.12/5.42 % sin_coeff_0
% 5.12/5.42 thf(fact_7218_cos__coeff__0,axiom,
% 5.12/5.42 ( ( cos_coeff @ zero_zero_nat )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % cos_coeff_0
% 5.12/5.42 thf(fact_7219_sgn__mult__dvd__iff,axiom,
% 5.12/5.42 ! [R4: int,L: int,K: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R4 ) @ L ) @ K )
% 5.12/5.42 = ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 & ( ( R4 = zero_zero_int )
% 5.12/5.42 => ( K = zero_zero_int ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mult_dvd_iff
% 5.12/5.42 thf(fact_7220_mult__sgn__dvd__iff,axiom,
% 5.12/5.42 ! [L: int,R4: int,K: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R4 ) ) @ K )
% 5.12/5.42 = ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 & ( ( R4 = zero_zero_int )
% 5.12/5.42 => ( K = zero_zero_int ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mult_sgn_dvd_iff
% 5.12/5.42 thf(fact_7221_dvd__sgn__mult__iff,axiom,
% 5.12/5.42 ! [L: int,R4: int,K: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R4 ) @ K ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 | ( R4 = zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % dvd_sgn_mult_iff
% 5.12/5.42 thf(fact_7222_dvd__mult__sgn__iff,axiom,
% 5.12/5.42 ! [L: int,K: int,R4: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R4 ) ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 | ( R4 = zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % dvd_mult_sgn_iff
% 5.12/5.42 thf(fact_7223_nat__abs__dvd__iff,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.12/5.42 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % nat_abs_dvd_iff
% 5.12/5.42 thf(fact_7224_dvd__nat__abs__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.12/5.42 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.12/5.42
% 5.12/5.42 % dvd_nat_abs_iff
% 5.12/5.42 thf(fact_7225_real__sqrt__divide,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 5.12/5.42 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_divide
% 5.12/5.42 thf(fact_7226_real__sqrt__minus,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.12/5.42 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_minus
% 5.12/5.42 thf(fact_7227_uminus__dvd__conv_I1_J,axiom,
% 5.12/5.42 ( dvd_dvd_int
% 5.12/5.42 = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_dvd_conv(1)
% 5.12/5.42 thf(fact_7228_uminus__dvd__conv_I2_J,axiom,
% 5.12/5.42 ( dvd_dvd_int
% 5.12/5.42 = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % uminus_dvd_conv(2)
% 5.12/5.42 thf(fact_7229_zdvd__zdiffD,axiom,
% 5.12/5.42 ! [K: int,M2: int,N: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M2 @ N ) )
% 5.12/5.42 => ( ( dvd_dvd_int @ K @ N )
% 5.12/5.42 => ( dvd_dvd_int @ K @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_zdiffD
% 5.12/5.42 thf(fact_7230_zdvd__antisym__abs,axiom,
% 5.12/5.42 ! [A: int,B: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.12/5.42 => ( ( dvd_dvd_int @ B @ A )
% 5.12/5.42 => ( ( abs_abs_int @ A )
% 5.12/5.42 = ( abs_abs_int @ B ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_antisym_abs
% 5.12/5.42 thf(fact_7231_real__sqrt__ge__one,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.42 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_ge_one
% 5.12/5.42 thf(fact_7232_zdvd__antisym__nonneg,axiom,
% 5.12/5.42 ! [M2: int,N: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 5.12/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.12/5.42 => ( ( dvd_dvd_int @ M2 @ N )
% 5.12/5.42 => ( ( dvd_dvd_int @ N @ M2 )
% 5.12/5.42 => ( M2 = N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_antisym_nonneg
% 5.12/5.42 thf(fact_7233_zdvd__not__zless,axiom,
% 5.12/5.42 ! [M2: int,N: int] :
% 5.12/5.42 ( ( ord_less_int @ zero_zero_int @ M2 )
% 5.12/5.42 => ( ( ord_less_int @ M2 @ N )
% 5.12/5.42 => ~ ( dvd_dvd_int @ N @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_not_zless
% 5.12/5.42 thf(fact_7234_zdvd__mult__cancel,axiom,
% 5.12/5.42 ! [K: int,M2: int,N: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( times_times_int @ K @ M2 ) @ ( times_times_int @ K @ N ) )
% 5.12/5.42 => ( ( K != zero_zero_int )
% 5.12/5.42 => ( dvd_dvd_int @ M2 @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_mult_cancel
% 5.12/5.42 thf(fact_7235_zdvd__mono,axiom,
% 5.12/5.42 ! [K: int,M2: int,T: int] :
% 5.12/5.42 ( ( K != zero_zero_int )
% 5.12/5.42 => ( ( dvd_dvd_int @ M2 @ T )
% 5.12/5.42 = ( dvd_dvd_int @ ( times_times_int @ K @ M2 ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_mono
% 5.12/5.42 thf(fact_7236_zdvd__period,axiom,
% 5.12/5.42 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ A @ D )
% 5.12/5.42 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.12/5.42 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_period
% 5.12/5.42 thf(fact_7237_zdvd__reduce,axiom,
% 5.12/5.42 ! [K: int,N: int,M2: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M2 ) ) )
% 5.12/5.42 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_reduce
% 5.12/5.42 thf(fact_7238_abs__div,axiom,
% 5.12/5.42 ! [Y: int,X: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ Y @ X )
% 5.12/5.42 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 5.12/5.42 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % abs_div
% 5.12/5.42 thf(fact_7239_sin__coeff__Suc,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( sin_coeff @ ( suc @ N ) )
% 5.12/5.42 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_coeff_Suc
% 5.12/5.42 thf(fact_7240_real__div__sqrt,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.12/5.42 = ( sqrt @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_div_sqrt
% 5.12/5.42 thf(fact_7241_cos__coeff__Suc,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( cos_coeff @ ( suc @ N ) )
% 5.12/5.42 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_coeff_Suc
% 5.12/5.42 thf(fact_7242_zdvd__imp__le,axiom,
% 5.12/5.42 ! [Z2: int,N: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ Z2 @ N )
% 5.12/5.42 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.12/5.42 => ( ord_less_eq_int @ Z2 @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_imp_le
% 5.12/5.42 thf(fact_7243_dvd__imp__le__int,axiom,
% 5.12/5.42 ! [I: int,D: int] :
% 5.12/5.42 ( ( I != zero_zero_int )
% 5.12/5.42 => ( ( dvd_dvd_int @ D @ I )
% 5.12/5.42 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % dvd_imp_le_int
% 5.12/5.42 thf(fact_7244_of__int__divide__in__Ints,axiom,
% 5.12/5.42 ! [B: int,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.42 => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_divide_in_Ints
% 5.12/5.42 thf(fact_7245_of__int__divide__in__Ints,axiom,
% 5.12/5.42 ! [B: int,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.42 => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_divide_in_Ints
% 5.12/5.42 thf(fact_7246_of__int__divide__in__Ints,axiom,
% 5.12/5.42 ! [B: int,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.42 => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_divide_in_Ints
% 5.12/5.42 thf(fact_7247_of__int__divide__in__Ints,axiom,
% 5.12/5.42 ! [B: int,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ B @ A )
% 5.12/5.42 => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_divide_in_Ints
% 5.12/5.42 thf(fact_7248_real__of__int__div,axiom,
% 5.12/5.42 ! [D: int,N: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ D @ N )
% 5.12/5.42 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.12/5.42 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_of_int_div
% 5.12/5.42 thf(fact_7249_sgn__mod,axiom,
% 5.12/5.42 ! [L: int,K: int] :
% 5.12/5.42 ( ( L != zero_zero_int )
% 5.12/5.42 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.12/5.42 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.12/5.42 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mod
% 5.12/5.42 thf(fact_7250_sqrt__divide__self__eq,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.12/5.42 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sqrt_divide_self_eq
% 5.12/5.42 thf(fact_7251_zdvd__mult__cancel1,axiom,
% 5.12/5.42 ! [M2: int,N: int] :
% 5.12/5.42 ( ( M2 != zero_zero_int )
% 5.12/5.42 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N ) @ M2 )
% 5.12/5.42 = ( ( abs_abs_int @ N )
% 5.12/5.42 = one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % zdvd_mult_cancel1
% 5.12/5.42 thf(fact_7252_mod__int__pos__iff,axiom,
% 5.12/5.42 ! [K: int,L: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.12/5.42 = ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 | ( ( L = zero_zero_int )
% 5.12/5.42 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.12/5.42 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mod_int_pos_iff
% 5.12/5.42 thf(fact_7253_aset_I10_J,axiom,
% 5.12/5.42 ! [D: int,D6: int,A2: set_int,T: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.42 => ! [X4: int] :
% 5.12/5.42 ( ! [Xa3: int] :
% 5.12/5.42 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.42 => ! [Xb2: int] :
% 5.12/5.42 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.42 => ( X4
% 5.12/5.42 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.42 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.12/5.42 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % aset(10)
% 5.12/5.42 thf(fact_7254_aset_I9_J,axiom,
% 5.12/5.42 ! [D: int,D6: int,A2: set_int,T: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.42 => ! [X4: int] :
% 5.12/5.42 ( ! [Xa3: int] :
% 5.12/5.42 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.42 => ! [Xb2: int] :
% 5.12/5.42 ( ( member_int @ Xb2 @ A2 )
% 5.12/5.42 => ( X4
% 5.12/5.42 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.42 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.12/5.42 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % aset(9)
% 5.12/5.42 thf(fact_7255_bset_I10_J,axiom,
% 5.12/5.42 ! [D: int,D6: int,B5: set_int,T: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.42 => ! [X4: int] :
% 5.12/5.42 ( ! [Xa3: int] :
% 5.12/5.42 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.42 => ! [Xb2: int] :
% 5.12/5.42 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.42 => ( X4
% 5.12/5.42 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.42 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.12/5.42 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bset(10)
% 5.12/5.42 thf(fact_7256_bset_I9_J,axiom,
% 5.12/5.42 ! [D: int,D6: int,B5: set_int,T: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ D @ D6 )
% 5.12/5.42 => ! [X4: int] :
% 5.12/5.42 ( ! [Xa3: int] :
% 5.12/5.42 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D6 ) )
% 5.12/5.42 => ! [Xb2: int] :
% 5.12/5.42 ( ( member_int @ Xb2 @ B5 )
% 5.12/5.42 => ( X4
% 5.12/5.42 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.12/5.42 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.12/5.42 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D6 ) @ T ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bset(9)
% 5.12/5.42 thf(fact_7257_div__dvd__sgn__abs,axiom,
% 5.12/5.42 ! [L: int,K: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ L @ K )
% 5.12/5.42 => ( ( divide_divide_int @ K @ L )
% 5.12/5.42 = ( 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 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % div_dvd_sgn_abs
% 5.12/5.42 thf(fact_7258_tan__60,axiom,
% 5.12/5.42 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.12/5.42 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_60
% 5.12/5.42 thf(fact_7259_even__diff__iff,axiom,
% 5.12/5.42 ! [K: int,L: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.12/5.42 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_diff_iff
% 5.12/5.42 thf(fact_7260_lemma__real__divide__sqrt__less,axiom,
% 5.12/5.42 ! [U: real] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ U )
% 5.12/5.42 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.12/5.42
% 5.12/5.42 % lemma_real_divide_sqrt_less
% 5.12/5.42 thf(fact_7261_cos__45,axiom,
% 5.12/5.42 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_45
% 5.12/5.42 thf(fact_7262_sin__45,axiom,
% 5.12/5.42 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_45
% 5.12/5.42 thf(fact_7263_nat__dvd__iff,axiom,
% 5.12/5.42 ! [Z2: int,M2: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( nat2 @ Z2 ) @ M2 )
% 5.12/5.42 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.42 => ( dvd_dvd_int @ Z2 @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 5.12/5.42 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 5.12/5.42 => ( M2 = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % nat_dvd_iff
% 5.12/5.42 thf(fact_7264_tan__30,axiom,
% 5.12/5.42 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.12/5.42 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % tan_30
% 5.12/5.42 thf(fact_7265_sqrt__even__pow2,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sqrt_even_pow2
% 5.12/5.42 thf(fact_7266_ln__sqrt,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.12/5.42 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % ln_sqrt
% 5.12/5.42 thf(fact_7267_cos__30,axiom,
% 5.12/5.42 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.12/5.42 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_30
% 5.12/5.42 thf(fact_7268_sin__60,axiom,
% 5.12/5.42 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.12/5.42 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_60
% 5.12/5.42 thf(fact_7269_arsinh__real__aux,axiom,
% 5.12/5.42 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arsinh_real_aux
% 5.12/5.42 thf(fact_7270_real__sqrt__power__even,axiom,
% 5.12/5.42 ! [N: nat,X: real] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 5.12/5.42 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_power_even
% 5.12/5.42 thf(fact_7271_arith__geo__mean__sqrt,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.42 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arith_geo_mean_sqrt
% 5.12/5.42 thf(fact_7272_powr__half__sqrt,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( sqrt @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % powr_half_sqrt
% 5.12/5.42 thf(fact_7273_arsinh__real__def,axiom,
% 5.12/5.42 ( arsinh_real
% 5.12/5.42 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arsinh_real_def
% 5.12/5.42 thf(fact_7274_even__nat__iff,axiom,
% 5.12/5.42 ! [K: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.12/5.42 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_nat_iff
% 5.12/5.42 thf(fact_7275_cos__x__y__le__one,axiom,
% 5.12/5.42 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % cos_x_y_le_one
% 5.12/5.42 thf(fact_7276_real__sqrt__sum__squares__less,axiom,
% 5.12/5.42 ! [X: real,U: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % real_sqrt_sum_squares_less
% 5.12/5.42 thf(fact_7277_cos__arctan,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( cos_real @ ( arctan @ X ) )
% 5.12/5.42 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_arctan
% 5.12/5.42 thf(fact_7278_sin__arctan,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( sin_real @ ( arctan @ X ) )
% 5.12/5.42 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_arctan
% 5.12/5.42 thf(fact_7279_sqrt__sum__squares__half__less,axiom,
% 5.12/5.42 ! [X: real,U: real,Y: real] :
% 5.12/5.42 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.42 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sqrt_sum_squares_half_less
% 5.12/5.42 thf(fact_7280_sin__cos__sqrt,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.12/5.42 => ( ( sin_real @ X )
% 5.12/5.42 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_cos_sqrt
% 5.12/5.42 thf(fact_7281_arctan__half,axiom,
% 5.12/5.42 ( arctan
% 5.12/5.42 = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arctan_half
% 5.12/5.42 thf(fact_7282_arcosh__real__def,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.12/5.42 => ( ( arcosh_real @ X )
% 5.12/5.42 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcosh_real_def
% 5.12/5.42 thf(fact_7283_cos__zero__iff__int,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ( cos_real @ X )
% 5.12/5.42 = zero_zero_real )
% 5.12/5.42 = ( ? [I2: int] :
% 5.12/5.42 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.12/5.42 & ( X
% 5.12/5.42 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_zero_iff_int
% 5.12/5.42 thf(fact_7284_sin__zero__iff__int,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ( sin_real @ X )
% 5.12/5.42 = zero_zero_real )
% 5.12/5.42 = ( ? [I2: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.12/5.42 & ( X
% 5.12/5.42 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_zero_iff_int
% 5.12/5.42 thf(fact_7285_cos__arcsin,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( cos_real @ ( arcsin @ X ) )
% 5.12/5.42 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_arcsin
% 5.12/5.42 thf(fact_7286_sin__arccos__abs,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( sin_real @ ( arccos @ Y ) )
% 5.12/5.42 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_arccos_abs
% 5.12/5.42 thf(fact_7287_sin__arccos,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( sin_real @ ( arccos @ X ) )
% 5.12/5.42 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_arccos
% 5.12/5.42 thf(fact_7288_cis__multiple__2pi,axiom,
% 5.12/5.42 ! [N: real] :
% 5.12/5.42 ( ( member_real @ N @ ring_1_Ints_real )
% 5.12/5.42 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.12/5.42 = one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_multiple_2pi
% 5.12/5.42 thf(fact_7289_take__bit__numeral__minus__bit1,axiom,
% 5.12/5.42 ! [L: num,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.42 = ( 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 ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_minus_bit1
% 5.12/5.42 thf(fact_7290_take__bit__of__0,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_0
% 5.12/5.42 thf(fact_7291_take__bit__of__0,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_0
% 5.12/5.42 thf(fact_7292_arcsin__0,axiom,
% 5.12/5.42 ( ( arcsin @ zero_zero_real )
% 5.12/5.42 = zero_zero_real ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_0
% 5.12/5.42 thf(fact_7293_take__bit__0,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_0
% 5.12/5.42 thf(fact_7294_take__bit__0,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_0
% 5.12/5.42 thf(fact_7295_take__bit__Suc__1,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_1
% 5.12/5.42 thf(fact_7296_take__bit__Suc__1,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_1
% 5.12/5.42 thf(fact_7297_take__bit__numeral__1,axiom,
% 5.12/5.42 ! [L: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_1
% 5.12/5.42 thf(fact_7298_take__bit__numeral__1,axiom,
% 5.12/5.42 ! [L: num] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_1
% 5.12/5.42 thf(fact_7299_arccos__1,axiom,
% 5.12/5.42 ( ( arccos @ one_one_real )
% 5.12/5.42 = zero_zero_real ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_1
% 5.12/5.42 thf(fact_7300_norm__cis,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % norm_cis
% 5.12/5.42 thf(fact_7301_concat__bit__of__zero__2,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.12/5.42 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.12/5.42
% 5.12/5.42 % concat_bit_of_zero_2
% 5.12/5.42 thf(fact_7302_cis__zero,axiom,
% 5.12/5.42 ( ( cis @ zero_zero_real )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % cis_zero
% 5.12/5.42 thf(fact_7303_cis__inverse,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( invers8013647133539491842omplex @ ( cis @ A ) )
% 5.12/5.42 = ( cis @ ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_inverse
% 5.12/5.42 thf(fact_7304_take__bit__of__1__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_1_eq_0_iff
% 5.12/5.42 thf(fact_7305_take__bit__of__1__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_1_eq_0_iff
% 5.12/5.42 thf(fact_7306_of__nat__nat__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.12/5.42 = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_nat_take_bit_eq
% 5.12/5.42 thf(fact_7307_of__nat__nat__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.12/5.42 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_nat_take_bit_eq
% 5.12/5.42 thf(fact_7308_of__nat__nat__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.12/5.42 = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_nat_take_bit_eq
% 5.12/5.42 thf(fact_7309_of__nat__nat__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.12/5.42 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_nat_take_bit_eq
% 5.12/5.42 thf(fact_7310_arccos__minus__1,axiom,
% 5.12/5.42 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.42 = pi ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_minus_1
% 5.12/5.42 thf(fact_7311_cis__pi,axiom,
% 5.12/5.42 ( ( cis @ pi )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_pi
% 5.12/5.42 thf(fact_7312_cos__arccos,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( cos_real @ ( arccos @ Y ) )
% 5.12/5.42 = Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_arccos
% 5.12/5.42 thf(fact_7313_sin__arcsin,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.12/5.42 = Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_arcsin
% 5.12/5.42 thf(fact_7314_even__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,A: code_integer] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_take_bit_eq
% 5.12/5.42 thf(fact_7315_even__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_take_bit_eq
% 5.12/5.42 thf(fact_7316_even__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,A: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_take_bit_eq
% 5.12/5.42 thf(fact_7317_take__bit__Suc__0,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.12/5.42 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_0
% 5.12/5.42 thf(fact_7318_take__bit__Suc__0,axiom,
% 5.12/5.42 ! [A: code_natural] :
% 5.12/5.42 ( ( bit_se569199155075624693atural @ ( suc @ zero_zero_nat ) @ A )
% 5.12/5.42 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_0
% 5.12/5.42 thf(fact_7319_take__bit__Suc__0,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.12/5.42 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_0
% 5.12/5.42 thf(fact_7320_take__bit__Suc__0,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.12/5.42 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_0
% 5.12/5.42 thf(fact_7321_arccos__0,axiom,
% 5.12/5.42 ( ( arccos @ zero_zero_real )
% 5.12/5.42 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_0
% 5.12/5.42 thf(fact_7322_arcsin__1,axiom,
% 5.12/5.42 ( ( arcsin @ one_one_real )
% 5.12/5.42 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_1
% 5.12/5.42 thf(fact_7323_cis__2pi,axiom,
% 5.12/5.42 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % cis_2pi
% 5.12/5.42 thf(fact_7324_arcsin__minus__1,axiom,
% 5.12/5.42 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.12/5.42 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_minus_1
% 5.12/5.42 thf(fact_7325_take__bit__minus,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.12/5.42 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_minus
% 5.12/5.42 thf(fact_7326_take__bit__diff,axiom,
% 5.12/5.42 ! [N: nat,K: int,L: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.12/5.42 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_diff
% 5.12/5.42 thf(fact_7327_take__bit__of__nat,axiom,
% 5.12/5.42 ! [N: nat,M2: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M2 ) )
% 5.12/5.42 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_nat
% 5.12/5.42 thf(fact_7328_take__bit__of__nat,axiom,
% 5.12/5.42 ! [N: nat,M2: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M2 ) )
% 5.12/5.42 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_nat
% 5.12/5.42 thf(fact_7329_take__bit__int__less__eq__self__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.12/5.42 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_less_eq_self_iff
% 5.12/5.42 thf(fact_7330_take__bit__nonnegative,axiom,
% 5.12/5.42 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nonnegative
% 5.12/5.42 thf(fact_7331_not__take__bit__negative,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % not_take_bit_negative
% 5.12/5.42 thf(fact_7332_take__bit__int__greater__self__iff,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.12/5.42 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_greater_self_iff
% 5.12/5.42 thf(fact_7333_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.12/5.42 ! [N: nat,A: int,B: int] :
% 5.12/5.42 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.12/5.42 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.12/5.42 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.12/5.42 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_eq_iff_take_bit_eq
% 5.12/5.42 thf(fact_7334_cis__divide,axiom,
% 5.12/5.42 ! [A: real,B: real] :
% 5.12/5.42 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.12/5.42 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_divide
% 5.12/5.42 thf(fact_7335_take__bit__signed__take__bit,axiom,
% 5.12/5.42 ! [M2: nat,N: nat,A: int] :
% 5.12/5.42 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.12/5.42 = ( bit_se2923211474154528505it_int @ M2 @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_signed_take_bit
% 5.12/5.42 thf(fact_7336_take__bit__decr__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 != zero_zero_int )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.12/5.42 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_decr_eq
% 5.12/5.42 thf(fact_7337_arccos__le__arccos,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_le_arccos
% 5.12/5.42 thf(fact_7338_arccos__eq__iff,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.12/5.42 => ( ( ( arccos @ X )
% 5.12/5.42 = ( arccos @ Y ) )
% 5.12/5.42 = ( X = Y ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_eq_iff
% 5.12/5.42 thf(fact_7339_arccos__le__mono,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.12/5.42 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_le_mono
% 5.12/5.42 thf(fact_7340_arcsin__le__arcsin,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_le_arcsin
% 5.12/5.42 thf(fact_7341_arcsin__minus,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.12/5.42 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_minus
% 5.12/5.42 thf(fact_7342_arcsin__eq__iff,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( ( arcsin @ X )
% 5.12/5.42 = ( arcsin @ Y ) )
% 5.12/5.42 = ( X = Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_eq_iff
% 5.12/5.42 thf(fact_7343_arcsin__le__mono,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.12/5.42 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_le_mono
% 5.12/5.42 thf(fact_7344_take__bit__Suc__bit0,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.12/5.42 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_bit0
% 5.12/5.42 thf(fact_7345_take__bit__Suc__bit0,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.12/5.42 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_bit0
% 5.12/5.42 thf(fact_7346_arccos__lbound,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_lbound
% 5.12/5.42 thf(fact_7347_arccos__less__arccos,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_less_arccos
% 5.12/5.42 thf(fact_7348_arccos__less__mono,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.12/5.42 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_less_mono
% 5.12/5.42 thf(fact_7349_arccos__ubound,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_ubound
% 5.12/5.42 thf(fact_7350_arccos__cos,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.42 => ( ( arccos @ ( cos_real @ X ) )
% 5.12/5.42 = X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_cos
% 5.12/5.42 thf(fact_7351_arcsin__less__arcsin,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_less_arcsin
% 5.12/5.42 thf(fact_7352_arcsin__less__mono,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.12/5.42 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_less_mono
% 5.12/5.42 thf(fact_7353_cos__arccos__abs,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.12/5.42 => ( ( cos_real @ ( arccos @ Y ) )
% 5.12/5.42 = Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_arccos_abs
% 5.12/5.42 thf(fact_7354_arccos__cos__eq__abs,axiom,
% 5.12/5.42 ! [Theta: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.12/5.42 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.12/5.42 = ( abs_abs_real @ Theta ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_cos_eq_abs
% 5.12/5.42 thf(fact_7355_take__bit__int__less__exp,axiom,
% 5.12/5.42 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_less_exp
% 5.12/5.42 thf(fact_7356_take__bit__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat,A: code_integer] :
% 5.12/5.42 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.12/5.42 = zero_z3403309356797280102nteger )
% 5.12/5.42 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_eq_0_iff
% 5.12/5.42 thf(fact_7357_take__bit__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_eq_0_iff
% 5.12/5.42 thf(fact_7358_take__bit__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat,A: nat] :
% 5.12/5.42 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_eq_0_iff
% 5.12/5.42 thf(fact_7359_take__bit__Suc__minus__bit0,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.42 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_minus_bit0
% 5.12/5.42 thf(fact_7360_arccos__lt__bounded,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.12/5.42 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_lt_bounded
% 5.12/5.42 thf(fact_7361_arccos__bounded,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_bounded
% 5.12/5.42 thf(fact_7362_take__bit__int__greater__eq__self__iff,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.12/5.42 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_greater_eq_self_iff
% 5.12/5.42 thf(fact_7363_take__bit__int__less__self__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.12/5.42 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_less_self_iff
% 5.12/5.42 thf(fact_7364_sin__arccos__nonzero,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.42 => ( ( sin_real @ ( arccos @ X ) )
% 5.12/5.42 != zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sin_arccos_nonzero
% 5.12/5.42 thf(fact_7365_arccos__cos2,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.12/5.42 => ( ( arccos @ ( cos_real @ X ) )
% 5.12/5.42 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_cos2
% 5.12/5.42 thf(fact_7366_arccos__minus,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.12/5.42 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_minus
% 5.12/5.42 thf(fact_7367_cos__arcsin__nonzero,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.42 => ( ( cos_real @ ( arcsin @ X ) )
% 5.12/5.42 != zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cos_arcsin_nonzero
% 5.12/5.42 thf(fact_7368_take__bit__int__eq__self,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 = K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_eq_self
% 5.12/5.42 thf(fact_7369_take__bit__int__eq__self__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 = K )
% 5.12/5.42 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_eq_self_iff
% 5.12/5.42 thf(fact_7370_take__bit__numeral__minus__bit0,axiom,
% 5.12/5.42 ! [L: num,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.42 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_minus_bit0
% 5.12/5.42 thf(fact_7371_take__bit__incr__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.12/5.42 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_incr_eq
% 5.12/5.42 thf(fact_7372_arccos,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.12/5.42 & ( ( cos_real @ ( arccos @ Y ) )
% 5.12/5.42 = Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos
% 5.12/5.42 thf(fact_7373_arccos__minus__abs,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.42 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.12/5.42 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_minus_abs
% 5.12/5.42 thf(fact_7374_take__bit__Suc__minus__1__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.42 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_minus_1_eq
% 5.12/5.42 thf(fact_7375_take__bit__Suc__minus__1__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_minus_1_eq
% 5.12/5.42 thf(fact_7376_take__bit__Suc__bit1,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.12/5.42 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_bit1
% 5.12/5.42 thf(fact_7377_take__bit__Suc__bit1,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_bit1
% 5.12/5.42 thf(fact_7378_take__bit__numeral__minus__1__eq,axiom,
% 5.12/5.42 ! [K: num] :
% 5.12/5.42 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.42 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_minus_1_eq
% 5.12/5.42 thf(fact_7379_take__bit__numeral__minus__1__eq,axiom,
% 5.12/5.42 ! [K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_minus_1_eq
% 5.12/5.42 thf(fact_7380_take__bit__Suc,axiom,
% 5.12/5.42 ! [N: nat,A: code_integer] :
% 5.12/5.42 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.12/5.42 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc
% 5.12/5.42 thf(fact_7381_take__bit__Suc,axiom,
% 5.12/5.42 ! [N: nat,A: code_natural] :
% 5.12/5.42 ( ( bit_se569199155075624693atural @ ( suc @ N ) @ A )
% 5.12/5.42 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc
% 5.12/5.42 thf(fact_7382_take__bit__Suc,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.12/5.42 = ( 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 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc
% 5.12/5.42 thf(fact_7383_take__bit__Suc,axiom,
% 5.12/5.42 ! [N: nat,A: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.12/5.42 = ( 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 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc
% 5.12/5.42 thf(fact_7384_take__bit__int__less__eq,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.12/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.42 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_less_eq
% 5.12/5.42 thf(fact_7385_take__bit__int__greater__eq,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_int_greater_eq
% 5.12/5.42 thf(fact_7386_signed__take__bit__eq__take__bit__shift,axiom,
% 5.12/5.42 ( bit_ri631733984087533419it_int
% 5.12/5.42 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_eq_take_bit_shift
% 5.12/5.42 thf(fact_7387_stable__imp__take__bit__eq,axiom,
% 5.12/5.42 ! [A: code_integer,N: nat] :
% 5.12/5.42 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.12/5.42 = zero_z3403309356797280102nteger ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.12/5.42 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_take_bit_eq
% 5.12/5.42 thf(fact_7388_stable__imp__take__bit__eq,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.12/5.42 = zero_zero_int ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.12/5.42 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_take_bit_eq
% 5.12/5.42 thf(fact_7389_stable__imp__take__bit__eq,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.12/5.42 = zero_zero_nat ) )
% 5.12/5.42 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.12/5.42 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_take_bit_eq
% 5.12/5.42 thf(fact_7390_take__bit__numeral__bit1,axiom,
% 5.12/5.42 ! [L: num,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.12/5.42 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_bit1
% 5.12/5.42 thf(fact_7391_take__bit__numeral__bit1,axiom,
% 5.12/5.42 ! [L: num,K: num] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.12/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_numeral_bit1
% 5.12/5.42 thf(fact_7392_take__bit__minus__small__eq,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_int @ zero_zero_int @ K )
% 5.12/5.42 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.12/5.42 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_minus_small_eq
% 5.12/5.42 thf(fact_7393_arccos__le__pi2,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_le_pi2
% 5.12/5.42 thf(fact_7394_arcsin__lt__bounded,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.12/5.42 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_lt_bounded
% 5.12/5.42 thf(fact_7395_arcsin__bounded,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_bounded
% 5.12/5.42 thf(fact_7396_arcsin__ubound,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_ubound
% 5.12/5.42 thf(fact_7397_arcsin__lbound,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_lbound
% 5.12/5.42 thf(fact_7398_arcsin__sin,axiom,
% 5.12/5.42 ! [X: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( arcsin @ ( sin_real @ X ) )
% 5.12/5.42 = X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_sin
% 5.12/5.42 thf(fact_7399_take__bit__Suc__minus__bit1,axiom,
% 5.12/5.42 ! [N: nat,K: num] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.42 = ( 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 ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_minus_bit1
% 5.12/5.42 thf(fact_7400_take__bit__rec,axiom,
% 5.12/5.42 ( bit_se1745604003318907178nteger
% 5.12/5.42 = ( ^ [N4: nat,A3: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_rec
% 5.12/5.42 thf(fact_7401_take__bit__rec,axiom,
% 5.12/5.42 ( bit_se569199155075624693atural
% 5.12/5.42 = ( ^ [N4: nat,A3: code_natural] : ( if_Code_natural @ ( N4 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_rec
% 5.12/5.42 thf(fact_7402_take__bit__rec,axiom,
% 5.12/5.42 ( bit_se2923211474154528505it_int
% 5.12/5.42 = ( ^ [N4: nat,A3: int] : ( if_int @ ( N4 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_rec
% 5.12/5.42 thf(fact_7403_take__bit__rec,axiom,
% 5.12/5.42 ( bit_se2925701944663578781it_nat
% 5.12/5.42 = ( ^ [N4: nat,A3: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_rec
% 5.12/5.42 thf(fact_7404_le__arcsin__iff,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 5.12/5.42 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % le_arcsin_iff
% 5.12/5.42 thf(fact_7405_arcsin__le__iff,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 5.12/5.42 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_le_iff
% 5.12/5.42 thf(fact_7406_arcsin__pi,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.12/5.42 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.12/5.42 = Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin_pi
% 5.12/5.42 thf(fact_7407_arcsin,axiom,
% 5.12/5.42 ! [Y: real] :
% 5.12/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.12/5.42 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.12/5.42 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.12/5.42 = Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arcsin
% 5.12/5.42 thf(fact_7408_arccos__cos__eq__abs__2pi,axiom,
% 5.12/5.42 ! [Theta: real] :
% 5.12/5.42 ~ ! [K2: int] :
% 5.12/5.42 ( ( arccos @ ( cos_real @ Theta ) )
% 5.12/5.42 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % arccos_cos_eq_abs_2pi
% 5.12/5.42 thf(fact_7409_cis__minus__pi__half,axiom,
% 5.12/5.42 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_minus_pi_half
% 5.12/5.42 thf(fact_7410_exp__two__pi__i_H,axiom,
% 5.12/5.42 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % exp_two_pi_i'
% 5.12/5.42 thf(fact_7411_exp__two__pi__i,axiom,
% 5.12/5.42 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % exp_two_pi_i
% 5.12/5.42 thf(fact_7412_flip__bit__0,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.12/5.42 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % flip_bit_0
% 5.12/5.42 thf(fact_7413_flip__bit__0,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.12/5.42 = ( 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 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % flip_bit_0
% 5.12/5.42 thf(fact_7414_flip__bit__0,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.12/5.42 = ( 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 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % flip_bit_0
% 5.12/5.42 thf(fact_7415_set__decode__0,axiom,
% 5.12/5.42 ! [X: nat] :
% 5.12/5.42 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.12/5.42 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % set_decode_0
% 5.12/5.42 thf(fact_7416_nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % nat_of_bool
% 5.12/5.42 thf(fact_7417_of__bool__less__eq__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.12/5.42 = ( P
% 5.12/5.42 => Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_iff
% 5.12/5.42 thf(fact_7418_of__bool__less__eq__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.12/5.42 = ( P
% 5.12/5.42 => Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_iff
% 5.12/5.42 thf(fact_7419_of__bool__less__eq__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.12/5.42 = ( P
% 5.12/5.42 => Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_iff
% 5.12/5.42 thf(fact_7420_of__bool__eq__0__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.12/5.42 = zero_zero_real )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_0_iff
% 5.12/5.42 thf(fact_7421_of__bool__eq__0__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.12/5.42 = zero_zero_rat )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_0_iff
% 5.12/5.42 thf(fact_7422_of__bool__eq__0__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_0_iff
% 5.12/5.42 thf(fact_7423_of__bool__eq__0__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_0_iff
% 5.12/5.42 thf(fact_7424_of__bool__eq_I1_J,axiom,
% 5.12/5.42 ( ( zero_n3304061248610475627l_real @ $false )
% 5.12/5.42 = zero_zero_real ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(1)
% 5.12/5.42 thf(fact_7425_of__bool__eq_I1_J,axiom,
% 5.12/5.42 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.12/5.42 = zero_zero_rat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(1)
% 5.12/5.42 thf(fact_7426_of__bool__eq_I1_J,axiom,
% 5.12/5.42 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(1)
% 5.12/5.42 thf(fact_7427_of__bool__eq_I1_J,axiom,
% 5.12/5.42 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(1)
% 5.12/5.42 thf(fact_7428_of__bool__less__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.12/5.42 = ( ~ P
% 5.12/5.42 & Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_iff
% 5.12/5.42 thf(fact_7429_of__bool__less__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.12/5.42 = ( ~ P
% 5.12/5.42 & Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_iff
% 5.12/5.42 thf(fact_7430_of__bool__less__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.12/5.42 = ( ~ P
% 5.12/5.42 & Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_iff
% 5.12/5.42 thf(fact_7431_of__bool__less__iff,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.12/5.42 = ( ~ P
% 5.12/5.42 & Q ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_iff
% 5.12/5.42 thf(fact_7432_of__bool__eq__1__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.12/5.42 = one_one_complex )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_1_iff
% 5.12/5.42 thf(fact_7433_of__bool__eq__1__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.12/5.42 = one_one_real )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_1_iff
% 5.12/5.42 thf(fact_7434_of__bool__eq__1__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.12/5.42 = one_one_rat )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_1_iff
% 5.12/5.42 thf(fact_7435_of__bool__eq__1__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.12/5.42 = one_one_int )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_1_iff
% 5.12/5.42 thf(fact_7436_of__bool__eq__1__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.12/5.42 = one_one_nat )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_1_iff
% 5.12/5.42 thf(fact_7437_of__bool__eq_I2_J,axiom,
% 5.12/5.42 ( ( zero_n1201886186963655149omplex @ $true )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(2)
% 5.12/5.42 thf(fact_7438_of__bool__eq_I2_J,axiom,
% 5.12/5.42 ( ( zero_n3304061248610475627l_real @ $true )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(2)
% 5.12/5.42 thf(fact_7439_of__bool__eq_I2_J,axiom,
% 5.12/5.42 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.12/5.42 = one_one_rat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(2)
% 5.12/5.42 thf(fact_7440_of__bool__eq_I2_J,axiom,
% 5.12/5.42 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(2)
% 5.12/5.42 thf(fact_7441_of__bool__eq_I2_J,axiom,
% 5.12/5.42 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq(2)
% 5.12/5.42 thf(fact_7442_of__nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_of_bool
% 5.12/5.42 thf(fact_7443_of__nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_of_bool
% 5.12/5.42 thf(fact_7444_of__nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_of_bool
% 5.12/5.42 thf(fact_7445_of__nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_of_bool
% 5.12/5.42 thf(fact_7446_of__nat__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_of_bool
% 5.12/5.42 thf(fact_7447_abs__bool__eq,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % abs_bool_eq
% 5.12/5.42 thf(fact_7448_abs__bool__eq,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % abs_bool_eq
% 5.12/5.42 thf(fact_7449_abs__bool__eq,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % abs_bool_eq
% 5.12/5.42 thf(fact_7450_abs__bool__eq,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % abs_bool_eq
% 5.12/5.42 thf(fact_7451_of__int__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_of_bool
% 5.12/5.42 thf(fact_7452_of__int__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ring_1_of_int_rat @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_of_bool
% 5.12/5.42 thf(fact_7453_of__int__of__bool,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_int_of_bool
% 5.12/5.42 thf(fact_7454_zero__less__of__bool__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_of_bool_iff
% 5.12/5.42 thf(fact_7455_zero__less__of__bool__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_of_bool_iff
% 5.12/5.42 thf(fact_7456_zero__less__of__bool__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_of_bool_iff
% 5.12/5.42 thf(fact_7457_zero__less__of__bool__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.12/5.42 = P ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_of_bool_iff
% 5.12/5.42 thf(fact_7458_of__bool__less__one__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_one_iff
% 5.12/5.42 thf(fact_7459_of__bool__less__one__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_one_iff
% 5.12/5.42 thf(fact_7460_of__bool__less__one__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_one_iff
% 5.12/5.42 thf(fact_7461_of__bool__less__one__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.12/5.42 = ~ P ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_one_iff
% 5.12/5.42 thf(fact_7462_of__bool__not__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.12/5.42 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_not_iff
% 5.12/5.42 thf(fact_7463_of__bool__not__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.12/5.42 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_not_iff
% 5.12/5.42 thf(fact_7464_of__bool__not__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.12/5.42 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_not_iff
% 5.12/5.42 thf(fact_7465_of__bool__not__iff,axiom,
% 5.12/5.42 ! [P: $o] :
% 5.12/5.42 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.12/5.42 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_not_iff
% 5.12/5.42 thf(fact_7466_Suc__0__mod__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ( N
% 5.12/5.42 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Suc_0_mod_eq
% 5.12/5.42 thf(fact_7467_norm__ii,axiom,
% 5.12/5.42 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % norm_ii
% 5.12/5.42 thf(fact_7468_complex__i__mult__minus,axiom,
% 5.12/5.42 ! [X: complex] :
% 5.12/5.42 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.12/5.42
% 5.12/5.42 % complex_i_mult_minus
% 5.12/5.42 thf(fact_7469_inverse__i,axiom,
% 5.12/5.42 ( ( invers8013647133539491842omplex @ imaginary_unit )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.12/5.42
% 5.12/5.42 % inverse_i
% 5.12/5.42 thf(fact_7470_sgn__mult__self__eq,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mult_self_eq
% 5.12/5.42 thf(fact_7471_sgn__mult__self__eq,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mult_self_eq
% 5.12/5.42 thf(fact_7472_sgn__mult__self__eq,axiom,
% 5.12/5.42 ! [A: rat] :
% 5.12/5.42 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mult_self_eq
% 5.12/5.42 thf(fact_7473_sgn__mult__self__eq,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_mult_self_eq
% 5.12/5.42 thf(fact_7474_sgn__abs,axiom,
% 5.12/5.42 ! [A: complex] :
% 5.12/5.42 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 5.12/5.42 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_abs
% 5.12/5.42 thf(fact_7475_sgn__abs,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_abs
% 5.12/5.42 thf(fact_7476_sgn__abs,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_abs
% 5.12/5.42 thf(fact_7477_sgn__abs,axiom,
% 5.12/5.42 ! [A: rat] :
% 5.12/5.42 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_abs
% 5.12/5.42 thf(fact_7478_sgn__abs,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_abs
% 5.12/5.42 thf(fact_7479_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.12/5.42 ! [A: complex] :
% 5.12/5.42 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 5.12/5.42 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % idom_abs_sgn_class.abs_sgn
% 5.12/5.42 thf(fact_7480_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % idom_abs_sgn_class.abs_sgn
% 5.12/5.42 thf(fact_7481_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % idom_abs_sgn_class.abs_sgn
% 5.12/5.42 thf(fact_7482_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.12/5.42 ! [A: rat] :
% 5.12/5.42 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % idom_abs_sgn_class.abs_sgn
% 5.12/5.42 thf(fact_7483_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % idom_abs_sgn_class.abs_sgn
% 5.12/5.42 thf(fact_7484_take__bit__of__Suc__0,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_Suc_0
% 5.12/5.42 thf(fact_7485_divide__i,axiom,
% 5.12/5.42 ! [X: complex] :
% 5.12/5.42 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.12/5.42 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.12/5.42
% 5.12/5.42 % divide_i
% 5.12/5.42 thf(fact_7486_i__squared,axiom,
% 5.12/5.42 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % i_squared
% 5.12/5.42 thf(fact_7487_take__bit__of__1,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_1
% 5.12/5.42 thf(fact_7488_take__bit__of__1,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_1
% 5.12/5.42 thf(fact_7489_sgn__of__nat,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_of_nat
% 5.12/5.42 thf(fact_7490_sgn__of__nat,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.12/5.42 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_of_nat
% 5.12/5.42 thf(fact_7491_sgn__of__nat,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.12/5.42 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_of_nat
% 5.12/5.42 thf(fact_7492_sgn__of__nat,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % sgn_of_nat
% 5.12/5.42 thf(fact_7493_of__bool__half__eq__0,axiom,
% 5.12/5.42 ! [B: $o] :
% 5.12/5.42 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_half_eq_0
% 5.12/5.42 thf(fact_7494_of__bool__half__eq__0,axiom,
% 5.12/5.42 ! [B: $o] :
% 5.12/5.42 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_half_eq_0
% 5.12/5.42 thf(fact_7495_divide__numeral__i,axiom,
% 5.12/5.42 ! [Z2: complex,N: num] :
% 5.12/5.42 ( ( divide1717551699836669952omplex @ Z2 @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z2 ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divide_numeral_i
% 5.12/5.42 thf(fact_7496_set__decode__Suc,axiom,
% 5.12/5.42 ! [N: nat,X: nat] :
% 5.12/5.42 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.12/5.42 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % set_decode_Suc
% 5.12/5.42 thf(fact_7497_power2__i,axiom,
% 5.12/5.42 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % power2_i
% 5.12/5.42 thf(fact_7498_cis__pi__half,axiom,
% 5.12/5.42 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = imaginary_unit ) ).
% 5.12/5.42
% 5.12/5.42 % cis_pi_half
% 5.12/5.42 thf(fact_7499_i__even__power,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.42 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % i_even_power
% 5.12/5.42 thf(fact_7500_one__div__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_div_2_pow_eq
% 5.12/5.42 thf(fact_7501_one__div__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_div_2_pow_eq
% 5.12/5.42 thf(fact_7502_bits__1__div__exp,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bits_1_div_exp
% 5.12/5.42 thf(fact_7503_bits__1__div__exp,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bits_1_div_exp
% 5.12/5.42 thf(fact_7504_take__bit__of__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ M2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_exp
% 5.12/5.42 thf(fact_7505_take__bit__of__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( bit_se2925701944663578781it_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_of_exp
% 5.12/5.42 thf(fact_7506_exp__pi__i_H,axiom,
% 5.12/5.42 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_pi_i'
% 5.12/5.42 thf(fact_7507_exp__pi__i,axiom,
% 5.12/5.42 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.12/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_pi_i
% 5.12/5.42 thf(fact_7508_one__mod__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_mod_2_pow_eq
% 5.12/5.42 thf(fact_7509_one__mod__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_mod_2_pow_eq
% 5.12/5.42 thf(fact_7510_one__mod__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_mod_2_pow_eq
% 5.12/5.42 thf(fact_7511_one__mod__2__pow__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % one_mod_2_pow_eq
% 5.12/5.42 thf(fact_7512_of__bool__eq__iff,axiom,
% 5.12/5.42 ! [P4: $o,Q5: $o] :
% 5.12/5.42 ( ( ( zero_n2684676970156552555ol_int @ P4 )
% 5.12/5.42 = ( zero_n2684676970156552555ol_int @ Q5 ) )
% 5.12/5.42 = ( P4 = Q5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_iff
% 5.12/5.42 thf(fact_7513_of__bool__eq__iff,axiom,
% 5.12/5.42 ! [P4: $o,Q5: $o] :
% 5.12/5.42 ( ( ( zero_n2687167440665602831ol_nat @ P4 )
% 5.12/5.42 = ( zero_n2687167440665602831ol_nat @ Q5 ) )
% 5.12/5.42 = ( P4 = Q5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_eq_iff
% 5.12/5.42 thf(fact_7514_of__bool__conj,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( zero_n3304061248610475627l_real
% 5.12/5.42 @ ( P
% 5.12/5.42 & Q ) )
% 5.12/5.42 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_conj
% 5.12/5.42 thf(fact_7515_of__bool__conj,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( zero_n2052037380579107095ol_rat
% 5.12/5.42 @ ( P
% 5.12/5.42 & Q ) )
% 5.12/5.42 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_conj
% 5.12/5.42 thf(fact_7516_of__bool__conj,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( zero_n2684676970156552555ol_int
% 5.12/5.42 @ ( P
% 5.12/5.42 & Q ) )
% 5.12/5.42 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_conj
% 5.12/5.42 thf(fact_7517_of__bool__conj,axiom,
% 5.12/5.42 ! [P: $o,Q: $o] :
% 5.12/5.42 ( ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ( P
% 5.12/5.42 & Q ) )
% 5.12/5.42 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_conj
% 5.12/5.42 thf(fact_7518_complex__i__not__one,axiom,
% 5.12/5.42 imaginary_unit != one_one_complex ).
% 5.12/5.42
% 5.12/5.42 % complex_i_not_one
% 5.12/5.42 thf(fact_7519_zero__less__eq__of__bool,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_eq_of_bool
% 5.12/5.42 thf(fact_7520_zero__less__eq__of__bool,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_eq_of_bool
% 5.12/5.42 thf(fact_7521_zero__less__eq__of__bool,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_eq_of_bool
% 5.12/5.42 thf(fact_7522_zero__less__eq__of__bool,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.12/5.42
% 5.12/5.42 % zero_less_eq_of_bool
% 5.12/5.42 thf(fact_7523_of__bool__less__eq__one,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_one
% 5.12/5.42 thf(fact_7524_of__bool__less__eq__one,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_one
% 5.12/5.42 thf(fact_7525_of__bool__less__eq__one,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_one
% 5.12/5.42 thf(fact_7526_of__bool__less__eq__one,axiom,
% 5.12/5.42 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_less_eq_one
% 5.12/5.42 thf(fact_7527_split__of__bool__asm,axiom,
% 5.12/5.42 ! [P: complex > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.12/5.42 = ( ~ ( ( P4
% 5.12/5.42 & ~ ( P @ one_one_complex ) )
% 5.12/5.42 | ( ~ P4
% 5.12/5.42 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool_asm
% 5.12/5.42 thf(fact_7528_split__of__bool__asm,axiom,
% 5.12/5.42 ! [P: real > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.12/5.42 = ( ~ ( ( P4
% 5.12/5.42 & ~ ( P @ one_one_real ) )
% 5.12/5.42 | ( ~ P4
% 5.12/5.42 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool_asm
% 5.12/5.42 thf(fact_7529_split__of__bool__asm,axiom,
% 5.12/5.42 ! [P: rat > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.12/5.42 = ( ~ ( ( P4
% 5.12/5.42 & ~ ( P @ one_one_rat ) )
% 5.12/5.42 | ( ~ P4
% 5.12/5.42 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool_asm
% 5.12/5.42 thf(fact_7530_split__of__bool__asm,axiom,
% 5.12/5.42 ! [P: int > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.12/5.42 = ( ~ ( ( P4
% 5.12/5.42 & ~ ( P @ one_one_int ) )
% 5.12/5.42 | ( ~ P4
% 5.12/5.42 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool_asm
% 5.12/5.42 thf(fact_7531_split__of__bool__asm,axiom,
% 5.12/5.42 ! [P: nat > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.12/5.42 = ( ~ ( ( P4
% 5.12/5.42 & ~ ( P @ one_one_nat ) )
% 5.12/5.42 | ( ~ P4
% 5.12/5.42 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool_asm
% 5.12/5.42 thf(fact_7532_split__of__bool,axiom,
% 5.12/5.42 ! [P: complex > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.12/5.42 = ( ( P4
% 5.12/5.42 => ( P @ one_one_complex ) )
% 5.12/5.42 & ( ~ P4
% 5.12/5.42 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool
% 5.12/5.42 thf(fact_7533_split__of__bool,axiom,
% 5.12/5.42 ! [P: real > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.12/5.42 = ( ( P4
% 5.12/5.42 => ( P @ one_one_real ) )
% 5.12/5.42 & ( ~ P4
% 5.12/5.42 => ( P @ zero_zero_real ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool
% 5.12/5.42 thf(fact_7534_split__of__bool,axiom,
% 5.12/5.42 ! [P: rat > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.12/5.42 = ( ( P4
% 5.12/5.42 => ( P @ one_one_rat ) )
% 5.12/5.42 & ( ~ P4
% 5.12/5.42 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool
% 5.12/5.42 thf(fact_7535_split__of__bool,axiom,
% 5.12/5.42 ! [P: int > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.12/5.42 = ( ( P4
% 5.12/5.42 => ( P @ one_one_int ) )
% 5.12/5.42 & ( ~ P4
% 5.12/5.42 => ( P @ zero_zero_int ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool
% 5.12/5.42 thf(fact_7536_split__of__bool,axiom,
% 5.12/5.42 ! [P: nat > $o,P4: $o] :
% 5.12/5.42 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.12/5.42 = ( ( P4
% 5.12/5.42 => ( P @ one_one_nat ) )
% 5.12/5.42 & ( ~ P4
% 5.12/5.42 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_of_bool
% 5.12/5.42 thf(fact_7537_of__bool__def,axiom,
% 5.12/5.42 ( zero_n1201886186963655149omplex
% 5.12/5.42 = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_def
% 5.12/5.42 thf(fact_7538_of__bool__def,axiom,
% 5.12/5.42 ( zero_n3304061248610475627l_real
% 5.12/5.42 = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_def
% 5.12/5.42 thf(fact_7539_of__bool__def,axiom,
% 5.12/5.42 ( zero_n2052037380579107095ol_rat
% 5.12/5.42 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_def
% 5.12/5.42 thf(fact_7540_of__bool__def,axiom,
% 5.12/5.42 ( zero_n2684676970156552555ol_int
% 5.12/5.42 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_def
% 5.12/5.42 thf(fact_7541_of__bool__def,axiom,
% 5.12/5.42 ( zero_n2687167440665602831ol_nat
% 5.12/5.42 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_bool_def
% 5.12/5.42 thf(fact_7542_i__times__eq__iff,axiom,
% 5.12/5.42 ! [W: complex,Z2: complex] :
% 5.12/5.42 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.12/5.42 = Z2 )
% 5.12/5.42 = ( W
% 5.12/5.42 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z2 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % i_times_eq_iff
% 5.12/5.42 thf(fact_7543_complex__i__not__neg__numeral,axiom,
% 5.12/5.42 ! [W: num] :
% 5.12/5.42 ( imaginary_unit
% 5.12/5.42 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % complex_i_not_neg_numeral
% 5.12/5.42 thf(fact_7544_imaginary__unit_Ocode,axiom,
% 5.12/5.42 ( imaginary_unit
% 5.12/5.42 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % imaginary_unit.code
% 5.12/5.42 thf(fact_7545_Complex__eq__i,axiom,
% 5.12/5.42 ! [X: real,Y: real] :
% 5.12/5.42 ( ( ( complex2 @ X @ Y )
% 5.12/5.42 = imaginary_unit )
% 5.12/5.42 = ( ( X = zero_zero_real )
% 5.12/5.42 & ( Y = one_one_real ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Complex_eq_i
% 5.12/5.42 thf(fact_7546_i__mult__Complex,axiom,
% 5.12/5.42 ! [A: real,B: real] :
% 5.12/5.42 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.12/5.42 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % i_mult_Complex
% 5.12/5.42 thf(fact_7547_Complex__mult__i,axiom,
% 5.12/5.42 ! [A: real,B: real] :
% 5.12/5.42 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.12/5.42 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % Complex_mult_i
% 5.12/5.42 thf(fact_7548_take__bit__nat__eq,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.12/5.42 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nat_eq
% 5.12/5.42 thf(fact_7549_nat__take__bit__eq,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.12/5.42 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % nat_take_bit_eq
% 5.12/5.42 thf(fact_7550_subset__decode__imp__le,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N ) )
% 5.12/5.42 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % subset_decode_imp_le
% 5.12/5.42 thf(fact_7551_take__bit__nat__eq__self__iff,axiom,
% 5.12/5.42 ! [N: nat,M2: nat] :
% 5.12/5.42 ( ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 5.12/5.42 = M2 )
% 5.12/5.42 = ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nat_eq_self_iff
% 5.12/5.42 thf(fact_7552_take__bit__nat__less__exp,axiom,
% 5.12/5.42 ! [N: nat,M2: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nat_less_exp
% 5.12/5.42 thf(fact_7553_take__bit__nat__eq__self,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 => ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 5.12/5.42 = M2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nat_eq_self
% 5.12/5.42 thf(fact_7554_take__bit__nat__less__self__iff,axiom,
% 5.12/5.42 ! [N: nat,M2: nat] :
% 5.12/5.42 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 5.12/5.42 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_nat_less_self_iff
% 5.12/5.42 thf(fact_7555_bits__induct,axiom,
% 5.12/5.42 ! [P: int > $o,A: int] :
% 5.12/5.42 ( ! [A4: int] :
% 5.12/5.42 ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = A4 )
% 5.12/5.42 => ( P @ A4 ) )
% 5.12/5.42 => ( ! [A4: int,B3: $o] :
% 5.12/5.42 ( ( P @ A4 )
% 5.12/5.42 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = A4 )
% 5.12/5.42 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.12/5.42 => ( P @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bits_induct
% 5.12/5.42 thf(fact_7556_bits__induct,axiom,
% 5.12/5.42 ! [P: nat > $o,A: nat] :
% 5.12/5.42 ( ! [A4: nat] :
% 5.12/5.42 ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = A4 )
% 5.12/5.42 => ( P @ A4 ) )
% 5.12/5.42 => ( ! [A4: nat,B3: $o] :
% 5.12/5.42 ( ( P @ A4 )
% 5.12/5.42 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = A4 )
% 5.12/5.42 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.12/5.42 => ( P @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bits_induct
% 5.12/5.42 thf(fact_7557_exp__mod__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M2 @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_mod_exp
% 5.12/5.42 thf(fact_7558_exp__mod__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M2 @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_mod_exp
% 5.12/5.42 thf(fact_7559_exp__mod__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_mod_exp
% 5.12/5.42 thf(fact_7560_exp__mod__exp,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_mod_exp
% 5.12/5.42 thf(fact_7561_div__noneq__sgn__abs,axiom,
% 5.12/5.42 ! [L: int,K: int] :
% 5.12/5.42 ( ( L != zero_zero_int )
% 5.12/5.42 => ( ( ( sgn_sgn_int @ K )
% 5.12/5.42 != ( sgn_sgn_int @ L ) )
% 5.12/5.42 => ( ( divide_divide_int @ K @ L )
% 5.12/5.42 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.12/5.42 @ ( zero_n2684676970156552555ol_int
% 5.12/5.42 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % div_noneq_sgn_abs
% 5.12/5.42 thf(fact_7562_exp__div__exp__eq,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_int
% 5.12/5.42 @ ( zero_n2684676970156552555ol_int
% 5.12/5.42 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 5.12/5.42 != zero_zero_int )
% 5.12/5.42 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 5.12/5.42 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_div_exp_eq
% 5.12/5.42 thf(fact_7563_exp__div__exp__eq,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.42 = ( times_times_nat
% 5.12/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.12/5.42 != zero_zero_nat )
% 5.12/5.42 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 5.12/5.42 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_div_exp_eq
% 5.12/5.42 thf(fact_7564_cmod__unit__one,axiom,
% 5.12/5.42 ! [A: real] :
% 5.12/5.42 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.12/5.42 = one_one_real ) ).
% 5.12/5.42
% 5.12/5.42 % cmod_unit_one
% 5.12/5.42 thf(fact_7565_divide__int__unfold,axiom,
% 5.12/5.42 ! [L: int,K: int,N: nat,M2: nat] :
% 5.12/5.42 ( ( ( ( ( sgn_sgn_int @ L )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ( sgn_sgn_int @ K )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( N = zero_zero_nat ) )
% 5.12/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = zero_zero_int ) )
% 5.12/5.42 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ( sgn_sgn_int @ K )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( N = zero_zero_nat ) )
% 5.12/5.42 => ( ( ( ( sgn_sgn_int @ K )
% 5.12/5.42 = ( sgn_sgn_int @ L ) )
% 5.12/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) )
% 5.12/5.42 & ( ( ( sgn_sgn_int @ K )
% 5.12/5.42 != ( sgn_sgn_int @ L ) )
% 5.12/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = ( uminus_uminus_int
% 5.12/5.42 @ ( semiri1314217659103216013at_int
% 5.12/5.42 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N )
% 5.12/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divide_int_unfold
% 5.12/5.42 thf(fact_7566_modulo__int__def,axiom,
% 5.12/5.42 ( modulo_modulo_int
% 5.12/5.42 = ( ^ [K3: int,L2: int] :
% 5.12/5.42 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 5.12/5.42 @ ( if_int
% 5.12/5.42 @ ( ( sgn_sgn_int @ K3 )
% 5.12/5.42 = ( sgn_sgn_int @ L2 ) )
% 5.12/5.42 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.12/5.42 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.12/5.42 @ ( minus_minus_int
% 5.12/5.42 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.12/5.42 @ ( zero_n2684676970156552555ol_int
% 5.12/5.42 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 5.12/5.42 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % modulo_int_def
% 5.12/5.42 thf(fact_7567_modulo__int__unfold,axiom,
% 5.12/5.42 ! [L: int,K: int,N: nat,M2: nat] :
% 5.12/5.42 ( ( ( ( ( sgn_sgn_int @ L )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ( sgn_sgn_int @ K )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( N = zero_zero_nat ) )
% 5.12/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 5.12/5.42 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( ( sgn_sgn_int @ K )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 | ( N = zero_zero_nat ) )
% 5.12/5.42 => ( ( ( ( sgn_sgn_int @ K )
% 5.12/5.42 = ( sgn_sgn_int @ L ) )
% 5.12/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) )
% 5.12/5.42 & ( ( ( sgn_sgn_int @ K )
% 5.12/5.42 != ( sgn_sgn_int @ L ) )
% 5.12/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.12/5.42 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.12/5.42 @ ( minus_minus_int
% 5.12/5.42 @ ( semiri1314217659103216013at_int
% 5.12/5.42 @ ( times_times_nat @ N
% 5.12/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) )
% 5.12/5.42 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % modulo_int_unfold
% 5.12/5.42 thf(fact_7568_divide__int__def,axiom,
% 5.12/5.42 ( divide_divide_int
% 5.12/5.42 = ( ^ [K3: int,L2: int] :
% 5.12/5.42 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.12/5.42 @ ( if_int
% 5.12/5.42 @ ( ( sgn_sgn_int @ K3 )
% 5.12/5.42 = ( sgn_sgn_int @ L2 ) )
% 5.12/5.42 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.12/5.42 @ ( uminus_uminus_int
% 5.12/5.42 @ ( semiri1314217659103216013at_int
% 5.12/5.42 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.12/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.42 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divide_int_def
% 5.12/5.42 thf(fact_7569_csqrt__ii,axiom,
% 5.12/5.42 ( ( csqrt @ imaginary_unit )
% 5.12/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % csqrt_ii
% 5.12/5.42 thf(fact_7570_Arg__minus__ii,axiom,
% 5.12/5.42 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.12/5.42 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Arg_minus_ii
% 5.12/5.42 thf(fact_7571_Arg__ii,axiom,
% 5.12/5.42 ( ( arg @ imaginary_unit )
% 5.12/5.42 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Arg_ii
% 5.12/5.42 thf(fact_7572_Arg__correct,axiom,
% 5.12/5.42 ! [Z2: complex] :
% 5.12/5.42 ( ( Z2 != zero_zero_complex )
% 5.12/5.42 => ( ( ( sgn_sgn_complex @ Z2 )
% 5.12/5.42 = ( cis @ ( arg @ Z2 ) ) )
% 5.12/5.42 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Arg_correct
% 5.12/5.42 thf(fact_7573_cis__Arg__unique,axiom,
% 5.12/5.42 ! [Z2: complex,X: real] :
% 5.12/5.42 ( ( ( sgn_sgn_complex @ Z2 )
% 5.12/5.42 = ( cis @ X ) )
% 5.12/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_real @ X @ pi )
% 5.12/5.42 => ( ( arg @ Z2 )
% 5.12/5.42 = X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % cis_Arg_unique
% 5.12/5.42 thf(fact_7574_csqrt__eq__1,axiom,
% 5.12/5.42 ! [Z2: complex] :
% 5.12/5.42 ( ( ( csqrt @ Z2 )
% 5.12/5.42 = one_one_complex )
% 5.12/5.42 = ( Z2 = one_one_complex ) ) ).
% 5.12/5.42
% 5.12/5.42 % csqrt_eq_1
% 5.12/5.42 thf(fact_7575_csqrt__1,axiom,
% 5.12/5.42 ( ( csqrt @ one_one_complex )
% 5.12/5.42 = one_one_complex ) ).
% 5.12/5.42
% 5.12/5.42 % csqrt_1
% 5.12/5.42 thf(fact_7576_Arg__bounded,axiom,
% 5.12/5.42 ! [Z2: complex] :
% 5.12/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z2 ) )
% 5.12/5.42 & ( ord_less_eq_real @ ( arg @ Z2 ) @ pi ) ) ).
% 5.12/5.42
% 5.12/5.42 % Arg_bounded
% 5.12/5.42 thf(fact_7577_buildup__gives__empty,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.12/5.42 = bot_bot_set_nat ) ).
% 5.12/5.42
% 5.12/5.42 % buildup_gives_empty
% 5.12/5.42 thf(fact_7578_signed__take__bit__eq__take__bit__minus,axiom,
% 5.12/5.42 ( bit_ri631733984087533419it_int
% 5.12/5.42 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_eq_take_bit_minus
% 5.12/5.42 thf(fact_7579_mask__numeral,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.42 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_numeral
% 5.12/5.42 thf(fact_7580_mask__numeral,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.12/5.42 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_numeral
% 5.12/5.42 thf(fact_7581_num_Osize__gen_I3_J,axiom,
% 5.12/5.42 ! [X32: num] :
% 5.12/5.42 ( ( size_num @ ( bit1 @ X32 ) )
% 5.12/5.42 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % num.size_gen(3)
% 5.12/5.42 thf(fact_7582_invar__vebt_Ocases,axiom,
% 5.12/5.42 ! [A1: vEBT_VEBT,A22: nat] :
% 5.12/5.42 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.12/5.42 => ( ( ? [A4: $o,B3: $o] :
% 5.12/5.42 ( A1
% 5.12/5.42 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.42 => ( A22
% 5.12/5.42 != ( suc @ zero_zero_nat ) ) )
% 5.12/5.42 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 5.12/5.42 ( ( A1
% 5.12/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.42 => ( ( A22 = Deg2 )
% 5.12/5.42 => ( ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( M3 = N2 )
% 5.12/5.42 => ( ( Deg2
% 5.12/5.42 = ( plus_plus_nat @ N2 @ M3 ) )
% 5.12/5.42 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.12/5.42 => ~ ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.12/5.42 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 5.12/5.42 ( ( A1
% 5.12/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.42 => ( ( A22 = Deg2 )
% 5.12/5.42 => ( ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( M3
% 5.12/5.42 = ( suc @ N2 ) )
% 5.12/5.42 => ( ( Deg2
% 5.12/5.42 = ( plus_plus_nat @ N2 @ M3 ) )
% 5.12/5.42 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.12/5.42 => ~ ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.12/5.42 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi: nat,Ma2: nat] :
% 5.12/5.42 ( ( A1
% 5.12/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.42 => ( ( A22 = Deg2 )
% 5.12/5.42 => ( ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( M3 = N2 )
% 5.12/5.42 => ( ( Deg2
% 5.12/5.42 = ( plus_plus_nat @ N2 @ M3 ) )
% 5.12/5.42 => ( ! [I4: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.12/5.42 => ( ( ( Mi = Ma2 )
% 5.12/5.42 => ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.12/5.42 => ( ( ord_less_eq_nat @ Mi @ Ma2 )
% 5.12/5.42 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.42 => ~ ( ( Mi != Ma2 )
% 5.12/5.42 => ! [I4: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.12/5.42 = I4 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.12/5.42 & ! [X4: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 5.12/5.42 = I4 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi @ X4 )
% 5.12/5.42 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.12/5.42 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi: nat,Ma2: nat] :
% 5.12/5.42 ( ( A1
% 5.12/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.42 => ( ( A22 = Deg2 )
% 5.12/5.42 => ( ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( M3
% 5.12/5.42 = ( suc @ N2 ) )
% 5.12/5.42 => ( ( Deg2
% 5.12/5.42 = ( plus_plus_nat @ N2 @ M3 ) )
% 5.12/5.42 => ( ! [I4: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.12/5.42 => ( ( ( Mi = Ma2 )
% 5.12/5.42 => ! [X4: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.42 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.12/5.42 => ( ( ord_less_eq_nat @ Mi @ Ma2 )
% 5.12/5.42 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.42 => ~ ( ( Mi != Ma2 )
% 5.12/5.42 => ! [I4: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.12/5.42 = I4 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.12/5.42 & ! [X4: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 5.12/5.42 = I4 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi @ X4 )
% 5.12/5.42 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % invar_vebt.cases
% 5.12/5.42 thf(fact_7583_option_Oinject,axiom,
% 5.12/5.42 ! [X23: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.12/5.42 ( ( ( some_P7363390416028606310at_nat @ X23 )
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.12/5.42 = ( X23 = Y2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.inject
% 5.12/5.42 thf(fact_7584_option_Oinject,axiom,
% 5.12/5.42 ! [X23: num,Y2: num] :
% 5.12/5.42 ( ( ( some_num @ X23 )
% 5.12/5.42 = ( some_num @ Y2 ) )
% 5.12/5.42 = ( X23 = Y2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.inject
% 5.12/5.42 thf(fact_7585_mask__nat__positive__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.12/5.42 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_nat_positive_iff
% 5.12/5.42 thf(fact_7586_not__Some__eq,axiom,
% 5.12/5.42 ! [X: option4927543243414619207at_nat] :
% 5.12/5.42 ( ( ! [Y6: product_prod_nat_nat] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( some_P7363390416028606310at_nat @ Y6 ) ) )
% 5.12/5.42 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_Some_eq
% 5.12/5.42 thf(fact_7587_not__Some__eq,axiom,
% 5.12/5.42 ! [X: option_num] :
% 5.12/5.42 ( ( ! [Y6: num] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( some_num @ Y6 ) ) )
% 5.12/5.42 = ( X = none_num ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_Some_eq
% 5.12/5.42 thf(fact_7588_not__None__eq,axiom,
% 5.12/5.42 ! [X: option4927543243414619207at_nat] :
% 5.12/5.42 ( ( X != none_P5556105721700978146at_nat )
% 5.12/5.42 = ( ? [Y6: product_prod_nat_nat] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ Y6 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_None_eq
% 5.12/5.42 thf(fact_7589_not__None__eq,axiom,
% 5.12/5.42 ! [X: option_num] :
% 5.12/5.42 ( ( X != none_num )
% 5.12/5.42 = ( ? [Y6: num] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( some_num @ Y6 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_None_eq
% 5.12/5.42 thf(fact_7590_mi__ma__2__deg,axiom,
% 5.12/5.42 ! [Mi2: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.12/5.42 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.12/5.42 => ( ( ord_less_eq_nat @ Mi2 @ Ma )
% 5.12/5.42 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mi_ma_2_deg
% 5.12/5.42 thf(fact_7591_atLeastatMost__empty,axiom,
% 5.12/5.42 ! [B: rat,A: rat] :
% 5.12/5.42 ( ( ord_less_rat @ B @ A )
% 5.12/5.42 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.12/5.42 = bot_bot_set_rat ) ) ).
% 5.12/5.42
% 5.12/5.42 % atLeastatMost_empty
% 5.12/5.42 thf(fact_7592_atLeastatMost__empty,axiom,
% 5.12/5.42 ! [B: num,A: num] :
% 5.12/5.42 ( ( ord_less_num @ B @ A )
% 5.12/5.42 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.12/5.42 = bot_bot_set_num ) ) ).
% 5.12/5.42
% 5.12/5.42 % atLeastatMost_empty
% 5.12/5.42 thf(fact_7593_atLeastatMost__empty,axiom,
% 5.12/5.42 ! [B: int,A: int] :
% 5.12/5.42 ( ( ord_less_int @ B @ A )
% 5.12/5.42 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.12/5.42 = bot_bot_set_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % atLeastatMost_empty
% 5.12/5.42 thf(fact_7594_atLeastatMost__empty,axiom,
% 5.12/5.42 ! [B: nat,A: nat] :
% 5.12/5.42 ( ( ord_less_nat @ B @ A )
% 5.12/5.42 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.12/5.42 = bot_bot_set_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % atLeastatMost_empty
% 5.12/5.42 thf(fact_7595_atLeastatMost__empty,axiom,
% 5.12/5.42 ! [B: real,A: real] :
% 5.12/5.42 ( ( ord_less_real @ B @ A )
% 5.12/5.42 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.12/5.42 = bot_bot_set_real ) ) ).
% 5.12/5.42
% 5.12/5.42 % atLeastatMost_empty
% 5.12/5.42 thf(fact_7596_mask__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_eq_0_iff
% 5.12/5.42 thf(fact_7597_mask__eq__0__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_eq_0_iff
% 5.12/5.42 thf(fact_7598_mask__0,axiom,
% 5.12/5.42 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % mask_0
% 5.12/5.42 thf(fact_7599_mask__0,axiom,
% 5.12/5.42 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % mask_0
% 5.12/5.42 thf(fact_7600_both__member__options__from__complete__tree__to__child,axiom,
% 5.12/5.42 ! [Deg: nat,Mi2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.12/5.42 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.12/5.42 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.12/5.42 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 | ( X = Mi2 )
% 5.12/5.42 | ( X = Ma ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % both_member_options_from_complete_tree_to_child
% 5.12/5.42 thf(fact_7601_set__decode__zero,axiom,
% 5.12/5.42 ( ( nat_set_decode @ zero_zero_nat )
% 5.12/5.42 = bot_bot_set_nat ) ).
% 5.12/5.42
% 5.12/5.42 % set_decode_zero
% 5.12/5.42 thf(fact_7602_member__inv,axiom,
% 5.12/5.42 ! [Mi2: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.12/5.42 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.12/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.12/5.42 & ( ( X = Mi2 )
% 5.12/5.42 | ( X = Ma )
% 5.12/5.42 | ( ( ord_less_nat @ X @ Ma )
% 5.12/5.42 & ( ord_less_nat @ Mi2 @ X )
% 5.12/5.42 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.42 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % member_inv
% 5.12/5.42 thf(fact_7603_bit__numeral__Bit0__Suc__iff,axiom,
% 5.12/5.42 ! [M2: num,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M2 ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_Bit0_Suc_iff
% 5.12/5.42 thf(fact_7604_bit__numeral__Bit0__Suc__iff,axiom,
% 5.12/5.42 ! [M2: num,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_Bit0_Suc_iff
% 5.12/5.42 thf(fact_7605_bit__numeral__Bit1__Suc__iff,axiom,
% 5.12/5.42 ! [M2: num,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M2 ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_Bit1_Suc_iff
% 5.12/5.42 thf(fact_7606_bit__numeral__Bit1__Suc__iff,axiom,
% 5.12/5.42 ! [M2: num,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_Bit1_Suc_iff
% 5.12/5.42 thf(fact_7607_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.12/5.42 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.12/5.42 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.42 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.12/5.42 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % both_member_options_from_chilf_to_complete_tree
% 5.12/5.42 thf(fact_7608_mask__Suc__0,axiom,
% 5.12/5.42 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % mask_Suc_0
% 5.12/5.42 thf(fact_7609_mask__Suc__0,axiom,
% 5.12/5.42 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % mask_Suc_0
% 5.12/5.42 thf(fact_7610_take__bit__minus__one__eq__mask,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.42 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_minus_one_eq_mask
% 5.12/5.42 thf(fact_7611_take__bit__minus__one__eq__mask,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_minus_one_eq_mask
% 5.12/5.42 thf(fact_7612_signed__take__bit__nonnegative__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.12/5.42 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_nonnegative_iff
% 5.12/5.42 thf(fact_7613_signed__take__bit__negative__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_negative_iff
% 5.12/5.42 thf(fact_7614_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.12/5.42 ! [W: num,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_minus_numeral_Bit0_Suc_iff
% 5.12/5.42 thf(fact_7615_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.12/5.42 ! [W: num,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.12/5.42 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_minus_numeral_Bit1_Suc_iff
% 5.12/5.42 thf(fact_7616_bit__0,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.12/5.42 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_0
% 5.12/5.42 thf(fact_7617_bit__0,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.12/5.42 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_0
% 5.12/5.42 thf(fact_7618_bit__0,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.12/5.42 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_0
% 5.12/5.42 thf(fact_7619_bit__minus__numeral__int_I1_J,axiom,
% 5.12/5.42 ! [W: num,N: num] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_minus_numeral_int(1)
% 5.12/5.42 thf(fact_7620_bit__minus__numeral__int_I2_J,axiom,
% 5.12/5.42 ! [W: num,N: num] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.42 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_minus_numeral_int(2)
% 5.12/5.42 thf(fact_7621_bit__mod__2__iff,axiom,
% 5.12/5.42 ! [A: code_integer,N: nat] :
% 5.12/5.42 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_mod_2_iff
% 5.12/5.42 thf(fact_7622_bit__mod__2__iff,axiom,
% 5.12/5.42 ! [A: code_natural,N: nat] :
% 5.12/5.42 ( ( bit_se8040316288895769887atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ N )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_mod_2_iff
% 5.12/5.42 thf(fact_7623_bit__mod__2__iff,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_mod_2_iff
% 5.12/5.42 thf(fact_7624_bit__mod__2__iff,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.12/5.42 = ( ( N = zero_zero_nat )
% 5.12/5.42 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_mod_2_iff
% 5.12/5.42 thf(fact_7625_of__nat__mask__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.12/5.42 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_mask_eq
% 5.12/5.42 thf(fact_7626_of__nat__mask__eq,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.12/5.42 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % of_nat_mask_eq
% 5.12/5.42 thf(fact_7627_bit__of__nat__iff__bit,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M2 ) @ N )
% 5.12/5.42 = ( bit_se1148574629649215175it_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_of_nat_iff_bit
% 5.12/5.42 thf(fact_7628_bit__of__nat__iff__bit,axiom,
% 5.12/5.42 ! [M2: nat,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ N )
% 5.12/5.42 = ( bit_se1148574629649215175it_nat @ M2 @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_of_nat_iff_bit
% 5.12/5.42 thf(fact_7629_prod__decode__aux_Ocases,axiom,
% 5.12/5.42 ! [X: product_prod_nat_nat] :
% 5.12/5.42 ~ ! [K2: nat,M3: nat] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( product_Pair_nat_nat @ K2 @ M3 ) ) ).
% 5.12/5.42
% 5.12/5.42 % prod_decode_aux.cases
% 5.12/5.42 thf(fact_7630_option_Odistinct_I1_J,axiom,
% 5.12/5.42 ! [X23: product_prod_nat_nat] :
% 5.12/5.42 ( none_P5556105721700978146at_nat
% 5.12/5.42 != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.distinct(1)
% 5.12/5.42 thf(fact_7631_option_Odistinct_I1_J,axiom,
% 5.12/5.42 ! [X23: num] :
% 5.12/5.42 ( none_num
% 5.12/5.42 != ( some_num @ X23 ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.distinct(1)
% 5.12/5.42 thf(fact_7632_option_OdiscI,axiom,
% 5.12/5.42 ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 5.12/5.42 ( ( Option
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ X23 ) )
% 5.12/5.42 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.discI
% 5.12/5.42 thf(fact_7633_option_OdiscI,axiom,
% 5.12/5.42 ! [Option: option_num,X23: num] :
% 5.12/5.42 ( ( Option
% 5.12/5.42 = ( some_num @ X23 ) )
% 5.12/5.42 => ( Option != none_num ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.discI
% 5.12/5.42 thf(fact_7634_option_Oexhaust,axiom,
% 5.12/5.42 ! [Y: option4927543243414619207at_nat] :
% 5.12/5.42 ( ( Y != none_P5556105721700978146at_nat )
% 5.12/5.42 => ~ ! [X24: product_prod_nat_nat] :
% 5.12/5.42 ( Y
% 5.12/5.42 != ( some_P7363390416028606310at_nat @ X24 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.exhaust
% 5.12/5.42 thf(fact_7635_option_Oexhaust,axiom,
% 5.12/5.42 ! [Y: option_num] :
% 5.12/5.42 ( ( Y != none_num )
% 5.12/5.42 => ~ ! [X24: num] :
% 5.12/5.42 ( Y
% 5.12/5.42 != ( some_num @ X24 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.exhaust
% 5.12/5.42 thf(fact_7636_split__option__ex,axiom,
% 5.12/5.42 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.12/5.42 ? [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 5.12/5.42 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.12/5.42 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.12/5.42 | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_option_ex
% 5.12/5.42 thf(fact_7637_split__option__ex,axiom,
% 5.12/5.42 ( ( ^ [P2: option_num > $o] :
% 5.12/5.42 ? [X5: option_num] : ( P2 @ X5 ) )
% 5.12/5.42 = ( ^ [P3: option_num > $o] :
% 5.12/5.42 ( ( P3 @ none_num )
% 5.12/5.42 | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_option_ex
% 5.12/5.42 thf(fact_7638_split__option__all,axiom,
% 5.12/5.42 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.12/5.42 ! [X5: option4927543243414619207at_nat] : ( P2 @ X5 ) )
% 5.12/5.42 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.12/5.42 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.12/5.42 & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_option_all
% 5.12/5.42 thf(fact_7639_split__option__all,axiom,
% 5.12/5.42 ( ( ^ [P2: option_num > $o] :
% 5.12/5.42 ! [X5: option_num] : ( P2 @ X5 ) )
% 5.12/5.42 = ( ^ [P3: option_num > $o] :
% 5.12/5.42 ( ( P3 @ none_num )
% 5.12/5.42 & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % split_option_all
% 5.12/5.42 thf(fact_7640_combine__options__cases,axiom,
% 5.12/5.42 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.12/5.42 ( ( ( X = none_P5556105721700978146at_nat )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 5.12/5.42 ( ( X
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ A4 ) )
% 5.12/5.42 => ( ( Y
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.12/5.42 => ( P @ X @ Y ) ) )
% 5.12/5.42 => ( P @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % combine_options_cases
% 5.12/5.42 thf(fact_7641_combine__options__cases,axiom,
% 5.12/5.42 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.12/5.42 ( ( ( X = none_P5556105721700978146at_nat )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ( ( Y = none_num )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ! [A4: product_prod_nat_nat,B3: num] :
% 5.12/5.42 ( ( X
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ A4 ) )
% 5.12/5.42 => ( ( Y
% 5.12/5.42 = ( some_num @ B3 ) )
% 5.12/5.42 => ( P @ X @ Y ) ) )
% 5.12/5.42 => ( P @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % combine_options_cases
% 5.12/5.42 thf(fact_7642_combine__options__cases,axiom,
% 5.12/5.42 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.12/5.42 ( ( ( X = none_num )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ! [A4: num,B3: product_prod_nat_nat] :
% 5.12/5.42 ( ( X
% 5.12/5.42 = ( some_num @ A4 ) )
% 5.12/5.42 => ( ( Y
% 5.12/5.42 = ( some_P7363390416028606310at_nat @ B3 ) )
% 5.12/5.42 => ( P @ X @ Y ) ) )
% 5.12/5.42 => ( P @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % combine_options_cases
% 5.12/5.42 thf(fact_7643_combine__options__cases,axiom,
% 5.12/5.42 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.12/5.42 ( ( ( X = none_num )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ( ( Y = none_num )
% 5.12/5.42 => ( P @ X @ Y ) )
% 5.12/5.42 => ( ! [A4: num,B3: num] :
% 5.12/5.42 ( ( X
% 5.12/5.42 = ( some_num @ A4 ) )
% 5.12/5.42 => ( ( Y
% 5.12/5.42 = ( some_num @ B3 ) )
% 5.12/5.42 => ( P @ X @ Y ) ) )
% 5.12/5.42 => ( P @ X @ Y ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % combine_options_cases
% 5.12/5.42 thf(fact_7644_bot_Oextremum__strict,axiom,
% 5.12/5.42 ! [A: set_nat] :
% 5.12/5.42 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.12/5.42
% 5.12/5.42 % bot.extremum_strict
% 5.12/5.42 thf(fact_7645_bot_Oextremum__strict,axiom,
% 5.12/5.42 ! [A: set_int] :
% 5.12/5.42 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.12/5.42
% 5.12/5.42 % bot.extremum_strict
% 5.12/5.42 thf(fact_7646_bot_Oextremum__strict,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.12/5.42
% 5.12/5.42 % bot.extremum_strict
% 5.12/5.42 thf(fact_7647_bot_Onot__eq__extremum,axiom,
% 5.12/5.42 ! [A: set_nat] :
% 5.12/5.42 ( ( A != bot_bot_set_nat )
% 5.12/5.42 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bot.not_eq_extremum
% 5.12/5.42 thf(fact_7648_bot_Onot__eq__extremum,axiom,
% 5.12/5.42 ! [A: set_int] :
% 5.12/5.42 ( ( A != bot_bot_set_int )
% 5.12/5.42 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bot.not_eq_extremum
% 5.12/5.42 thf(fact_7649_bot_Onot__eq__extremum,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( A != bot_bot_nat )
% 5.12/5.42 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bot.not_eq_extremum
% 5.12/5.42 thf(fact_7650_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.12/5.42 ! [Mi2: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.12/5.42 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 5.12/5.42 = ( ( X = Mi2 )
% 5.12/5.42 | ( X = Ma ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % VEBT_internal.membermima.simps(3)
% 5.12/5.42 thf(fact_7651_not__bit__1__Suc,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_bit_1_Suc
% 5.12/5.42 thf(fact_7652_not__bit__1__Suc,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % not_bit_1_Suc
% 5.12/5.42 thf(fact_7653_bit__1__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_1_iff
% 5.12/5.42 thf(fact_7654_bit__1__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_1_iff
% 5.12/5.42 thf(fact_7655_bit__numeral__simps_I1_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_simps(1)
% 5.12/5.42 thf(fact_7656_bit__numeral__simps_I1_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_numeral_simps(1)
% 5.12/5.42 thf(fact_7657_diff__shunt__var,axiom,
% 5.12/5.42 ! [X: set_int,Y: set_int] :
% 5.12/5.42 ( ( ( minus_minus_set_int @ X @ Y )
% 5.12/5.42 = bot_bot_set_int )
% 5.12/5.42 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % diff_shunt_var
% 5.12/5.42 thf(fact_7658_diff__shunt__var,axiom,
% 5.12/5.42 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 5.12/5.42 = bot_bo2099793752762293965at_nat )
% 5.12/5.42 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % diff_shunt_var
% 5.12/5.42 thf(fact_7659_diff__shunt__var,axiom,
% 5.12/5.42 ! [X: set_nat,Y: set_nat] :
% 5.12/5.42 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.12/5.42 = bot_bot_set_nat )
% 5.12/5.42 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.12/5.42
% 5.12/5.42 % diff_shunt_var
% 5.12/5.42 thf(fact_7660_bit__take__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: int,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M2 @ A ) @ N )
% 5.12/5.42 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_take_bit_iff
% 5.12/5.42 thf(fact_7661_bit__take__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,A: nat,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M2 @ A ) @ N )
% 5.12/5.42 = ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_take_bit_iff
% 5.12/5.42 thf(fact_7662_bit__of__bool__iff,axiom,
% 5.12/5.42 ! [B: $o,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N )
% 5.12/5.42 = ( B
% 5.12/5.42 & ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_of_bool_iff
% 5.12/5.42 thf(fact_7663_bit__of__bool__iff,axiom,
% 5.12/5.42 ! [B: $o,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N )
% 5.12/5.42 = ( B
% 5.12/5.42 & ( N = zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_of_bool_iff
% 5.12/5.42 thf(fact_7664_mask__nonnegative__int,axiom,
% 5.12/5.42 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_nonnegative_int
% 5.12/5.42 thf(fact_7665_not__mask__negative__int,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % not_mask_negative_int
% 5.12/5.42 thf(fact_7666_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.12/5.42 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.12/5.42 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 5.12/5.42
% 5.12/5.42 % VEBT_internal.minNull.simps(5)
% 5.12/5.42 thf(fact_7667_bit__not__int__iff_H,axiom,
% 5.12/5.42 ! [K: int,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.12/5.42 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_not_int_iff'
% 5.12/5.42 thf(fact_7668_vebt__member_Osimps_I3_J,axiom,
% 5.12/5.42 ! [V: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.12/5.42 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 5.12/5.42
% 5.12/5.42 % vebt_member.simps(3)
% 5.12/5.42 thf(fact_7669_VEBT__internal_OminNull_Ocases,axiom,
% 5.12/5.42 ! [X: vEBT_VEBT] :
% 5.12/5.42 ( ( X
% 5.12/5.42 != ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.42 => ( ! [Uv2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.12/5.42 => ( ! [Uu2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.12/5.42 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) )
% 5.12/5.42 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % VEBT_internal.minNull.cases
% 5.12/5.42 thf(fact_7670_less__mask,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.42 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % less_mask
% 5.12/5.42 thf(fact_7671_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.12/5.42 ! [X: vEBT_VEBT] :
% 5.12/5.42 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.12/5.42 => ( ! [Uv2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.12/5.42 => ( ! [Uu2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.12/5.42 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.42 ( X
% 5.12/5.42 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % VEBT_internal.minNull.elims(3)
% 5.12/5.42 thf(fact_7672_option_Osize_I4_J,axiom,
% 5.12/5.42 ! [X23: product_prod_nat_nat] :
% 5.12/5.42 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.12/5.42 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.size(4)
% 5.12/5.42 thf(fact_7673_option_Osize_I4_J,axiom,
% 5.12/5.42 ! [X23: num] :
% 5.12/5.42 ( ( size_size_option_num @ ( some_num @ X23 ) )
% 5.12/5.42 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.size(4)
% 5.12/5.42 thf(fact_7674_bit__imp__take__bit__positive,axiom,
% 5.12/5.42 ! [N: nat,M2: nat,K: int] :
% 5.12/5.42 ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.12/5.42 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M2 @ K ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_imp_take_bit_positive
% 5.12/5.42 thf(fact_7675_bit__concat__bit__iff,axiom,
% 5.12/5.42 ! [M2: nat,K: int,L: int,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K @ L ) @ N )
% 5.12/5.42 = ( ( ( ord_less_nat @ N @ M2 )
% 5.12/5.42 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.12/5.42 | ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.42 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_concat_bit_iff
% 5.12/5.42 thf(fact_7676_vebt__member_Osimps_I4_J,axiom,
% 5.12/5.42 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.12/5.42 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.12/5.42
% 5.12/5.42 % vebt_member.simps(4)
% 5.12/5.42 thf(fact_7677_signed__take__bit__eq__concat__bit,axiom,
% 5.12/5.42 ( bit_ri631733984087533419it_int
% 5.12/5.42 = ( ^ [N4: nat,K3: int] : ( bit_concat_bit @ N4 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % signed_take_bit_eq_concat_bit
% 5.12/5.42 thf(fact_7678_option_Osize__gen_I2_J,axiom,
% 5.12/5.42 ! [X: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 5.12/5.42 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.12/5.42 = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.size_gen(2)
% 5.12/5.42 thf(fact_7679_option_Osize__gen_I2_J,axiom,
% 5.12/5.42 ! [X: num > nat,X23: num] :
% 5.12/5.42 ( ( size_option_num @ X @ ( some_num @ X23 ) )
% 5.12/5.42 = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % option.size_gen(2)
% 5.12/5.42 thf(fact_7680_exp__eq__0__imp__not__bit,axiom,
% 5.12/5.42 ! [N: nat,A: int] :
% 5.12/5.42 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_int )
% 5.12/5.42 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_eq_0_imp_not_bit
% 5.12/5.42 thf(fact_7681_exp__eq__0__imp__not__bit,axiom,
% 5.12/5.42 ! [N: nat,A: nat] :
% 5.12/5.42 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.42 = zero_zero_nat )
% 5.12/5.42 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % exp_eq_0_imp_not_bit
% 5.12/5.42 thf(fact_7682_bit__Suc,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_Suc
% 5.12/5.42 thf(fact_7683_bit__Suc,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.12/5.42 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_Suc
% 5.12/5.42 thf(fact_7684_stable__imp__bit__iff__odd,axiom,
% 5.12/5.42 ! [A: code_integer,N: nat] :
% 5.12/5.42 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.12/5.42 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_bit_iff_odd
% 5.12/5.42 thf(fact_7685_stable__imp__bit__iff__odd,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.12/5.42 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_bit_iff_odd
% 5.12/5.42 thf(fact_7686_stable__imp__bit__iff__odd,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = A )
% 5.12/5.42 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.12/5.42 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % stable_imp_bit_iff_odd
% 5.12/5.42 thf(fact_7687_bit__iff__idd__imp__stable,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ! [N2: nat] :
% 5.12/5.42 ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.12/5.42 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.42 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_idd_imp_stable
% 5.12/5.42 thf(fact_7688_bit__iff__idd__imp__stable,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ! [N2: nat] :
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.12/5.42 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.42 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_idd_imp_stable
% 5.12/5.42 thf(fact_7689_bit__iff__idd__imp__stable,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ! [N2: nat] :
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.12/5.42 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.42 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.42 = A ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_idd_imp_stable
% 5.12/5.42 thf(fact_7690_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.12/5.42 ! [X: vEBT_VEBT,Y: $o] :
% 5.12/5.42 ( ( ( vEBT_VEBT_minNull @ X )
% 5.12/5.42 = Y )
% 5.12/5.42 => ( ( ( X
% 5.12/5.42 = ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.42 => ~ Y )
% 5.12/5.42 => ( ( ? [Uv2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.12/5.42 => Y )
% 5.12/5.42 => ( ( ? [Uu2: $o] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.12/5.42 => Y )
% 5.12/5.42 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) )
% 5.12/5.42 => ~ Y )
% 5.12/5.42 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.42 ( X
% 5.12/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.12/5.42 => Y ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % VEBT_internal.minNull.elims(1)
% 5.12/5.42 thf(fact_7691_take__bit__eq__mask__iff,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.12/5.42 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.12/5.42 = zero_zero_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_eq_mask_iff
% 5.12/5.42 thf(fact_7692_int__bit__bound,axiom,
% 5.12/5.42 ! [K: int] :
% 5.12/5.42 ~ ! [N2: nat] :
% 5.12/5.42 ( ! [M: nat] :
% 5.12/5.42 ( ( ord_less_eq_nat @ N2 @ M )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ K @ M )
% 5.12/5.42 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 5.12/5.42 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.12/5.42 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % int_bit_bound
% 5.12/5.42 thf(fact_7693_num_Osize__gen_I1_J,axiom,
% 5.12/5.42 ( ( size_num @ one )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % num.size_gen(1)
% 5.12/5.42 thf(fact_7694_bit__iff__odd,axiom,
% 5.12/5.42 ( bit_se9216721137139052372nteger
% 5.12/5.42 = ( ^ [A3: code_integer,N4: nat] :
% 5.12/5.42 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_odd
% 5.12/5.42 thf(fact_7695_bit__iff__odd,axiom,
% 5.12/5.42 ( bit_se1146084159140164899it_int
% 5.12/5.42 = ( ^ [A3: int,N4: nat] :
% 5.12/5.42 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_odd
% 5.12/5.42 thf(fact_7696_bit__iff__odd,axiom,
% 5.12/5.42 ( bit_se1148574629649215175it_nat
% 5.12/5.42 = ( ^ [A3: nat,N4: nat] :
% 5.12/5.42 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_iff_odd
% 5.12/5.42 thf(fact_7697_Suc__mask__eq__exp,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % Suc_mask_eq_exp
% 5.12/5.42 thf(fact_7698_mask__nat__less__exp,axiom,
% 5.12/5.42 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_nat_less_exp
% 5.12/5.42 thf(fact_7699_bit__int__def,axiom,
% 5.12/5.42 ( bit_se1146084159140164899it_int
% 5.12/5.42 = ( ^ [K3: int,N4: nat] :
% 5.12/5.42 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_int_def
% 5.12/5.42 thf(fact_7700_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % semiring_bit_operations_class.even_mask_iff
% 5.12/5.42 thf(fact_7701_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % semiring_bit_operations_class.even_mask_iff
% 5.12/5.42 thf(fact_7702_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.12/5.42 = ( N = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % semiring_bit_operations_class.even_mask_iff
% 5.12/5.42 thf(fact_7703_even__bit__succ__iff,axiom,
% 5.12/5.42 ! [A: code_integer,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.12/5.42 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_bit_succ_iff
% 5.12/5.42 thf(fact_7704_even__bit__succ__iff,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.12/5.42 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_bit_succ_iff
% 5.12/5.42 thf(fact_7705_even__bit__succ__iff,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.12/5.42 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % even_bit_succ_iff
% 5.12/5.42 thf(fact_7706_odd__bit__iff__bit__pred,axiom,
% 5.12/5.42 ! [A: code_integer,N: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.12/5.42 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_bit_iff_bit_pred
% 5.12/5.42 thf(fact_7707_odd__bit__iff__bit__pred,axiom,
% 5.12/5.42 ! [A: int,N: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.12/5.42 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_bit_iff_bit_pred
% 5.12/5.42 thf(fact_7708_odd__bit__iff__bit__pred,axiom,
% 5.12/5.42 ! [A: nat,N: nat] :
% 5.12/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.12/5.42 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.12/5.42 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.12/5.42 | ( N = zero_zero_nat ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % odd_bit_iff_bit_pred
% 5.12/5.42 thf(fact_7709_mask__nat__def,axiom,
% 5.12/5.42 ( bit_se2002935070580805687sk_nat
% 5.12/5.42 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_nat_def
% 5.12/5.42 thf(fact_7710_mask__half__int,axiom,
% 5.12/5.42 ! [N: nat] :
% 5.12/5.42 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.42 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_half_int
% 5.12/5.42 thf(fact_7711_mask__int__def,axiom,
% 5.12/5.42 ( bit_se2000444600071755411sk_int
% 5.12/5.42 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_int_def
% 5.12/5.42 thf(fact_7712_bit__sum__mult__2__cases,axiom,
% 5.12/5.42 ! [A: code_integer,B: code_integer,N: nat] :
% 5.12/5.42 ( ! [J: nat] :
% 5.12/5.42 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J ) )
% 5.12/5.42 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.12/5.42 = ( ( ( N = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 & ( ( N != zero_zero_nat )
% 5.12/5.42 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_sum_mult_2_cases
% 5.12/5.42 thf(fact_7713_bit__sum__mult__2__cases,axiom,
% 5.12/5.42 ! [A: int,B: int,N: nat] :
% 5.12/5.42 ( ! [J: nat] :
% 5.12/5.42 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J ) )
% 5.12/5.42 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.12/5.42 = ( ( ( N = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 & ( ( N != zero_zero_nat )
% 5.12/5.42 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_sum_mult_2_cases
% 5.12/5.42 thf(fact_7714_bit__sum__mult__2__cases,axiom,
% 5.12/5.42 ! [A: nat,B: nat,N: nat] :
% 5.12/5.42 ( ! [J: nat] :
% 5.12/5.42 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J ) )
% 5.12/5.42 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.12/5.42 = ( ( ( N = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.12/5.42 & ( ( N != zero_zero_nat )
% 5.12/5.42 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_sum_mult_2_cases
% 5.12/5.42 thf(fact_7715_bit__rec,axiom,
% 5.12/5.42 ( bit_se9216721137139052372nteger
% 5.12/5.42 = ( ^ [A3: code_integer,N4: nat] :
% 5.12/5.42 ( ( ( N4 = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 5.12/5.42 & ( ( N4 != zero_zero_nat )
% 5.12/5.42 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_rec
% 5.12/5.42 thf(fact_7716_bit__rec,axiom,
% 5.12/5.42 ( bit_se1146084159140164899it_int
% 5.12/5.42 = ( ^ [A3: int,N4: nat] :
% 5.12/5.42 ( ( ( N4 = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 5.12/5.42 & ( ( N4 != zero_zero_nat )
% 5.12/5.42 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_rec
% 5.12/5.42 thf(fact_7717_bit__rec,axiom,
% 5.12/5.42 ( bit_se1148574629649215175it_nat
% 5.12/5.42 = ( ^ [A3: nat,N4: nat] :
% 5.12/5.42 ( ( ( N4 = zero_zero_nat )
% 5.12/5.42 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 5.12/5.42 & ( ( N4 != zero_zero_nat )
% 5.12/5.42 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % bit_rec
% 5.12/5.42 thf(fact_7718_mask__eq__exp__minus__1,axiom,
% 5.12/5.42 ( bit_se2002935070580805687sk_nat
% 5.12/5.42 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_eq_exp_minus_1
% 5.12/5.42 thf(fact_7719_mask__eq__exp__minus__1,axiom,
% 5.12/5.42 ( bit_se2000444600071755411sk_int
% 5.12/5.42 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % mask_eq_exp_minus_1
% 5.12/5.42 thf(fact_7720_invar__vebt_Ointros_I4_J,axiom,
% 5.12/5.42 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi2: nat,Ma: nat] :
% 5.12/5.42 ( ! [X3: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( M2 = N )
% 5.12/5.42 => ( ( Deg
% 5.12/5.42 = ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.42 => ( ! [I3: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.12/5.42 => ( ( ( Mi2 = Ma )
% 5.12/5.42 => ! [X3: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.42 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.12/5.42 => ( ( ord_less_eq_nat @ Mi2 @ Ma )
% 5.12/5.42 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.12/5.42 => ( ( ( Mi2 != Ma )
% 5.12/5.42 => ! [I3: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.12/5.42 = I3 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.12/5.42 & ! [X3: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.12/5.42 = I3 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.12/5.42 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % invar_vebt.intros(4)
% 5.12/5.42 thf(fact_7721_invar__vebt_Ointros_I5_J,axiom,
% 5.12/5.42 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi2: nat,Ma: nat] :
% 5.12/5.42 ( ! [X3: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.12/5.42 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 5.12/5.42 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( M2
% 5.12/5.42 = ( suc @ N ) )
% 5.12/5.42 => ( ( Deg
% 5.12/5.42 = ( plus_plus_nat @ N @ M2 ) )
% 5.12/5.42 => ( ! [I3: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.12/5.42 => ( ( ( Mi2 = Ma )
% 5.12/5.42 => ! [X3: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.42 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.12/5.42 => ( ( ord_less_eq_nat @ Mi2 @ Ma )
% 5.12/5.42 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.12/5.42 => ( ( ( Mi2 != Ma )
% 5.12/5.42 => ! [I3: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.12/5.42 = I3 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.12/5.42 & ! [X3: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.12/5.42 = I3 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.12/5.42 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % invar_vebt.intros(5)
% 5.12/5.42 thf(fact_7722_unset__bit__eq,axiom,
% 5.12/5.42 ( bit_se4203085406695923979it_int
% 5.12/5.42 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % unset_bit_eq
% 5.12/5.42 thf(fact_7723_take__bit__Suc__from__most,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.12/5.42 = ( 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 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_Suc_from_most
% 5.12/5.42 thf(fact_7724_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.12/5.42 ! [N: nat,K: int] :
% 5.12/5.42 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.12/5.42 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.12/5.42 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % take_bit_eq_mask_iff_exp_dvd
% 5.12/5.42 thf(fact_7725_num_Osize__gen_I2_J,axiom,
% 5.12/5.42 ! [X23: num] :
% 5.12/5.42 ( ( size_num @ ( bit0 @ X23 ) )
% 5.12/5.42 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % num.size_gen(2)
% 5.12/5.42 thf(fact_7726_invar__vebt_Osimps,axiom,
% 5.12/5.42 ( vEBT_invar_vebt
% 5.12/5.42 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.12/5.42 ( ( ? [A3: $o,B2: $o] :
% 5.12/5.42 ( A12
% 5.12/5.42 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.12/5.42 & ( A23
% 5.12/5.42 = ( suc @ zero_zero_nat ) ) )
% 5.12/5.42 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.12/5.42 ( ( A12
% 5.12/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X2 @ N4 ) )
% 5.12/5.42 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.12/5.42 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.12/5.42 & ( A23
% 5.12/5.42 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.12/5.42 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.42 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.12/5.42 ( ( A12
% 5.12/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X2 @ N4 ) )
% 5.12/5.42 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.12/5.42 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.12/5.42 & ( A23
% 5.12/5.42 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.12/5.42 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.42 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.12/5.42 ( ( A12
% 5.12/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X2 @ N4 ) )
% 5.12/5.42 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.12/5.42 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.12/5.42 & ( A23
% 5.12/5.42 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.12/5.42 & ! [I2: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.12/5.42 & ( ( Mi3 = Ma3 )
% 5.12/5.42 => ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.42 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.42 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.12/5.42 & ( ( Mi3 != Ma3 )
% 5.12/5.42 => ! [I2: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.12/5.42 = I2 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.12/5.42 & ! [X2: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X2 @ N4 )
% 5.12/5.42 = I2 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X2 @ N4 ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.42 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.12/5.42 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.12/5.42 ( ( A12
% 5.12/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.12/5.42 & ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ( vEBT_invar_vebt @ X2 @ N4 ) )
% 5.12/5.42 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.12/5.42 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.12/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.12/5.42 & ( A23
% 5.12/5.42 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.12/5.42 & ! [I2: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.12/5.42 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X7 ) )
% 5.12/5.42 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.12/5.42 & ( ( Mi3 = Ma3 )
% 5.12/5.42 => ! [X2: vEBT_VEBT] :
% 5.12/5.42 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.12/5.42 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.42 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.42 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.12/5.42 & ( ( Mi3 != Ma3 )
% 5.12/5.42 => ! [I2: nat] :
% 5.12/5.42 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.12/5.42 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.12/5.42 = I2 )
% 5.12/5.42 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.12/5.42 & ! [X2: nat] :
% 5.12/5.42 ( ( ( ( vEBT_VEBT_high @ X2 @ N4 )
% 5.12/5.42 = I2 )
% 5.12/5.42 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X2 @ N4 ) ) )
% 5.12/5.42 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.42 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % invar_vebt.simps
% 5.12/5.42 thf(fact_7727_divmod__step__eq,axiom,
% 5.12/5.42 ! [L: num,R4: nat,Q5: nat] :
% 5.12/5.42 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R4 )
% 5.12/5.42 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q5 @ R4 ) )
% 5.12/5.42 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.12/5.42 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R4 )
% 5.12/5.42 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q5 @ R4 ) )
% 5.12/5.42 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divmod_step_eq
% 5.12/5.42 thf(fact_7728_divmod__step__eq,axiom,
% 5.12/5.42 ! [L: num,R4: int,Q5: int] :
% 5.12/5.42 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R4 )
% 5.12/5.42 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.42 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.12/5.42 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R4 )
% 5.12/5.42 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.42 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divmod_step_eq
% 5.12/5.42 thf(fact_7729_divmod__step__eq,axiom,
% 5.12/5.42 ! [L: num,R4: code_integer,Q5: code_integer] :
% 5.12/5.42 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R4 )
% 5.12/5.42 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q5 @ R4 ) )
% 5.12/5.42 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.12/5.42 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R4 )
% 5.12/5.42 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q5 @ R4 ) )
% 5.12/5.42 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % divmod_step_eq
% 5.12/5.42 thf(fact_7730_Diff__eq__empty__iff,axiom,
% 5.12/5.42 ! [A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( ( minus_minus_set_int @ A2 @ B5 )
% 5.12/5.42 = bot_bot_set_int )
% 5.12/5.42 = ( ord_less_eq_set_int @ A2 @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_eq_empty_iff
% 5.12/5.42 thf(fact_7731_Diff__eq__empty__iff,axiom,
% 5.12/5.42 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( ( minus_1356011639430497352at_nat @ A2 @ B5 )
% 5.12/5.42 = bot_bo2099793752762293965at_nat )
% 5.12/5.42 = ( ord_le3146513528884898305at_nat @ A2 @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_eq_empty_iff
% 5.12/5.42 thf(fact_7732_Diff__eq__empty__iff,axiom,
% 5.12/5.42 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( ( minus_minus_set_nat @ A2 @ B5 )
% 5.12/5.42 = bot_bot_set_nat )
% 5.12/5.42 = ( ord_less_eq_set_nat @ A2 @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_eq_empty_iff
% 5.12/5.42 thf(fact_7733_divides__aux__eq,axiom,
% 5.12/5.42 ! [Q5: nat,R4: nat] :
% 5.12/5.42 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q5 @ R4 ) )
% 5.12/5.42 = ( R4 = zero_zero_nat ) ) ).
% 5.12/5.42
% 5.12/5.42 % divides_aux_eq
% 5.12/5.42 thf(fact_7734_divides__aux__eq,axiom,
% 5.12/5.42 ! [Q5: int,R4: int] :
% 5.12/5.42 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.42 = ( R4 = zero_zero_int ) ) ).
% 5.12/5.42
% 5.12/5.42 % divides_aux_eq
% 5.12/5.42 thf(fact_7735_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_num,Ys2: list_num] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) @ ( nth_num @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7736_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7737_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7738_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7739_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7740_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7741_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_o,Ys2: list_o] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7742_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_o,Ys2: list_nat] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7743_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_o,Ys2: list_int] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7744_product__nth,axiom,
% 5.12/5.42 ! [N: nat,Xs: list_nat,Ys2: list_num] :
% 5.12/5.42 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_num @ Ys2 ) ) )
% 5.12/5.42 => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs @ Ys2 ) @ N )
% 5.12/5.42 = ( product_Pair_nat_num @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) @ ( nth_num @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % product_nth
% 5.12/5.42 thf(fact_7745_and__int__unfold,axiom,
% 5.12/5.42 ( bit_se725231765392027082nd_int
% 5.12/5.42 = ( ^ [K3: int,L2: int] :
% 5.12/5.42 ( if_int
% 5.12/5.42 @ ( ( K3 = zero_zero_int )
% 5.12/5.42 | ( L2 = zero_zero_int ) )
% 5.12/5.42 @ zero_zero_int
% 5.12/5.42 @ ( if_int
% 5.12/5.42 @ ( K3
% 5.12/5.42 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 @ L2
% 5.12/5.42 @ ( if_int
% 5.12/5.42 @ ( L2
% 5.12/5.42 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 @ K3
% 5.12/5.42 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( 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 @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % and_int_unfold
% 5.12/5.42 thf(fact_7746_Compl__anti__mono,axiom,
% 5.12/5.42 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 5.12/5.42 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B5 ) @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Compl_anti_mono
% 5.12/5.42 thf(fact_7747_Compl__subset__Compl__iff,axiom,
% 5.12/5.42 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B5 ) )
% 5.12/5.42 = ( ord_less_eq_set_nat @ B5 @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Compl_subset_Compl_iff
% 5.12/5.42 thf(fact_7748_Diff__idemp,axiom,
% 5.12/5.42 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) @ B5 )
% 5.12/5.42 = ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_idemp
% 5.12/5.42 thf(fact_7749_Diff__idemp,axiom,
% 5.12/5.42 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ B5 )
% 5.12/5.42 = ( minus_minus_set_nat @ A2 @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_idemp
% 5.12/5.42 thf(fact_7750_Diff__iff,axiom,
% 5.12/5.42 ! [C: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.42 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member_complex @ C @ A2 )
% 5.12/5.42 & ~ ( member_complex @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7751_Diff__iff,axiom,
% 5.12/5.42 ! [C: real,A2: set_real,B5: set_real] :
% 5.12/5.42 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member_real @ C @ A2 )
% 5.12/5.42 & ~ ( member_real @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7752_Diff__iff,axiom,
% 5.12/5.42 ! [C: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.42 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member_set_nat @ C @ A2 )
% 5.12/5.42 & ~ ( member_set_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7753_Diff__iff,axiom,
% 5.12/5.42 ! [C: int,A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member_int @ C @ A2 )
% 5.12/5.42 & ~ ( member_int @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7754_Diff__iff,axiom,
% 5.12/5.42 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.12/5.42 & ~ ( member8440522571783428010at_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7755_Diff__iff,axiom,
% 5.12/5.42 ! [C: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B5 ) )
% 5.12/5.42 = ( ( member_nat @ C @ A2 )
% 5.12/5.42 & ~ ( member_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_iff
% 5.12/5.42 thf(fact_7756_DiffI,axiom,
% 5.12/5.42 ! [C: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.42 ( ( member_complex @ C @ A2 )
% 5.12/5.42 => ( ~ ( member_complex @ C @ B5 )
% 5.12/5.42 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7757_DiffI,axiom,
% 5.12/5.42 ! [C: real,A2: set_real,B5: set_real] :
% 5.12/5.42 ( ( member_real @ C @ A2 )
% 5.12/5.42 => ( ~ ( member_real @ C @ B5 )
% 5.12/5.42 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7758_DiffI,axiom,
% 5.12/5.42 ! [C: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.42 ( ( member_set_nat @ C @ A2 )
% 5.12/5.42 => ( ~ ( member_set_nat @ C @ B5 )
% 5.12/5.42 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7759_DiffI,axiom,
% 5.12/5.42 ! [C: int,A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( member_int @ C @ A2 )
% 5.12/5.42 => ( ~ ( member_int @ C @ B5 )
% 5.12/5.42 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7760_DiffI,axiom,
% 5.12/5.42 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.12/5.42 => ( ~ ( member8440522571783428010at_nat @ C @ B5 )
% 5.12/5.42 => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7761_DiffI,axiom,
% 5.12/5.42 ! [C: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( member_nat @ C @ A2 )
% 5.12/5.42 => ( ~ ( member_nat @ C @ B5 )
% 5.12/5.42 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffI
% 5.12/5.42 thf(fact_7762_Diff__cancel,axiom,
% 5.12/5.42 ! [A2: set_int] :
% 5.12/5.42 ( ( minus_minus_set_int @ A2 @ A2 )
% 5.12/5.42 = bot_bot_set_int ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_cancel
% 5.12/5.42 thf(fact_7763_Diff__cancel,axiom,
% 5.12/5.42 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 5.12/5.42 = bot_bo2099793752762293965at_nat ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_cancel
% 5.12/5.42 thf(fact_7764_Diff__cancel,axiom,
% 5.12/5.42 ! [A2: set_nat] :
% 5.12/5.42 ( ( minus_minus_set_nat @ A2 @ A2 )
% 5.12/5.42 = bot_bot_set_nat ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_cancel
% 5.12/5.42 thf(fact_7765_empty__Diff,axiom,
% 5.12/5.42 ! [A2: set_int] :
% 5.12/5.42 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 5.12/5.42 = bot_bot_set_int ) ).
% 5.12/5.42
% 5.12/5.42 % empty_Diff
% 5.12/5.42 thf(fact_7766_empty__Diff,axiom,
% 5.12/5.42 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 5.12/5.42 = bot_bo2099793752762293965at_nat ) ).
% 5.12/5.42
% 5.12/5.42 % empty_Diff
% 5.12/5.42 thf(fact_7767_empty__Diff,axiom,
% 5.12/5.42 ! [A2: set_nat] :
% 5.12/5.42 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 5.12/5.42 = bot_bot_set_nat ) ).
% 5.12/5.42
% 5.12/5.42 % empty_Diff
% 5.12/5.42 thf(fact_7768_Diff__empty,axiom,
% 5.12/5.42 ! [A2: set_int] :
% 5.12/5.42 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 5.12/5.42 = A2 ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_empty
% 5.12/5.42 thf(fact_7769_Diff__empty,axiom,
% 5.12/5.42 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 5.12/5.42 = A2 ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_empty
% 5.12/5.42 thf(fact_7770_Diff__empty,axiom,
% 5.12/5.42 ! [A2: set_nat] :
% 5.12/5.42 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 5.12/5.42 = A2 ) ).
% 5.12/5.42
% 5.12/5.42 % Diff_empty
% 5.12/5.42 thf(fact_7771_bit_Oconj__zero__right,axiom,
% 5.12/5.42 ! [X: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % bit.conj_zero_right
% 5.12/5.42 thf(fact_7772_bit_Oconj__zero__left,axiom,
% 5.12/5.42 ! [X: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % bit.conj_zero_left
% 5.12/5.42 thf(fact_7773_zero__and__eq,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % zero_and_eq
% 5.12/5.42 thf(fact_7774_zero__and__eq,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % zero_and_eq
% 5.12/5.42 thf(fact_7775_and__zero__eq,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_zero_eq
% 5.12/5.42 thf(fact_7776_and__zero__eq,axiom,
% 5.12/5.42 ! [A: nat] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % and_zero_eq
% 5.12/5.42 thf(fact_7777_bit__0__eq,axiom,
% 5.12/5.42 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.12/5.42 = bot_bot_nat_o ) ).
% 5.12/5.42
% 5.12/5.42 % bit_0_eq
% 5.12/5.42 thf(fact_7778_bit__0__eq,axiom,
% 5.12/5.42 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.12/5.42 = bot_bot_nat_o ) ).
% 5.12/5.42
% 5.12/5.42 % bit_0_eq
% 5.12/5.42 thf(fact_7779_and_Oleft__neutral,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.12/5.42 = A ) ).
% 5.12/5.42
% 5.12/5.42 % and.left_neutral
% 5.12/5.42 thf(fact_7780_and_Oleft__neutral,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.12/5.42 = A ) ).
% 5.12/5.42
% 5.12/5.42 % and.left_neutral
% 5.12/5.42 thf(fact_7781_and_Oright__neutral,axiom,
% 5.12/5.42 ! [A: code_integer] :
% 5.12/5.42 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.42 = A ) ).
% 5.12/5.42
% 5.12/5.42 % and.right_neutral
% 5.12/5.42 thf(fact_7782_and_Oright__neutral,axiom,
% 5.12/5.42 ! [A: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 = A ) ).
% 5.12/5.42
% 5.12/5.42 % and.right_neutral
% 5.12/5.42 thf(fact_7783_bit_Oconj__one__right,axiom,
% 5.12/5.42 ! [X: code_integer] :
% 5.12/5.42 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.42 = X ) ).
% 5.12/5.42
% 5.12/5.42 % bit.conj_one_right
% 5.12/5.42 thf(fact_7784_bit_Oconj__one__right,axiom,
% 5.12/5.42 ! [X: int] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.42 = X ) ).
% 5.12/5.42
% 5.12/5.42 % bit.conj_one_right
% 5.12/5.42 thf(fact_7785_and__nonnegative__int__iff,axiom,
% 5.12/5.42 ! [K: int,L: int] :
% 5.12/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.12/5.42 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.42 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % and_nonnegative_int_iff
% 5.12/5.42 thf(fact_7786_and__negative__int__iff,axiom,
% 5.12/5.42 ! [K: int,L: int] :
% 5.12/5.42 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.12/5.42 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.42 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % and_negative_int_iff
% 5.12/5.42 thf(fact_7787_length__product,axiom,
% 5.12/5.42 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.12/5.42 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7788_length__product,axiom,
% 5.12/5.42 ! [Xs: list_VEBT_VEBT,Ys2: list_o] :
% 5.12/5.42 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7789_length__product,axiom,
% 5.12/5.42 ! [Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 5.12/5.42 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7790_length__product,axiom,
% 5.12/5.42 ! [Xs: list_VEBT_VEBT,Ys2: list_int] :
% 5.12/5.42 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7791_length__product,axiom,
% 5.12/5.42 ! [Xs: list_o,Ys2: list_VEBT_VEBT] :
% 5.12/5.42 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7792_length__product,axiom,
% 5.12/5.42 ! [Xs: list_o,Ys2: list_o] :
% 5.12/5.42 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7793_length__product,axiom,
% 5.12/5.42 ! [Xs: list_o,Ys2: list_nat] :
% 5.12/5.42 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7794_length__product,axiom,
% 5.12/5.42 ! [Xs: list_o,Ys2: list_int] :
% 5.12/5.42 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7795_length__product,axiom,
% 5.12/5.42 ! [Xs: list_nat,Ys2: list_VEBT_VEBT] :
% 5.12/5.42 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7796_length__product,axiom,
% 5.12/5.42 ! [Xs: list_nat,Ys2: list_o] :
% 5.12/5.42 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys2 ) )
% 5.12/5.42 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % length_product
% 5.12/5.42 thf(fact_7797_and__numerals_I2_J,axiom,
% 5.12/5.42 ! [Y: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(2)
% 5.12/5.42 thf(fact_7798_and__numerals_I2_J,axiom,
% 5.12/5.42 ! [Y: num] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(2)
% 5.12/5.42 thf(fact_7799_and__numerals_I8_J,axiom,
% 5.12/5.42 ! [X: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(8)
% 5.12/5.42 thf(fact_7800_and__numerals_I8_J,axiom,
% 5.12/5.42 ! [X: num] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.12/5.42 = one_one_nat ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(8)
% 5.12/5.42 thf(fact_7801_and__numerals_I5_J,axiom,
% 5.12/5.42 ! [X: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(5)
% 5.12/5.42 thf(fact_7802_and__numerals_I5_J,axiom,
% 5.12/5.42 ! [X: num] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(5)
% 5.12/5.42 thf(fact_7803_and__numerals_I1_J,axiom,
% 5.12/5.42 ! [Y: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(1)
% 5.12/5.42 thf(fact_7804_and__numerals_I1_J,axiom,
% 5.12/5.42 ! [Y: num] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.42 = zero_zero_nat ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(1)
% 5.12/5.42 thf(fact_7805_and__minus__numerals_I2_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_minus_numerals(2)
% 5.12/5.42 thf(fact_7806_and__minus__numerals_I6_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.12/5.42 = one_one_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_minus_numerals(6)
% 5.12/5.42 thf(fact_7807_and__minus__numerals_I5_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_minus_numerals(5)
% 5.12/5.42 thf(fact_7808_and__minus__numerals_I1_J,axiom,
% 5.12/5.42 ! [N: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.42 = zero_zero_int ) ).
% 5.12/5.42
% 5.12/5.42 % and_minus_numerals(1)
% 5.12/5.42 thf(fact_7809_and__numerals_I7_J,axiom,
% 5.12/5.42 ! [X: num,Y: num] :
% 5.12/5.42 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.12/5.42 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(7)
% 5.12/5.42 thf(fact_7810_and__numerals_I7_J,axiom,
% 5.12/5.42 ! [X: num,Y: num] :
% 5.12/5.42 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.42 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % and_numerals(7)
% 5.12/5.42 thf(fact_7811_bot__nat__def,axiom,
% 5.12/5.42 bot_bot_nat = zero_zero_nat ).
% 5.12/5.42
% 5.12/5.42 % bot_nat_def
% 5.12/5.42 thf(fact_7812_DiffD2,axiom,
% 5.12/5.42 ! [C: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.42 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member_complex @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7813_DiffD2,axiom,
% 5.12/5.42 ! [C: real,A2: set_real,B5: set_real] :
% 5.12/5.42 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member_real @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7814_DiffD2,axiom,
% 5.12/5.42 ! [C: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.42 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member_set_nat @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7815_DiffD2,axiom,
% 5.12/5.42 ! [C: int,A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member_int @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7816_DiffD2,axiom,
% 5.12/5.42 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member8440522571783428010at_nat @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7817_DiffD2,axiom,
% 5.12/5.42 ! [C: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( member_nat @ C @ B5 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD2
% 5.12/5.42 thf(fact_7818_DiffD1,axiom,
% 5.12/5.42 ! [C: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.42 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B5 ) )
% 5.12/5.42 => ( member_complex @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7819_DiffD1,axiom,
% 5.12/5.42 ! [C: real,A2: set_real,B5: set_real] :
% 5.12/5.42 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B5 ) )
% 5.12/5.42 => ( member_real @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7820_DiffD1,axiom,
% 5.12/5.42 ! [C: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.42 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) )
% 5.12/5.42 => ( member_set_nat @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7821_DiffD1,axiom,
% 5.12/5.42 ! [C: int,A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B5 ) )
% 5.12/5.42 => ( member_int @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7822_DiffD1,axiom,
% 5.12/5.42 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) )
% 5.12/5.42 => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7823_DiffD1,axiom,
% 5.12/5.42 ! [C: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B5 ) )
% 5.12/5.42 => ( member_nat @ C @ A2 ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffD1
% 5.12/5.42 thf(fact_7824_DiffE,axiom,
% 5.12/5.42 ! [C: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.42 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member_complex @ C @ A2 )
% 5.12/5.42 => ( member_complex @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7825_DiffE,axiom,
% 5.12/5.42 ! [C: real,A2: set_real,B5: set_real] :
% 5.12/5.42 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member_real @ C @ A2 )
% 5.12/5.42 => ( member_real @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7826_DiffE,axiom,
% 5.12/5.42 ! [C: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.42 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member_set_nat @ C @ A2 )
% 5.12/5.42 => ( member_set_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7827_DiffE,axiom,
% 5.12/5.42 ! [C: int,A2: set_int,B5: set_int] :
% 5.12/5.42 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member_int @ C @ A2 )
% 5.12/5.42 => ( member_int @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7828_DiffE,axiom,
% 5.12/5.42 ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.42 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.12/5.42 => ( member8440522571783428010at_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7829_DiffE,axiom,
% 5.12/5.42 ! [C: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.42 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B5 ) )
% 5.12/5.42 => ~ ( ( member_nat @ C @ A2 )
% 5.12/5.42 => ( member_nat @ C @ B5 ) ) ) ).
% 5.12/5.42
% 5.12/5.42 % DiffE
% 5.12/5.42 thf(fact_7830_of__nat__and__eq,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_and_eq
% 5.12/5.43 thf(fact_7831_of__nat__and__eq,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_and_eq
% 5.12/5.43 thf(fact_7832_and__eq__minus__1__iff,axiom,
% 5.12/5.43 ! [A: code_integer,B: code_integer] :
% 5.12/5.43 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 = ( ( A
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 & ( B
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_eq_minus_1_iff
% 5.12/5.43 thf(fact_7833_and__eq__minus__1__iff,axiom,
% 5.12/5.43 ! [A: int,B: int] :
% 5.12/5.43 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = ( ( A
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 & ( B
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_eq_minus_1_iff
% 5.12/5.43 thf(fact_7834_bit__Suc__0__iff,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.43 = ( N = zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_Suc_0_iff
% 5.12/5.43 thf(fact_7835_not__bit__Suc__0__Suc,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_bit_Suc_0_Suc
% 5.12/5.43 thf(fact_7836_AND__upper2_H,axiom,
% 5.12/5.43 ! [Y: int,Z2: int,X: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ( ord_less_eq_int @ Y @ Z2 )
% 5.12/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper2'
% 5.12/5.43 thf(fact_7837_AND__upper1_H,axiom,
% 5.12/5.43 ! [Y: int,Z2: int,Ya: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ( ord_less_eq_int @ Y @ Z2 )
% 5.12/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper1'
% 5.12/5.43 thf(fact_7838_AND__upper2,axiom,
% 5.12/5.43 ! [Y: int,X: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper2
% 5.12/5.43 thf(fact_7839_AND__upper1,axiom,
% 5.12/5.43 ! [X: int,Y: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper1
% 5.12/5.43 thf(fact_7840_AND__lower,axiom,
% 5.12/5.43 ! [X: int,Y: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_lower
% 5.12/5.43 thf(fact_7841_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.12/5.43 ! [X: produc9072475918466114483BT_nat] :
% 5.12/5.43 ( ! [Uu2: $o,Uv2: $o,D5: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D5 ) )
% 5.12/5.43 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.valid'.cases
% 5.12/5.43 thf(fact_7842_not__bit__Suc__0__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_bit_Suc_0_numeral
% 5.12/5.43 thf(fact_7843_and__less__eq,axiom,
% 5.12/5.43 ! [L: int,K: int] :
% 5.12/5.43 ( ( ord_less_int @ L @ zero_zero_int )
% 5.12/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_less_eq
% 5.12/5.43 thf(fact_7844_AND__upper1_H_H,axiom,
% 5.12/5.43 ! [Y: int,Z2: int,Ya: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ( ord_less_int @ Y @ Z2 )
% 5.12/5.43 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper1''
% 5.12/5.43 thf(fact_7845_AND__upper2_H_H,axiom,
% 5.12/5.43 ! [Y: int,Z2: int,X: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ( ord_less_int @ Y @ Z2 )
% 5.12/5.43 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % AND_upper2''
% 5.12/5.43 thf(fact_7846_Diff__mono,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,D6: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le3146513528884898305at_nat @ A2 @ C4 )
% 5.12/5.43 => ( ( ord_le3146513528884898305at_nat @ D6 @ B5 )
% 5.12/5.43 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) @ ( minus_1356011639430497352at_nat @ C4 @ D6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_mono
% 5.12/5.43 thf(fact_7847_Diff__mono,axiom,
% 5.12/5.43 ! [A2: set_nat,C4: set_nat,D6: set_nat,B5: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.12/5.43 => ( ( ord_less_eq_set_nat @ D6 @ B5 )
% 5.12/5.43 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ ( minus_minus_set_nat @ C4 @ D6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_mono
% 5.12/5.43 thf(fact_7848_Diff__subset,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) @ A2 ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_subset
% 5.12/5.43 thf(fact_7849_Diff__subset,axiom,
% 5.12/5.43 ! [A2: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ A2 ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_subset
% 5.12/5.43 thf(fact_7850_double__diff,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le3146513528884898305at_nat @ A2 @ B5 )
% 5.12/5.43 => ( ( ord_le3146513528884898305at_nat @ B5 @ C4 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ B5 @ ( minus_1356011639430497352at_nat @ C4 @ A2 ) )
% 5.12/5.43 = A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % double_diff
% 5.12/5.43 thf(fact_7851_double__diff,axiom,
% 5.12/5.43 ! [A2: set_nat,B5: set_nat,C4: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ B5 )
% 5.12/5.43 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ B5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.12/5.43 = A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % double_diff
% 5.12/5.43 thf(fact_7852_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_complex,B5: set_complex] :
% 5.12/5.43 ( ( ord_less_set_complex @ A2 @ B5 )
% 5.12/5.43 => ? [B3: complex] : ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7853_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_real,B5: set_real] :
% 5.12/5.43 ( ( ord_less_set_real @ A2 @ B5 )
% 5.12/5.43 => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7854_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.43 ( ( ord_less_set_set_nat @ A2 @ B5 )
% 5.12/5.43 => ? [B3: set_nat] : ( member_set_nat @ B3 @ ( minus_2163939370556025621et_nat @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7855_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_int,B5: set_int] :
% 5.12/5.43 ( ( ord_less_set_int @ A2 @ B5 )
% 5.12/5.43 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7856_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le7866589430770878221at_nat @ A2 @ B5 )
% 5.12/5.43 => ? [B3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7857_psubset__imp__ex__mem,axiom,
% 5.12/5.43 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.43 ( ( ord_less_set_nat @ A2 @ B5 )
% 5.12/5.43 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_imp_ex_mem
% 5.12/5.43 thf(fact_7858_bit__nat__iff,axiom,
% 5.12/5.43 ! [K: int,N: nat] :
% 5.12/5.43 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.12/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.43 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_nat_iff
% 5.12/5.43 thf(fact_7859_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.12/5.43 ! [X: produc9072475918466114483BT_nat] :
% 5.12/5.43 ( ! [A4: $o,B3: $o,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 5.12/5.43 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.12/5.43 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ X3 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.naive_member.cases
% 5.12/5.43 thf(fact_7860_and__one__eq,axiom,
% 5.12/5.43 ! [A: code_integer] :
% 5.12/5.43 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.12/5.43 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_one_eq
% 5.12/5.43 thf(fact_7861_and__one__eq,axiom,
% 5.12/5.43 ! [A: code_natural] :
% 5.12/5.43 ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 5.12/5.43 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_one_eq
% 5.12/5.43 thf(fact_7862_and__one__eq,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.12/5.43 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_one_eq
% 5.12/5.43 thf(fact_7863_and__one__eq,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.12/5.43 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_one_eq
% 5.12/5.43 thf(fact_7864_one__and__eq,axiom,
% 5.12/5.43 ! [A: code_integer] :
% 5.12/5.43 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.12/5.43 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_and_eq
% 5.12/5.43 thf(fact_7865_one__and__eq,axiom,
% 5.12/5.43 ! [A: code_natural] :
% 5.12/5.43 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 5.12/5.43 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_and_eq
% 5.12/5.43 thf(fact_7866_one__and__eq,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.12/5.43 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_and_eq
% 5.12/5.43 thf(fact_7867_one__and__eq,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.12/5.43 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_and_eq
% 5.12/5.43 thf(fact_7868_and__exp__eq__0__iff__not__bit,axiom,
% 5.12/5.43 ! [A: int,N: nat] :
% 5.12/5.43 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_exp_eq_0_iff_not_bit
% 5.12/5.43 thf(fact_7869_and__exp__eq__0__iff__not__bit,axiom,
% 5.12/5.43 ! [A: nat,N: nat] :
% 5.12/5.43 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.43 = zero_zero_nat )
% 5.12/5.43 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_exp_eq_0_iff_not_bit
% 5.12/5.43 thf(fact_7870_bit__nat__def,axiom,
% 5.12/5.43 ( bit_se1148574629649215175it_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.43 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_nat_def
% 5.12/5.43 thf(fact_7871_subset__Compl__self__eq,axiom,
% 5.12/5.43 ! [A2: set_int] :
% 5.12/5.43 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.12/5.43 = ( A2 = bot_bot_set_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_self_eq
% 5.12/5.43 thf(fact_7872_subset__Compl__self__eq,axiom,
% 5.12/5.43 ! [A2: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.12/5.43 = ( A2 = bot_bot_set_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_self_eq
% 5.12/5.43 thf(fact_7873_vebt__member_Ocases,axiom,
% 5.12/5.43 ! [X: produc9072475918466114483BT_nat] :
% 5.12/5.43 ( ! [A4: $o,B3: $o,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X3 ) )
% 5.12/5.43 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.12/5.43 => ( ! [V3: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 5.12/5.43 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.12/5.43 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_member.cases
% 5.12/5.43 thf(fact_7874_VEBT__internal_Omembermima_Ocases,axiom,
% 5.12/5.43 ! [X: produc9072475918466114483BT_nat] :
% 5.12/5.43 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.12/5.43 => ( ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) @ Uz2 ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 5.12/5.43 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ X3 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.cases
% 5.12/5.43 thf(fact_7875_and__int__rec,axiom,
% 5.12/5.43 ( bit_se725231765392027082nd_int
% 5.12/5.43 = ( ^ [K3: int,L2: int] :
% 5.12/5.43 ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int_rec
% 5.12/5.43 thf(fact_7876_divmod__algorithm__code_I7_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(7)
% 5.12/5.43 thf(fact_7877_divmod__algorithm__code_I7_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(7)
% 5.12/5.43 thf(fact_7878_divmod__algorithm__code_I7_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 5.12/5.43 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(7)
% 5.12/5.43 thf(fact_7879_divmod__algorithm__code_I8_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(8)
% 5.12/5.43 thf(fact_7880_divmod__algorithm__code_I8_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(8)
% 5.12/5.43 thf(fact_7881_divmod__algorithm__code_I8_J,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 5.12/5.43 & ( ~ ( ord_less_num @ M2 @ N )
% 5.12/5.43 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.43 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(8)
% 5.12/5.43 thf(fact_7882_neg__eucl__rel__int__mult__2,axiom,
% 5.12/5.43 ! [B: int,A: int,Q5: int,R4: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.12/5.43 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 => ( 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 @ Q5 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % neg_eucl_rel_int_mult_2
% 5.12/5.43 thf(fact_7883_and__int_Oelims,axiom,
% 5.12/5.43 ! [X: int,Xa: int,Y: int] :
% 5.12/5.43 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( uminus_uminus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.12/5.43 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int.elims
% 5.12/5.43 thf(fact_7884_and__int_Osimps,axiom,
% 5.12/5.43 ( bit_se725231765392027082nd_int
% 5.12/5.43 = ( ^ [K3: int,L2: int] :
% 5.12/5.43 ( if_int
% 5.12/5.43 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 @ ( uminus_uminus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.12/5.43 @ ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int.simps
% 5.12/5.43 thf(fact_7885_ComplI,axiom,
% 5.12/5.43 ! [C: complex,A2: set_complex] :
% 5.12/5.43 ( ~ ( member_complex @ C @ A2 )
% 5.12/5.43 => ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplI
% 5.12/5.43 thf(fact_7886_ComplI,axiom,
% 5.12/5.43 ! [C: real,A2: set_real] :
% 5.12/5.43 ( ~ ( member_real @ C @ A2 )
% 5.12/5.43 => ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplI
% 5.12/5.43 thf(fact_7887_ComplI,axiom,
% 5.12/5.43 ! [C: set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ~ ( member_set_nat @ C @ A2 )
% 5.12/5.43 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplI
% 5.12/5.43 thf(fact_7888_ComplI,axiom,
% 5.12/5.43 ! [C: nat,A2: set_nat] :
% 5.12/5.43 ( ~ ( member_nat @ C @ A2 )
% 5.12/5.43 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplI
% 5.12/5.43 thf(fact_7889_ComplI,axiom,
% 5.12/5.43 ! [C: int,A2: set_int] :
% 5.12/5.43 ( ~ ( member_int @ C @ A2 )
% 5.12/5.43 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplI
% 5.12/5.43 thf(fact_7890_Compl__iff,axiom,
% 5.12/5.43 ! [C: complex,A2: set_complex] :
% 5.12/5.43 ( ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) )
% 5.12/5.43 = ( ~ ( member_complex @ C @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_iff
% 5.12/5.43 thf(fact_7891_Compl__iff,axiom,
% 5.12/5.43 ! [C: real,A2: set_real] :
% 5.12/5.43 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 5.12/5.43 = ( ~ ( member_real @ C @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_iff
% 5.12/5.43 thf(fact_7892_Compl__iff,axiom,
% 5.12/5.43 ! [C: set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 5.12/5.43 = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_iff
% 5.12/5.43 thf(fact_7893_Compl__iff,axiom,
% 5.12/5.43 ! [C: nat,A2: set_nat] :
% 5.12/5.43 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.12/5.43 = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_iff
% 5.12/5.43 thf(fact_7894_Compl__iff,axiom,
% 5.12/5.43 ! [C: int,A2: set_int] :
% 5.12/5.43 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.12/5.43 = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_iff
% 5.12/5.43 thf(fact_7895_Diff__insert0,axiom,
% 5.12/5.43 ! [X: complex,A2: set_complex,B5: set_complex] :
% 5.12/5.43 ( ~ ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B5 ) )
% 5.12/5.43 = ( minus_811609699411566653omplex @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7896_Diff__insert0,axiom,
% 5.12/5.43 ! [X: real,A2: set_real,B5: set_real] :
% 5.12/5.43 ( ~ ( member_real @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_real @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7897_Diff__insert0,axiom,
% 5.12/5.43 ! [X: set_nat,A2: set_set_nat,B5: set_set_nat] :
% 5.12/5.43 ( ~ ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B5 ) )
% 5.12/5.43 = ( minus_2163939370556025621et_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7898_Diff__insert0,axiom,
% 5.12/5.43 ! [X: int,A2: set_int,B5: set_int] :
% 5.12/5.43 ( ~ ( member_int @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_int @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7899_Diff__insert0,axiom,
% 5.12/5.43 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7900_Diff__insert0,axiom,
% 5.12/5.43 ! [X: nat,A2: set_nat,B5: set_nat] :
% 5.12/5.43 ( ~ ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert0
% 5.12/5.43 thf(fact_7901_insert__Diff1,axiom,
% 5.12/5.43 ! [X: complex,B5: set_complex,A2: set_complex] :
% 5.12/5.43 ( ( member_complex @ X @ B5 )
% 5.12/5.43 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_811609699411566653omplex @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7902_insert__Diff1,axiom,
% 5.12/5.43 ! [X: real,B5: set_real,A2: set_real] :
% 5.12/5.43 ( ( member_real @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_real @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7903_insert__Diff1,axiom,
% 5.12/5.43 ! [X: set_nat,B5: set_set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ( member_set_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_2163939370556025621et_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7904_insert__Diff1,axiom,
% 5.12/5.43 ! [X: int,B5: set_int,A2: set_int] :
% 5.12/5.43 ( ( member_int @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_int @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7905_insert__Diff1,axiom,
% 5.12/5.43 ! [X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( member8440522571783428010at_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7906_insert__Diff1,axiom,
% 5.12/5.43 ! [X: nat,B5: set_nat,A2: set_nat] :
% 5.12/5.43 ( ( member_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_nat @ A2 @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff1
% 5.12/5.43 thf(fact_7907_insert__Diff__single,axiom,
% 5.12/5.43 ! [A: int,A2: set_int] :
% 5.12/5.43 ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.12/5.43 = ( insert_int @ A @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_single
% 5.12/5.43 thf(fact_7908_insert__Diff__single,axiom,
% 5.12/5.43 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.12/5.43 = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_single
% 5.12/5.43 thf(fact_7909_insert__Diff__single,axiom,
% 5.12/5.43 ! [A: nat,A2: set_nat] :
% 5.12/5.43 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.12/5.43 = ( insert_nat @ A @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_single
% 5.12/5.43 thf(fact_7910_subset__Compl__singleton,axiom,
% 5.12/5.43 ! [A2: set_complex,B: complex] :
% 5.12/5.43 ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 5.12/5.43 = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_singleton
% 5.12/5.43 thf(fact_7911_subset__Compl__singleton,axiom,
% 5.12/5.43 ! [A2: set_real,B: real] :
% 5.12/5.43 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 5.12/5.43 = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_singleton
% 5.12/5.43 thf(fact_7912_subset__Compl__singleton,axiom,
% 5.12/5.43 ! [A2: set_set_nat,B: set_nat] :
% 5.12/5.43 ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 5.12/5.43 = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_singleton
% 5.12/5.43 thf(fact_7913_subset__Compl__singleton,axiom,
% 5.12/5.43 ! [A2: set_int,B: int] :
% 5.12/5.43 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 5.12/5.43 = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_singleton
% 5.12/5.43 thf(fact_7914_subset__Compl__singleton,axiom,
% 5.12/5.43 ! [A2: set_nat,B: nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 5.12/5.43 = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Compl_singleton
% 5.12/5.43 thf(fact_7915_divmod__algorithm__code_I2_J,axiom,
% 5.12/5.43 ! [M2: num] :
% 5.12/5.43 ( ( unique5052692396658037445od_int @ M2 @ one )
% 5.12/5.43 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(2)
% 5.12/5.43 thf(fact_7916_divmod__algorithm__code_I2_J,axiom,
% 5.12/5.43 ! [M2: num] :
% 5.12/5.43 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 5.12/5.43 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(2)
% 5.12/5.43 thf(fact_7917_divmod__algorithm__code_I2_J,axiom,
% 5.12/5.43 ! [M2: num] :
% 5.12/5.43 ( ( unique3479559517661332726nteger @ M2 @ one )
% 5.12/5.43 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(2)
% 5.12/5.43 thf(fact_7918_and__nat__numerals_I3_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_numerals(3)
% 5.12/5.43 thf(fact_7919_and__nat__numerals_I1_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.43 = zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_numerals(1)
% 5.12/5.43 thf(fact_7920_divmod__algorithm__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.12/5.43 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(3)
% 5.12/5.43 thf(fact_7921_divmod__algorithm__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.12/5.43 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(3)
% 5.12/5.43 thf(fact_7922_divmod__algorithm__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.12/5.43 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(3)
% 5.12/5.43 thf(fact_7923_divmod__algorithm__code_I4_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(4)
% 5.12/5.43 thf(fact_7924_divmod__algorithm__code_I4_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.12/5.43 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(4)
% 5.12/5.43 thf(fact_7925_divmod__algorithm__code_I4_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.12/5.43 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_algorithm_code(4)
% 5.12/5.43 thf(fact_7926_and__nat__numerals_I2_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.43 = one_one_nat ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_numerals(2)
% 5.12/5.43 thf(fact_7927_and__nat__numerals_I4_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = one_one_nat ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_numerals(4)
% 5.12/5.43 thf(fact_7928_Suc__0__and__eq,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.43 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Suc_0_and_eq
% 5.12/5.43 thf(fact_7929_and__Suc__0__eq,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_Suc_0_eq
% 5.12/5.43 thf(fact_7930_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: complex,B5: set_complex,A2: set_complex] :
% 5.12/5.43 ( ( ( member_complex @ X @ B5 )
% 5.12/5.43 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_811609699411566653omplex @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member_complex @ X @ B5 )
% 5.12/5.43 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7931_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: real,B5: set_real,A2: set_real] :
% 5.12/5.43 ( ( ( member_real @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_real @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member_real @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7932_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: set_nat,B5: set_set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ( ( member_set_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_2163939370556025621et_nat @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member_set_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7933_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: int,B5: set_int,A2: set_int] :
% 5.12/5.43 ( ( ( member_int @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_int @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member_int @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7934_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ( member8440522571783428010at_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member8440522571783428010at_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7935_insert__Diff__if,axiom,
% 5.12/5.43 ! [X: nat,B5: set_nat,A2: set_nat] :
% 5.12/5.43 ( ( ( member_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( minus_minus_set_nat @ A2 @ B5 ) ) )
% 5.12/5.43 & ( ~ ( member_nat @ X @ B5 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B5 )
% 5.12/5.43 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B5 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff_if
% 5.12/5.43 thf(fact_7936_ComplD,axiom,
% 5.12/5.43 ! [C: complex,A2: set_complex] :
% 5.12/5.43 ( ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) )
% 5.12/5.43 => ~ ( member_complex @ C @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplD
% 5.12/5.43 thf(fact_7937_ComplD,axiom,
% 5.12/5.43 ! [C: real,A2: set_real] :
% 5.12/5.43 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 5.12/5.43 => ~ ( member_real @ C @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplD
% 5.12/5.43 thf(fact_7938_ComplD,axiom,
% 5.12/5.43 ! [C: set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 5.12/5.43 => ~ ( member_set_nat @ C @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplD
% 5.12/5.43 thf(fact_7939_ComplD,axiom,
% 5.12/5.43 ! [C: nat,A2: set_nat] :
% 5.12/5.43 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.12/5.43 => ~ ( member_nat @ C @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplD
% 5.12/5.43 thf(fact_7940_ComplD,axiom,
% 5.12/5.43 ! [C: int,A2: set_int] :
% 5.12/5.43 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.12/5.43 => ~ ( member_int @ C @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % ComplD
% 5.12/5.43 thf(fact_7941_eucl__rel__int__by0,axiom,
% 5.12/5.43 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int_by0
% 5.12/5.43 thf(fact_7942_div__int__unique,axiom,
% 5.12/5.43 ! [K: int,L: int,Q5: int,R4: int] :
% 5.12/5.43 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 => ( ( divide_divide_int @ K @ L )
% 5.12/5.43 = Q5 ) ) ).
% 5.12/5.43
% 5.12/5.43 % div_int_unique
% 5.12/5.43 thf(fact_7943_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: complex,A2: set_complex] :
% 5.12/5.43 ( ~ ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7944_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: real,A2: set_real] :
% 5.12/5.43 ( ~ ( member_real @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7945_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ~ ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7946_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: int,A2: set_int] :
% 5.12/5.43 ( ~ ( member_int @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7947_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7948_Diff__insert__absorb,axiom,
% 5.12/5.43 ! [X: nat,A2: set_nat] :
% 5.12/5.43 ( ~ ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert_absorb
% 5.12/5.43 thf(fact_7949_Diff__insert2,axiom,
% 5.12/5.43 ! [A2: set_int,A: int,B5: set_int] :
% 5.12/5.43 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B5 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert2
% 5.12/5.43 thf(fact_7950_Diff__insert2,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B5 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert2
% 5.12/5.43 thf(fact_7951_Diff__insert2,axiom,
% 5.12/5.43 ! [A2: set_nat,A: nat,B5: set_nat] :
% 5.12/5.43 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B5 ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert2
% 5.12/5.43 thf(fact_7952_insert__Diff,axiom,
% 5.12/5.43 ! [A: complex,A2: set_complex] :
% 5.12/5.43 ( ( member_complex @ A @ A2 )
% 5.12/5.43 => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7953_insert__Diff,axiom,
% 5.12/5.43 ! [A: real,A2: set_real] :
% 5.12/5.43 ( ( member_real @ A @ A2 )
% 5.12/5.43 => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7954_insert__Diff,axiom,
% 5.12/5.43 ! [A: set_nat,A2: set_set_nat] :
% 5.12/5.43 ( ( member_set_nat @ A @ A2 )
% 5.12/5.43 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7955_insert__Diff,axiom,
% 5.12/5.43 ! [A: int,A2: set_int] :
% 5.12/5.43 ( ( member_int @ A @ A2 )
% 5.12/5.43 => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7956_insert__Diff,axiom,
% 5.12/5.43 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( member8440522571783428010at_nat @ A @ A2 )
% 5.12/5.43 => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7957_insert__Diff,axiom,
% 5.12/5.43 ! [A: nat,A2: set_nat] :
% 5.12/5.43 ( ( member_nat @ A @ A2 )
% 5.12/5.43 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.12/5.43 = A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % insert_Diff
% 5.12/5.43 thf(fact_7958_Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_int,A: int,B5: set_int] :
% 5.12/5.43 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B5 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert
% 5.12/5.43 thf(fact_7959_Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B5 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert
% 5.12/5.43 thf(fact_7960_Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_nat,A: nat,B5: set_nat] :
% 5.12/5.43 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B5 ) )
% 5.12/5.43 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B5 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_insert
% 5.12/5.43 thf(fact_7961_Compl__insert,axiom,
% 5.12/5.43 ! [X: int,A2: set_int] :
% 5.12/5.43 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 5.12/5.43 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_insert
% 5.12/5.43 thf(fact_7962_Compl__insert,axiom,
% 5.12/5.43 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 5.12/5.43 = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_insert
% 5.12/5.43 thf(fact_7963_Compl__insert,axiom,
% 5.12/5.43 ! [X: nat,A2: set_nat] :
% 5.12/5.43 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 5.12/5.43 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_insert
% 5.12/5.43 thf(fact_7964_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_complex,B5: set_complex,X: complex,C4: set_complex] :
% 5.12/5.43 ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B5 @ ( insert_complex @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member_complex @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7965_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_real,B5: set_real,X: real,C4: set_real] :
% 5.12/5.43 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B5 @ ( insert_real @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member_real @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7966_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_set_nat,B5: set_set_nat,X: set_nat,C4: set_set_nat] :
% 5.12/5.43 ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B5 @ ( insert_set_nat @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7967_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_int,B5: set_int,X: int,C4: set_int] :
% 5.12/5.43 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B5 @ ( insert_int @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member_int @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7968_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B5 @ ( insert8211810215607154385at_nat @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7969_subset__Diff__insert,axiom,
% 5.12/5.43 ! [A2: set_nat,B5: set_nat,X: nat,C4: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B5 @ ( insert_nat @ X @ C4 ) ) )
% 5.12/5.43 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B5 @ C4 ) )
% 5.12/5.43 & ~ ( member_nat @ X @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_Diff_insert
% 5.12/5.43 thf(fact_7970_and__nat__def,axiom,
% 5.12/5.43 ( bit_se727722235901077358nd_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_def
% 5.12/5.43 thf(fact_7971_eucl__rel__int__dividesI,axiom,
% 5.12/5.43 ! [L: int,K: int,Q5: int] :
% 5.12/5.43 ( ( L != zero_zero_int )
% 5.12/5.43 => ( ( K
% 5.12/5.43 = ( times_times_int @ Q5 @ L ) )
% 5.12/5.43 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q5 @ zero_zero_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int_dividesI
% 5.12/5.43 thf(fact_7972_Diff__single__insert,axiom,
% 5.12/5.43 ! [A2: set_int,X: int,B5: set_int] :
% 5.12/5.43 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 )
% 5.12/5.43 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_single_insert
% 5.12/5.43 thf(fact_7973_Diff__single__insert,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 )
% 5.12/5.43 => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_single_insert
% 5.12/5.43 thf(fact_7974_Diff__single__insert,axiom,
% 5.12/5.43 ! [A2: set_nat,X: nat,B5: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 )
% 5.12/5.43 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B5 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Diff_single_insert
% 5.12/5.43 thf(fact_7975_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_complex,X: complex,B5: set_complex] :
% 5.12/5.43 ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ord_le211207098394363844omplex @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7976_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_real,X: real,B5: set_real] :
% 5.12/5.43 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_real @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_real @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_real @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7977_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_set_nat,X: set_nat,B5: set_set_nat] :
% 5.12/5.43 ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le6893508408891458716et_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7978_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_int,X: int,B5: set_int] :
% 5.12/5.43 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_int @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_int @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_int @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7979_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le3146513528884898305at_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7980_subset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_nat,X: nat,B5: set_nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_insert_iff
% 5.12/5.43 thf(fact_7981_eucl__rel__int,axiom,
% 5.12/5.43 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int
% 5.12/5.43 thf(fact_7982_divmod__int__def,axiom,
% 5.12/5.43 ( unique5052692396658037445od_int
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_int_def
% 5.12/5.43 thf(fact_7983_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_complex,X: complex,B5: set_complex] :
% 5.12/5.43 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_complex @ X @ B5 )
% 5.12/5.43 => ( ord_less_set_complex @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member_complex @ X @ B5 )
% 5.12/5.43 => ( ( ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_complex @ X @ A2 )
% 5.12/5.43 => ( ord_le211207098394363844omplex @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7984_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_real,X: real,B5: set_real] :
% 5.12/5.43 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_real @ X @ B5 )
% 5.12/5.43 => ( ord_less_set_real @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member_real @ X @ B5 )
% 5.12/5.43 => ( ( ( member_real @ X @ A2 )
% 5.12/5.43 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_real @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_real @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7985_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_set_nat,X: set_nat,B5: set_set_nat] :
% 5.12/5.43 ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_set_nat @ X @ B5 )
% 5.12/5.43 => ( ord_less_set_set_nat @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member_set_nat @ X @ B5 )
% 5.12/5.43 => ( ( ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_set_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le6893508408891458716et_nat @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7986_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_int,X: int,B5: set_int] :
% 5.12/5.43 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_int @ X @ B5 )
% 5.12/5.43 => ( ord_less_set_int @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member_int @ X @ B5 )
% 5.12/5.43 => ( ( ( member_int @ X @ A2 )
% 5.12/5.43 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_int @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_int @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7987_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member8440522571783428010at_nat @ X @ B5 )
% 5.12/5.43 => ( ord_le7866589430770878221at_nat @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member8440522571783428010at_nat @ X @ B5 )
% 5.12/5.43 => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 5.12/5.43 => ( ord_le3146513528884898305at_nat @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7988_psubset__insert__iff,axiom,
% 5.12/5.43 ! [A2: set_nat,X: nat,B5: set_nat] :
% 5.12/5.43 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B5 ) )
% 5.12/5.43 = ( ( ( member_nat @ X @ B5 )
% 5.12/5.43 => ( ord_less_set_nat @ A2 @ B5 ) )
% 5.12/5.43 & ( ~ ( member_nat @ X @ B5 )
% 5.12/5.43 => ( ( ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 ) )
% 5.12/5.43 & ( ~ ( member_nat @ X @ A2 )
% 5.12/5.43 => ( ord_less_eq_set_nat @ A2 @ B5 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % psubset_insert_iff
% 5.12/5.43 thf(fact_7989_atLeastAtMostPlus1__int__conv,axiom,
% 5.12/5.43 ! [M2: int,N: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 5.12/5.43 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 5.12/5.43 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % atLeastAtMostPlus1_int_conv
% 5.12/5.43 thf(fact_7990_simp__from__to,axiom,
% 5.12/5.43 ( set_or1266510415728281911st_int
% 5.12/5.43 = ( ^ [I2: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I2 ) @ bot_bot_set_int @ ( insert_int @ I2 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % simp_from_to
% 5.12/5.43 thf(fact_7991_divmod__def,axiom,
% 5.12/5.43 ( unique5052692396658037445od_int
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_def
% 5.12/5.43 thf(fact_7992_divmod__def,axiom,
% 5.12/5.43 ( unique5055182867167087721od_nat
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_def
% 5.12/5.43 thf(fact_7993_divmod__def,axiom,
% 5.12/5.43 ( unique3479559517661332726nteger
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_def
% 5.12/5.43 thf(fact_7994_divmod_H__nat__def,axiom,
% 5.12/5.43 ( unique5055182867167087721od_nat
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod'_nat_def
% 5.12/5.43 thf(fact_7995_zminus1__lemma,axiom,
% 5.12/5.43 ! [A: int,B: int,Q5: int,R4: int] :
% 5.12/5.43 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 => ( ( B != zero_zero_int )
% 5.12/5.43 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R4 = zero_zero_int ) @ ( uminus_uminus_int @ Q5 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q5 ) @ one_one_int ) ) @ ( if_int @ ( R4 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % zminus1_lemma
% 5.12/5.43 thf(fact_7996_eucl__rel__int__iff,axiom,
% 5.12/5.43 ! [K: int,L: int,Q5: int,R4: int] :
% 5.12/5.43 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 = ( ( K
% 5.12/5.43 = ( plus_plus_int @ ( times_times_int @ L @ Q5 ) @ R4 ) )
% 5.12/5.43 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.12/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.12/5.43 & ( ord_less_int @ R4 @ L ) ) )
% 5.12/5.43 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.12/5.43 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.12/5.43 => ( ( ord_less_int @ L @ R4 )
% 5.12/5.43 & ( ord_less_eq_int @ R4 @ zero_zero_int ) ) )
% 5.12/5.43 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.12/5.43 => ( Q5 = zero_zero_int ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int_iff
% 5.12/5.43 thf(fact_7997_and__nat__unfold,axiom,
% 5.12/5.43 ( bit_se727722235901077358nd_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.43 ( if_nat
% 5.12/5.43 @ ( ( M5 = zero_zero_nat )
% 5.12/5.43 | ( N4 = zero_zero_nat ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_unfold
% 5.12/5.43 thf(fact_7998_eucl__rel__int__remainderI,axiom,
% 5.12/5.43 ! [R4: int,L: int,K: int,Q5: int] :
% 5.12/5.43 ( ( ( sgn_sgn_int @ R4 )
% 5.12/5.43 = ( sgn_sgn_int @ L ) )
% 5.12/5.43 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L ) )
% 5.12/5.43 => ( ( K
% 5.12/5.43 = ( plus_plus_int @ ( times_times_int @ Q5 @ L ) @ R4 ) )
% 5.12/5.43 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q5 @ R4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int_remainderI
% 5.12/5.43 thf(fact_7999_and__nat__rec,axiom,
% 5.12/5.43 ( bit_se727722235901077358nd_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.43 ( plus_plus_nat
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.12/5.43 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.43 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_nat_rec
% 5.12/5.43 thf(fact_8000_eucl__rel__int_Osimps,axiom,
% 5.12/5.43 ( eucl_rel_int
% 5.12/5.43 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 5.12/5.43 ( ? [K3: int] :
% 5.12/5.43 ( ( A12 = K3 )
% 5.12/5.43 & ( A23 = zero_zero_int )
% 5.12/5.43 & ( A32
% 5.12/5.43 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.12/5.43 | ? [L2: int,K3: int,Q4: int] :
% 5.12/5.43 ( ( A12 = K3 )
% 5.12/5.43 & ( A23 = L2 )
% 5.12/5.43 & ( A32
% 5.12/5.43 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.12/5.43 & ( L2 != zero_zero_int )
% 5.12/5.43 & ( K3
% 5.12/5.43 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.12/5.43 | ? [R: int,L2: int,K3: int,Q4: int] :
% 5.12/5.43 ( ( A12 = K3 )
% 5.12/5.43 & ( A23 = L2 )
% 5.12/5.43 & ( A32
% 5.12/5.43 = ( product_Pair_int_int @ Q4 @ R ) )
% 5.12/5.43 & ( ( sgn_sgn_int @ R )
% 5.12/5.43 = ( sgn_sgn_int @ L2 ) )
% 5.12/5.43 & ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 5.12/5.43 & ( K3
% 5.12/5.43 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int.simps
% 5.12/5.43 thf(fact_8001_eucl__rel__int_Ocases,axiom,
% 5.12/5.43 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 5.12/5.43 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 5.12/5.43 => ( ( ( A22 = zero_zero_int )
% 5.12/5.43 => ( A33
% 5.12/5.43 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.12/5.43 => ( ! [Q3: int] :
% 5.12/5.43 ( ( A33
% 5.12/5.43 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.12/5.43 => ( ( A22 != zero_zero_int )
% 5.12/5.43 => ( A1
% 5.12/5.43 != ( times_times_int @ Q3 @ A22 ) ) ) )
% 5.12/5.43 => ~ ! [R3: int,Q3: int] :
% 5.12/5.43 ( ( A33
% 5.12/5.43 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.12/5.43 => ( ( ( sgn_sgn_int @ R3 )
% 5.12/5.43 = ( sgn_sgn_int @ A22 ) )
% 5.12/5.43 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.12/5.43 => ( A1
% 5.12/5.43 != ( plus_plus_int @ ( times_times_int @ Q3 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eucl_rel_int.cases
% 5.12/5.43 thf(fact_8002_divmod__divmod__step,axiom,
% 5.12/5.43 ( unique5055182867167087721od_nat
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M5 @ N4 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M5 ) ) @ ( unique5026877609467782581ep_nat @ N4 @ ( unique5055182867167087721od_nat @ M5 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_divmod_step
% 5.12/5.43 thf(fact_8003_divmod__divmod__step,axiom,
% 5.12/5.43 ( unique5052692396658037445od_int
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M5 @ N4 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M5 ) ) @ ( unique5024387138958732305ep_int @ N4 @ ( unique5052692396658037445od_int @ M5 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_divmod_step
% 5.12/5.43 thf(fact_8004_divmod__divmod__step,axiom,
% 5.12/5.43 ( unique3479559517661332726nteger
% 5.12/5.43 = ( ^ [M5: num,N4: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M5 @ N4 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M5 ) ) @ ( unique4921790084139445826nteger @ N4 @ ( unique3479559517661332726nteger @ M5 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_divmod_step
% 5.12/5.43 thf(fact_8005_pos__eucl__rel__int__mult__2,axiom,
% 5.12/5.43 ! [B: int,A: int,Q5: int,R4: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.12/5.43 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 => ( 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 @ Q5 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pos_eucl_rel_int_mult_2
% 5.12/5.43 thf(fact_8006_minus__one__div__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_one_div_numeral
% 5.12/5.43 thf(fact_8007_one__div__minus__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_div_minus_numeral
% 5.12/5.43 thf(fact_8008_Divides_Oadjust__div__eq,axiom,
% 5.12/5.43 ! [Q5: int,R4: int] :
% 5.12/5.43 ( ( adjust_div @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.12/5.43 = ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R4 != zero_zero_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Divides.adjust_div_eq
% 5.12/5.43 thf(fact_8009_and__int_Opsimps,axiom,
% 5.12/5.43 ! [K: int,L: int] :
% 5.12/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.12/5.43 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.12/5.43 = ( uminus_uminus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.12/5.43 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.12/5.43 = ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int.psimps
% 5.12/5.43 thf(fact_8010_and__int_Opelims,axiom,
% 5.12/5.43 ! [X: int,Xa: int,Y: int] :
% 5.12/5.43 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.12/5.43 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( uminus_uminus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.12/5.43 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.12/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.12/5.43 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int.pelims
% 5.12/5.43 thf(fact_8011_minus__numeral__div__numeral,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_numeral_div_numeral
% 5.12/5.43 thf(fact_8012_numeral__div__minus__numeral,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_div_minus_numeral
% 5.12/5.43 thf(fact_8013_atLeast0__atMost__Suc,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.12/5.43 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % atLeast0_atMost_Suc
% 5.12/5.43 thf(fact_8014_atLeastAtMost__insertL,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.12/5.43 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % atLeastAtMost_insertL
% 5.12/5.43 thf(fact_8015_atLeastAtMostSuc__conv,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % atLeastAtMostSuc_conv
% 5.12/5.43 thf(fact_8016_Icc__eq__insert__lb__nat,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 5.12/5.43 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Icc_eq_insert_lb_nat
% 5.12/5.43 thf(fact_8017_set__decode__plus__power__2,axiom,
% 5.12/5.43 ! [N: nat,Z2: nat] :
% 5.12/5.43 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z2 ) )
% 5.12/5.43 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z2 ) )
% 5.12/5.43 = ( insert_nat @ N @ ( nat_set_decode @ Z2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_decode_plus_power_2
% 5.12/5.43 thf(fact_8018_and__int_Opinduct,axiom,
% 5.12/5.43 ! [A0: int,A1: int,P: int > int > $o] :
% 5.12/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.12/5.43 => ( ! [K2: int,L3: int] :
% 5.12/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L3 ) )
% 5.12/5.43 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.12/5.43 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.12/5.43 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 => ( P @ K2 @ L3 ) ) )
% 5.12/5.43 => ( P @ A0 @ A1 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % and_int.pinduct
% 5.12/5.43 thf(fact_8019_upto_Opinduct,axiom,
% 5.12/5.43 ! [A0: int,A1: int,P: int > int > $o] :
% 5.12/5.43 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.12/5.43 => ( ! [I3: int,J: int] :
% 5.12/5.43 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J ) )
% 5.12/5.43 => ( ( ( ord_less_eq_int @ I3 @ J )
% 5.12/5.43 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J ) )
% 5.12/5.43 => ( P @ I3 @ J ) ) )
% 5.12/5.43 => ( P @ A0 @ A1 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % upto.pinduct
% 5.12/5.43 thf(fact_8020_divmod__BitM__2__eq,axiom,
% 5.12/5.43 ! [M2: num] :
% 5.12/5.43 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 5.12/5.43 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % divmod_BitM_2_eq
% 5.12/5.43 thf(fact_8021_sinh__ln__real,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.43 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.12/5.43 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_ln_real
% 5.12/5.43 thf(fact_8022_one__mod__minus__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_mod_minus_numeral
% 5.12/5.43 thf(fact_8023_minus__one__mod__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.43 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_one_mod_numeral
% 5.12/5.43 thf(fact_8024_sinh__real__eq__iff,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( ( sinh_real @ X )
% 5.12/5.43 = ( sinh_real @ Y ) )
% 5.12/5.43 = ( X = Y ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_eq_iff
% 5.12/5.43 thf(fact_8025_sinh__0,axiom,
% 5.12/5.43 ( ( sinh_real @ zero_zero_real )
% 5.12/5.43 = zero_zero_real ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_0
% 5.12/5.43 thf(fact_8026_sinh__minus,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( sinh_real @ ( uminus_uminus_real @ X ) )
% 5.12/5.43 = ( uminus_uminus_real @ ( sinh_real @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_minus
% 5.12/5.43 thf(fact_8027_sinh__minus,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( sinh_complex @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.43 = ( uminus1482373934393186551omplex @ ( sinh_complex @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_minus
% 5.12/5.43 thf(fact_8028_sinh__real__zero__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ( sinh_real @ X )
% 5.12/5.43 = zero_zero_real )
% 5.12/5.43 = ( X = zero_zero_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_zero_iff
% 5.12/5.43 thf(fact_8029_sinh__real__less__iff,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.12/5.43 = ( ord_less_real @ X @ Y ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_less_iff
% 5.12/5.43 thf(fact_8030_sinh__real__le__iff,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.12/5.43 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_le_iff
% 5.12/5.43 thf(fact_8031_sinh__real__abs,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( sinh_real @ ( abs_abs_real @ X ) )
% 5.12/5.43 = ( abs_abs_real @ ( sinh_real @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_abs
% 5.12/5.43 thf(fact_8032_sinh__real__neg__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.12/5.43 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_neg_iff
% 5.12/5.43 thf(fact_8033_sinh__real__pos__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.12/5.43 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_pos_iff
% 5.12/5.43 thf(fact_8034_sinh__real__nonpos__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.12/5.43 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_nonpos_iff
% 5.12/5.43 thf(fact_8035_sinh__real__nonneg__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.12/5.43 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_real_nonneg_iff
% 5.12/5.43 thf(fact_8036_dbl__dec__simps_I5_J,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.12/5.43 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % dbl_dec_simps(5)
% 5.12/5.43 thf(fact_8037_dbl__dec__simps_I5_J,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.12/5.43 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % dbl_dec_simps(5)
% 5.12/5.43 thf(fact_8038_dbl__dec__simps_I5_J,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.12/5.43 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % dbl_dec_simps(5)
% 5.12/5.43 thf(fact_8039_dbl__dec__simps_I5_J,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.12/5.43 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % dbl_dec_simps(5)
% 5.12/5.43 thf(fact_8040_pred__numeral__simps_I2_J,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pred_numeral_simps(2)
% 5.12/5.43 thf(fact_8041_one__mod__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.12/5.43 = ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_mod_numeral
% 5.12/5.43 thf(fact_8042_one__mod__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.12/5.43 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_mod_numeral
% 5.12/5.43 thf(fact_8043_one__mod__numeral,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.12/5.43 = ( produc6174133586879617921nteger @ ( unique3479559517661332726nteger @ one @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_mod_numeral
% 5.12/5.43 thf(fact_8044_minus__numeral__mod__numeral,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.43 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_numeral_mod_numeral
% 5.12/5.43 thf(fact_8045_numeral__mod__minus__numeral,axiom,
% 5.12/5.43 ! [M2: num,N: num] :
% 5.12/5.43 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_mod_minus_numeral
% 5.12/5.43 thf(fact_8046_arsinh__sinh__real,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( arsinh_real @ ( sinh_real @ X ) )
% 5.12/5.43 = X ) ).
% 5.12/5.43
% 5.12/5.43 % arsinh_sinh_real
% 5.12/5.43 thf(fact_8047_sinh__less__cosh__real,axiom,
% 5.12/5.43 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_less_cosh_real
% 5.12/5.43 thf(fact_8048_sinh__le__cosh__real,axiom,
% 5.12/5.43 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_le_cosh_real
% 5.12/5.43 thf(fact_8049_inc__BitM__eq,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( inc @ ( bitM @ N ) )
% 5.12/5.43 = ( bit0 @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % inc_BitM_eq
% 5.12/5.43 thf(fact_8050_divides__aux__def,axiom,
% 5.12/5.43 ( unique6322359934112328802ux_nat
% 5.12/5.43 = ( ^ [Qr: product_prod_nat_nat] :
% 5.12/5.43 ( ( product_snd_nat_nat @ Qr )
% 5.12/5.43 = zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divides_aux_def
% 5.12/5.43 thf(fact_8051_divides__aux__def,axiom,
% 5.12/5.43 ( unique6319869463603278526ux_int
% 5.12/5.43 = ( ^ [Qr: product_prod_int_int] :
% 5.12/5.43 ( ( product_snd_int_int @ Qr )
% 5.12/5.43 = zero_zero_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % divides_aux_def
% 5.12/5.43 thf(fact_8052_BitM__inc__eq,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( bitM @ ( inc @ N ) )
% 5.12/5.43 = ( bit1 @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % BitM_inc_eq
% 5.12/5.43 thf(fact_8053_eval__nat__numeral_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.12/5.43 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % eval_nat_numeral(2)
% 5.12/5.43 thf(fact_8054_cosh__add,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( cosh_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.43 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_add
% 5.12/5.43 thf(fact_8055_sinh__add,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( sinh_real @ ( plus_plus_real @ X @ Y ) )
% 5.12/5.43 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_add
% 5.12/5.43 thf(fact_8056_sinh__diff,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( sinh_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.43 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_diff
% 5.12/5.43 thf(fact_8057_cosh__diff,axiom,
% 5.12/5.43 ! [X: real,Y: real] :
% 5.12/5.43 ( ( cosh_real @ ( minus_minus_real @ X @ Y ) )
% 5.12/5.43 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_diff
% 5.12/5.43 thf(fact_8058_BitM__plus__one,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.12/5.43 = ( bit0 @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % BitM_plus_one
% 5.12/5.43 thf(fact_8059_one__plus__BitM,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.12/5.43 = ( bit0 @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_plus_BitM
% 5.12/5.43 thf(fact_8060_sinh__plus__cosh,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( plus_plus_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) )
% 5.12/5.43 = ( exp_complex @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_plus_cosh
% 5.12/5.43 thf(fact_8061_sinh__plus__cosh,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( plus_plus_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) )
% 5.12/5.43 = ( exp_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_plus_cosh
% 5.12/5.43 thf(fact_8062_cosh__plus__sinh,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( plus_plus_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ X ) )
% 5.12/5.43 = ( exp_complex @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_plus_sinh
% 5.12/5.43 thf(fact_8063_cosh__plus__sinh,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( plus_plus_real @ ( cosh_real @ X ) @ ( sinh_real @ X ) )
% 5.12/5.43 = ( exp_real @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_plus_sinh
% 5.12/5.43 thf(fact_8064_tanh__def,axiom,
% 5.12/5.43 ( tanh_complex
% 5.12/5.43 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ X2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % tanh_def
% 5.12/5.43 thf(fact_8065_tanh__def,axiom,
% 5.12/5.43 ( tanh_real
% 5.12/5.43 = ( ^ [X2: real] : ( divide_divide_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % tanh_def
% 5.12/5.43 thf(fact_8066_numeral__BitM,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.12/5.43 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_BitM
% 5.12/5.43 thf(fact_8067_numeral__BitM,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.12/5.43 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_BitM
% 5.12/5.43 thf(fact_8068_numeral__BitM,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.12/5.43 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_BitM
% 5.12/5.43 thf(fact_8069_numeral__BitM,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.12/5.43 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_BitM
% 5.12/5.43 thf(fact_8070_cosh__minus__sinh,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( minus_minus_real @ ( cosh_real @ X ) @ ( sinh_real @ X ) )
% 5.12/5.43 = ( exp_real @ ( uminus_uminus_real @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_minus_sinh
% 5.12/5.43 thf(fact_8071_cosh__minus__sinh,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( minus_minus_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ X ) )
% 5.12/5.43 = ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_minus_sinh
% 5.12/5.43 thf(fact_8072_sinh__minus__cosh,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( minus_minus_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) )
% 5.12/5.43 = ( uminus_uminus_real @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_minus_cosh
% 5.12/5.43 thf(fact_8073_sinh__minus__cosh,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( minus_minus_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) )
% 5.12/5.43 = ( uminus1482373934393186551omplex @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_minus_cosh
% 5.12/5.43 thf(fact_8074_sinh__double,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.43 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X ) ) @ ( cosh_complex @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_double
% 5.12/5.43 thf(fact_8075_sinh__double,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.43 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X ) ) @ ( cosh_real @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_double
% 5.12/5.43 thf(fact_8076_sinh__zero__iff,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ( sinh_real @ X )
% 5.12/5.43 = zero_zero_real )
% 5.12/5.43 = ( member_real @ ( exp_real @ X ) @ ( insert_real @ one_one_real @ ( insert_real @ ( uminus_uminus_real @ one_one_real ) @ bot_bot_set_real ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_zero_iff
% 5.12/5.43 thf(fact_8077_sinh__zero__iff,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( ( sinh_complex @ X )
% 5.12/5.43 = zero_zero_complex )
% 5.12/5.43 = ( member_complex @ ( exp_complex @ X ) @ ( insert_complex @ one_one_complex @ ( insert_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ bot_bot_set_complex ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_zero_iff
% 5.12/5.43 thf(fact_8078_sinh__field__def,axiom,
% 5.12/5.43 ( sinh_real
% 5.12/5.43 = ( ^ [Z6: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z6 ) @ ( exp_real @ ( uminus_uminus_real @ Z6 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_field_def
% 5.12/5.43 thf(fact_8079_sinh__field__def,axiom,
% 5.12/5.43 ( sinh_complex
% 5.12/5.43 = ( ^ [Z6: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z6 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z6 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_field_def
% 5.12/5.43 thf(fact_8080_cosh__square__eq,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.43 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_square_eq
% 5.12/5.43 thf(fact_8081_cosh__square__eq,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.43 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_square_eq
% 5.12/5.43 thf(fact_8082_sinh__square__eq,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.43 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_square_eq
% 5.12/5.43 thf(fact_8083_sinh__square__eq,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.43 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % sinh_square_eq
% 5.12/5.43 thf(fact_8084_hyperbolic__pythagoras,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.43 = one_one_real ) ).
% 5.12/5.43
% 5.12/5.43 % hyperbolic_pythagoras
% 5.12/5.43 thf(fact_8085_hyperbolic__pythagoras,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.43 = one_one_complex ) ).
% 5.12/5.43
% 5.12/5.43 % hyperbolic_pythagoras
% 5.12/5.43 thf(fact_8086_cosh__double,axiom,
% 5.12/5.43 ! [X: complex] :
% 5.12/5.43 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.43 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_double
% 5.12/5.43 thf(fact_8087_cosh__double,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.12/5.43 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % cosh_double
% 5.12/5.43 thf(fact_8088_Suc__0__xor__eq,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Suc_0_xor_eq
% 5.12/5.43 thf(fact_8089_xor__Suc__0__eq,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_Suc_0_eq
% 5.12/5.43 thf(fact_8090_horner__sum__of__bool__2__less,axiom,
% 5.12/5.43 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % horner_sum_of_bool_2_less
% 5.12/5.43 thf(fact_8091_push__bit__numeral__minus__1,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_numeral_minus_1
% 5.12/5.43 thf(fact_8092_push__bit__numeral__minus__1,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_numeral_minus_1
% 5.12/5.43 thf(fact_8093_vebt__member_Oelims_I3_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ~ ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.43 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.12/5.43 => ( ! [V3: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.12/5.43 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.12/5.43 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Summary2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.43 => ( ( Xa != Mi )
% 5.12/5.43 => ( ( Xa != Ma2 )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_member.elims(3)
% 5.12/5.43 thf(fact_8094_set__vebt_H__def,axiom,
% 5.12/5.43 ( vEBT_VEBT_set_vebt
% 5.12/5.43 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_vebt'_def
% 5.12/5.43 thf(fact_8095_push__bit__nonnegative__int__iff,axiom,
% 5.12/5.43 ! [N: nat,K: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.12/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_nonnegative_int_iff
% 5.12/5.43 thf(fact_8096_push__bit__negative__int__iff,axiom,
% 5.12/5.43 ! [N: nat,K: int] :
% 5.12/5.43 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_negative_int_iff
% 5.12/5.43 thf(fact_8097_bit_Oxor__self,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ X @ X )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_self
% 5.12/5.43 thf(fact_8098_xor__self__eq,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ A @ A )
% 5.12/5.43 = zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % xor_self_eq
% 5.12/5.43 thf(fact_8099_xor__self__eq,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ A @ A )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % xor_self_eq
% 5.12/5.43 thf(fact_8100_xor_Oleft__neutral,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 5.12/5.43 = A ) ).
% 5.12/5.43
% 5.12/5.43 % xor.left_neutral
% 5.12/5.43 thf(fact_8101_xor_Oleft__neutral,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 5.12/5.43 = A ) ).
% 5.12/5.43
% 5.12/5.43 % xor.left_neutral
% 5.12/5.43 thf(fact_8102_xor_Oright__neutral,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 5.12/5.43 = A ) ).
% 5.12/5.43
% 5.12/5.43 % xor.right_neutral
% 5.12/5.43 thf(fact_8103_xor_Oright__neutral,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 5.12/5.43 = A ) ).
% 5.12/5.43
% 5.12/5.43 % xor.right_neutral
% 5.12/5.43 thf(fact_8104_push__bit__of__0,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ zero_zero_int )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_0
% 5.12/5.43 thf(fact_8105_push__bit__of__0,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ N @ zero_zero_nat )
% 5.12/5.43 = zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_0
% 5.12/5.43 thf(fact_8106_push__bit__eq__0__iff,axiom,
% 5.12/5.43 ! [N: nat,A: int] :
% 5.12/5.43 ( ( ( bit_se545348938243370406it_int @ N @ A )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 = ( A = zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_eq_0_iff
% 5.12/5.43 thf(fact_8107_push__bit__eq__0__iff,axiom,
% 5.12/5.43 ! [N: nat,A: nat] :
% 5.12/5.43 ( ( ( bit_se547839408752420682it_nat @ N @ A )
% 5.12/5.43 = zero_zero_nat )
% 5.12/5.43 = ( A = zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_eq_0_iff
% 5.12/5.43 thf(fact_8108_concat__bit__of__zero__1,axiom,
% 5.12/5.43 ! [N: nat,L: int] :
% 5.12/5.43 ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 5.12/5.43
% 5.12/5.43 % concat_bit_of_zero_1
% 5.12/5.43 thf(fact_8109_case__nat__numeral,axiom,
% 5.12/5.43 ! [A: $o,F: nat > $o,V: num] :
% 5.12/5.43 ( ( case_nat_o @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.12/5.43 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_numeral
% 5.12/5.43 thf(fact_8110_case__nat__numeral,axiom,
% 5.12/5.43 ! [A: nat,F: nat > nat,V: num] :
% 5.12/5.43 ( ( case_nat_nat @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.12/5.43 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_numeral
% 5.12/5.43 thf(fact_8111_case__nat__numeral,axiom,
% 5.12/5.43 ! [A: option_num,F: nat > option_num,V: num] :
% 5.12/5.43 ( ( case_nat_option_num @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.12/5.43 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_numeral
% 5.12/5.43 thf(fact_8112_push__bit__Suc__numeral,axiom,
% 5.12/5.43 ! [N: nat,K: num] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( numeral_numeral_int @ K ) )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ N @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc_numeral
% 5.12/5.43 thf(fact_8113_push__bit__Suc__numeral,axiom,
% 5.12/5.43 ! [N: nat,K: num] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.43 = ( bit_se547839408752420682it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc_numeral
% 5.12/5.43 thf(fact_8114_case__nat__add__eq__if,axiom,
% 5.12/5.43 ! [A: $o,F: nat > $o,V: num,N: nat] :
% 5.12/5.43 ( ( case_nat_o @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.12/5.43 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_add_eq_if
% 5.12/5.43 thf(fact_8115_case__nat__add__eq__if,axiom,
% 5.12/5.43 ! [A: nat,F: nat > nat,V: num,N: nat] :
% 5.12/5.43 ( ( case_nat_nat @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.12/5.43 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_add_eq_if
% 5.12/5.43 thf(fact_8116_case__nat__add__eq__if,axiom,
% 5.12/5.43 ! [A: option_num,F: nat > option_num,V: num,N: nat] :
% 5.12/5.43 ( ( case_nat_option_num @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.12/5.43 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % case_nat_add_eq_if
% 5.12/5.43 thf(fact_8117_push__bit__Suc__minus__numeral,axiom,
% 5.12/5.43 ! [N: nat,K: num] :
% 5.12/5.43 ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.12/5.43 = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc_minus_numeral
% 5.12/5.43 thf(fact_8118_push__bit__Suc__minus__numeral,axiom,
% 5.12/5.43 ! [N: nat,K: num] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc_minus_numeral
% 5.12/5.43 thf(fact_8119_xor__numerals_I8_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(8)
% 5.12/5.43 thf(fact_8120_xor__numerals_I8_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.12/5.43 = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(8)
% 5.12/5.43 thf(fact_8121_xor__numerals_I5_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(5)
% 5.12/5.43 thf(fact_8122_xor__numerals_I5_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.12/5.43 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(5)
% 5.12/5.43 thf(fact_8123_xor__numerals_I2_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(2)
% 5.12/5.43 thf(fact_8124_xor__numerals_I2_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(2)
% 5.12/5.43 thf(fact_8125_xor__numerals_I1_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(1)
% 5.12/5.43 thf(fact_8126_xor__numerals_I1_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(1)
% 5.12/5.43 thf(fact_8127_push__bit__Suc,axiom,
% 5.12/5.43 ! [N: nat,A: int] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc
% 5.12/5.43 thf(fact_8128_push__bit__Suc,axiom,
% 5.12/5.43 ! [N: nat,A: nat] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 5.12/5.43 = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_Suc
% 5.12/5.43 thf(fact_8129_push__bit__of__1,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 5.12/5.43 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_1
% 5.12/5.43 thf(fact_8130_push__bit__of__1,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 5.12/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_1
% 5.12/5.43 thf(fact_8131_push__bit__of__Suc__0,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_Suc_0
% 5.12/5.43 thf(fact_8132_even__push__bit__iff,axiom,
% 5.12/5.43 ! [N: nat,A: code_integer] :
% 5.12/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N @ A ) )
% 5.12/5.43 = ( ( N != zero_zero_nat )
% 5.12/5.43 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % even_push_bit_iff
% 5.12/5.43 thf(fact_8133_even__push__bit__iff,axiom,
% 5.12/5.43 ! [N: nat,A: int] :
% 5.12/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.12/5.43 = ( ( N != zero_zero_nat )
% 5.12/5.43 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % even_push_bit_iff
% 5.12/5.43 thf(fact_8134_even__push__bit__iff,axiom,
% 5.12/5.43 ! [N: nat,A: nat] :
% 5.12/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.12/5.43 = ( ( N != zero_zero_nat )
% 5.12/5.43 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % even_push_bit_iff
% 5.12/5.43 thf(fact_8135_push__bit__minus__numeral,axiom,
% 5.12/5.43 ! [L: num,K: num] :
% 5.12/5.43 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.12/5.43 = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus_numeral
% 5.12/5.43 thf(fact_8136_push__bit__minus__numeral,axiom,
% 5.12/5.43 ! [L: num,K: num] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus_numeral
% 5.12/5.43 thf(fact_8137_xor__nat__numerals_I1_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_numerals(1)
% 5.12/5.43 thf(fact_8138_xor__nat__numerals_I2_J,axiom,
% 5.12/5.43 ! [Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_numerals(2)
% 5.12/5.43 thf(fact_8139_xor__nat__numerals_I3_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_numerals(3)
% 5.12/5.43 thf(fact_8140_xor__nat__numerals_I4_J,axiom,
% 5.12/5.43 ! [X: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.43 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_numerals(4)
% 5.12/5.43 thf(fact_8141_Suc__0__mod__numeral,axiom,
% 5.12/5.43 ! [K: num] :
% 5.12/5.43 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.43 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Suc_0_mod_numeral
% 5.12/5.43 thf(fact_8142_xor__numerals_I4_J,axiom,
% 5.12/5.43 ! [X: num,Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.43 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(4)
% 5.12/5.43 thf(fact_8143_xor__numerals_I4_J,axiom,
% 5.12/5.43 ! [X: num,Y: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.12/5.43 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(4)
% 5.12/5.43 thf(fact_8144_xor__numerals_I6_J,axiom,
% 5.12/5.43 ! [X: num,Y: num] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.43 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(6)
% 5.12/5.43 thf(fact_8145_xor__numerals_I6_J,axiom,
% 5.12/5.43 ! [X: num,Y: num] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.12/5.43 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_numerals(6)
% 5.12/5.43 thf(fact_8146_Compl__eq,axiom,
% 5.12/5.43 ( uminus8566677241136511917omplex
% 5.12/5.43 = ( ^ [A6: set_complex] :
% 5.12/5.43 ( collect_complex
% 5.12/5.43 @ ^ [X2: complex] :
% 5.12/5.43 ~ ( member_complex @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8147_Compl__eq,axiom,
% 5.12/5.43 ( uminus612125837232591019t_real
% 5.12/5.43 = ( ^ [A6: set_real] :
% 5.12/5.43 ( collect_real
% 5.12/5.43 @ ^ [X2: real] :
% 5.12/5.43 ~ ( member_real @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8148_Compl__eq,axiom,
% 5.12/5.43 ( uminus3195874150345416415st_nat
% 5.12/5.43 = ( ^ [A6: set_list_nat] :
% 5.12/5.43 ( collect_list_nat
% 5.12/5.43 @ ^ [X2: list_nat] :
% 5.12/5.43 ~ ( member_list_nat @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8149_Compl__eq,axiom,
% 5.12/5.43 ( uminus613421341184616069et_nat
% 5.12/5.43 = ( ^ [A6: set_set_nat] :
% 5.12/5.43 ( collect_set_nat
% 5.12/5.43 @ ^ [X2: set_nat] :
% 5.12/5.43 ~ ( member_set_nat @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8150_Compl__eq,axiom,
% 5.12/5.43 ( uminus5710092332889474511et_nat
% 5.12/5.43 = ( ^ [A6: set_nat] :
% 5.12/5.43 ( collect_nat
% 5.12/5.43 @ ^ [X2: nat] :
% 5.12/5.43 ~ ( member_nat @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8151_Compl__eq,axiom,
% 5.12/5.43 ( uminus1532241313380277803et_int
% 5.12/5.43 = ( ^ [A6: set_int] :
% 5.12/5.43 ( collect_int
% 5.12/5.43 @ ^ [X2: int] :
% 5.12/5.43 ~ ( member_int @ X2 @ A6 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Compl_eq
% 5.12/5.43 thf(fact_8152_Collect__neg__eq,axiom,
% 5.12/5.43 ! [P: real > $o] :
% 5.12/5.43 ( ( collect_real
% 5.12/5.43 @ ^ [X2: real] :
% 5.12/5.43 ~ ( P @ X2 ) )
% 5.12/5.43 = ( uminus612125837232591019t_real @ ( collect_real @ P ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Collect_neg_eq
% 5.12/5.43 thf(fact_8153_Collect__neg__eq,axiom,
% 5.12/5.43 ! [P: list_nat > $o] :
% 5.12/5.43 ( ( collect_list_nat
% 5.12/5.43 @ ^ [X2: list_nat] :
% 5.12/5.43 ~ ( P @ X2 ) )
% 5.12/5.43 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Collect_neg_eq
% 5.12/5.43 thf(fact_8154_Collect__neg__eq,axiom,
% 5.12/5.43 ! [P: set_nat > $o] :
% 5.12/5.43 ( ( collect_set_nat
% 5.12/5.43 @ ^ [X2: set_nat] :
% 5.12/5.43 ~ ( P @ X2 ) )
% 5.12/5.43 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Collect_neg_eq
% 5.12/5.43 thf(fact_8155_Collect__neg__eq,axiom,
% 5.12/5.43 ! [P: nat > $o] :
% 5.12/5.43 ( ( collect_nat
% 5.12/5.43 @ ^ [X2: nat] :
% 5.12/5.43 ~ ( P @ X2 ) )
% 5.12/5.43 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Collect_neg_eq
% 5.12/5.43 thf(fact_8156_Collect__neg__eq,axiom,
% 5.12/5.43 ! [P: int > $o] :
% 5.12/5.43 ( ( collect_int
% 5.12/5.43 @ ^ [X2: int] :
% 5.12/5.43 ~ ( P @ X2 ) )
% 5.12/5.43 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Collect_neg_eq
% 5.12/5.43 thf(fact_8157_uminus__set__def,axiom,
% 5.12/5.43 ( uminus8566677241136511917omplex
% 5.12/5.43 = ( ^ [A6: set_complex] :
% 5.12/5.43 ( collect_complex
% 5.12/5.43 @ ( uminus1680532995456772888plex_o
% 5.12/5.43 @ ^ [X2: complex] : ( member_complex @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8158_uminus__set__def,axiom,
% 5.12/5.43 ( uminus612125837232591019t_real
% 5.12/5.43 = ( ^ [A6: set_real] :
% 5.12/5.43 ( collect_real
% 5.12/5.43 @ ( uminus_uminus_real_o
% 5.12/5.43 @ ^ [X2: real] : ( member_real @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8159_uminus__set__def,axiom,
% 5.12/5.43 ( uminus3195874150345416415st_nat
% 5.12/5.43 = ( ^ [A6: set_list_nat] :
% 5.12/5.43 ( collect_list_nat
% 5.12/5.43 @ ( uminus5770388063884162150_nat_o
% 5.12/5.43 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8160_uminus__set__def,axiom,
% 5.12/5.43 ( uminus613421341184616069et_nat
% 5.12/5.43 = ( ^ [A6: set_set_nat] :
% 5.12/5.43 ( collect_set_nat
% 5.12/5.43 @ ( uminus6401447641752708672_nat_o
% 5.12/5.43 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8161_uminus__set__def,axiom,
% 5.12/5.43 ( uminus5710092332889474511et_nat
% 5.12/5.43 = ( ^ [A6: set_nat] :
% 5.12/5.43 ( collect_nat
% 5.12/5.43 @ ( uminus_uminus_nat_o
% 5.12/5.43 @ ^ [X2: nat] : ( member_nat @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8162_uminus__set__def,axiom,
% 5.12/5.43 ( uminus1532241313380277803et_int
% 5.12/5.43 = ( ^ [A6: set_int] :
% 5.12/5.43 ( collect_int
% 5.12/5.43 @ ( uminus_uminus_int_o
% 5.12/5.43 @ ^ [X2: int] : ( member_int @ X2 @ A6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % uminus_set_def
% 5.12/5.43 thf(fact_8163_push__bit__minus,axiom,
% 5.12/5.43 ! [N: nat,A: code_integer] :
% 5.12/5.43 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus
% 5.12/5.43 thf(fact_8164_push__bit__minus,axiom,
% 5.12/5.43 ! [N: nat,A: int] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus
% 5.12/5.43 thf(fact_8165_numeral__code_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.12/5.43 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(2)
% 5.12/5.43 thf(fact_8166_numeral__code_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.12/5.43 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(2)
% 5.12/5.43 thf(fact_8167_numeral__code_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.12/5.43 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(2)
% 5.12/5.43 thf(fact_8168_numeral__code_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.12/5.43 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(2)
% 5.12/5.43 thf(fact_8169_numeral__code_I2_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.12/5.43 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(2)
% 5.12/5.43 thf(fact_8170_strict__subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: real,B: real] :
% 5.12/5.43 ( ( ord_less_set_real
% 5.12/5.43 @ ( collect_real
% 5.12/5.43 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.12/5.43 @ ( collect_real
% 5.12/5.43 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.12/5.43 = ( ( dvd_dvd_real @ A @ B )
% 5.12/5.43 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % strict_subset_divisors_dvd
% 5.12/5.43 thf(fact_8171_strict__subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: nat,B: nat] :
% 5.12/5.43 ( ( ord_less_set_nat
% 5.12/5.43 @ ( collect_nat
% 5.12/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.12/5.43 @ ( collect_nat
% 5.12/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.12/5.43 = ( ( dvd_dvd_nat @ A @ B )
% 5.12/5.43 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % strict_subset_divisors_dvd
% 5.12/5.43 thf(fact_8172_strict__subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: int,B: int] :
% 5.12/5.43 ( ( ord_less_set_int
% 5.12/5.43 @ ( collect_int
% 5.12/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.12/5.43 @ ( collect_int
% 5.12/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.12/5.43 = ( ( dvd_dvd_int @ A @ B )
% 5.12/5.43 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % strict_subset_divisors_dvd
% 5.12/5.43 thf(fact_8173_strict__subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: code_integer,B: code_integer] :
% 5.12/5.43 ( ( ord_le1307284697595431911nteger
% 5.12/5.43 @ ( collect_Code_integer
% 5.12/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.12/5.43 @ ( collect_Code_integer
% 5.12/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.12/5.43 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.12/5.43 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % strict_subset_divisors_dvd
% 5.12/5.43 thf(fact_8174_flip__bit__nat__def,axiom,
% 5.12/5.43 ( bit_se2161824704523386999it_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % flip_bit_nat_def
% 5.12/5.43 thf(fact_8175_lambda__one,axiom,
% 5.12/5.43 ( ( ^ [X2: complex] : X2 )
% 5.12/5.43 = ( times_times_complex @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_one
% 5.12/5.43 thf(fact_8176_lambda__one,axiom,
% 5.12/5.43 ( ( ^ [X2: real] : X2 )
% 5.12/5.43 = ( times_times_real @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_one
% 5.12/5.43 thf(fact_8177_lambda__one,axiom,
% 5.12/5.43 ( ( ^ [X2: rat] : X2 )
% 5.12/5.43 = ( times_times_rat @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_one
% 5.12/5.43 thf(fact_8178_lambda__one,axiom,
% 5.12/5.43 ( ( ^ [X2: nat] : X2 )
% 5.12/5.43 = ( times_times_nat @ one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_one
% 5.12/5.43 thf(fact_8179_lambda__one,axiom,
% 5.12/5.43 ( ( ^ [X2: int] : X2 )
% 5.12/5.43 = ( times_times_int @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_one
% 5.12/5.43 thf(fact_8180_flip__bit__eq__xor,axiom,
% 5.12/5.43 ( bit_se2159334234014336723it_int
% 5.12/5.43 = ( ^ [N4: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % flip_bit_eq_xor
% 5.12/5.43 thf(fact_8181_flip__bit__eq__xor,axiom,
% 5.12/5.43 ( bit_se2161824704523386999it_nat
% 5.12/5.43 = ( ^ [N4: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % flip_bit_eq_xor
% 5.12/5.43 thf(fact_8182_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_o @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8183_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: $o > nat,F1: $o,F22: nat > $o,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_nat @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8184_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: $o > option_num,F1: $o,F22: nat > $o,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_option_num @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8185_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_o @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8186_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: nat > nat,F1: nat,F22: nat > nat,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_nat @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8187_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: nat > option_num,F1: nat,F22: nat > nat,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_option_num @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8188_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_o @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8189_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: option_num > nat,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_nat @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8190_nat_Ocase__distrib,axiom,
% 5.12/5.43 ! [H: option_num > option_num,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.12/5.43 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.12/5.43 = ( case_nat_option_num @ ( H @ F1 )
% 5.12/5.43 @ ^ [X2: nat] : ( H @ ( F22 @ X2 ) )
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.case_distrib
% 5.12/5.43 thf(fact_8191_push__bit__of__nat,axiom,
% 5.12/5.43 ! [N: nat,M2: nat] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ ( semiri1314217659103216013at_int @ M2 ) )
% 5.12/5.43 = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N @ M2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_nat
% 5.12/5.43 thf(fact_8192_push__bit__of__nat,axiom,
% 5.12/5.43 ! [N: nat,M2: nat] :
% 5.12/5.43 ( ( bit_se547839408752420682it_nat @ N @ ( semiri1316708129612266289at_nat @ M2 ) )
% 5.12/5.43 = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N @ M2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_of_nat
% 5.12/5.43 thf(fact_8193_of__nat__push__bit,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ M2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_push_bit
% 5.12/5.43 thf(fact_8194_of__nat__push__bit,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se547839408752420682it_nat @ M2 @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_push_bit
% 5.12/5.43 thf(fact_8195_of__nat__xor__eq,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_xor_eq
% 5.12/5.43 thf(fact_8196_of__nat__xor__eq,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M2 @ N ) )
% 5.12/5.43 = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_xor_eq
% 5.12/5.43 thf(fact_8197_nat_Odisc__eq__case_I2_J,axiom,
% 5.12/5.43 ! [Nat: nat] :
% 5.12/5.43 ( ( Nat != zero_zero_nat )
% 5.12/5.43 = ( case_nat_o @ $false
% 5.12/5.43 @ ^ [Uu3: nat] : $true
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.disc_eq_case(2)
% 5.12/5.43 thf(fact_8198_nat_Odisc__eq__case_I1_J,axiom,
% 5.12/5.43 ! [Nat: nat] :
% 5.12/5.43 ( ( Nat = zero_zero_nat )
% 5.12/5.43 = ( case_nat_o @ $true
% 5.12/5.43 @ ^ [Uu3: nat] : $false
% 5.12/5.43 @ Nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat.disc_eq_case(1)
% 5.12/5.43 thf(fact_8199_lambda__zero,axiom,
% 5.12/5.43 ( ( ^ [H2: real] : zero_zero_real )
% 5.12/5.43 = ( times_times_real @ zero_zero_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_zero
% 5.12/5.43 thf(fact_8200_lambda__zero,axiom,
% 5.12/5.43 ( ( ^ [H2: rat] : zero_zero_rat )
% 5.12/5.43 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_zero
% 5.12/5.43 thf(fact_8201_lambda__zero,axiom,
% 5.12/5.43 ( ( ^ [H2: nat] : zero_zero_nat )
% 5.12/5.43 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_zero
% 5.12/5.43 thf(fact_8202_lambda__zero,axiom,
% 5.12/5.43 ( ( ^ [H2: int] : zero_zero_int )
% 5.12/5.43 = ( times_times_int @ zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % lambda_zero
% 5.12/5.43 thf(fact_8203_pred__def,axiom,
% 5.12/5.43 ( pred
% 5.12/5.43 = ( case_nat_nat @ zero_zero_nat
% 5.12/5.43 @ ^ [X25: nat] : X25 ) ) ).
% 5.12/5.43
% 5.12/5.43 % pred_def
% 5.12/5.43 thf(fact_8204_less__eq__nat_Osimps_I2_J,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 5.12/5.43 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N ) ) ).
% 5.12/5.43
% 5.12/5.43 % less_eq_nat.simps(2)
% 5.12/5.43 thf(fact_8205_set__diff__eq,axiom,
% 5.12/5.43 ( minus_811609699411566653omplex
% 5.12/5.43 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.12/5.43 ( collect_complex
% 5.12/5.43 @ ^ [X2: complex] :
% 5.12/5.43 ( ( member_complex @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8206_set__diff__eq,axiom,
% 5.12/5.43 ( minus_minus_set_real
% 5.12/5.43 = ( ^ [A6: set_real,B6: set_real] :
% 5.12/5.43 ( collect_real
% 5.12/5.43 @ ^ [X2: real] :
% 5.12/5.43 ( ( member_real @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8207_set__diff__eq,axiom,
% 5.12/5.43 ( minus_7954133019191499631st_nat
% 5.12/5.43 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.12/5.43 ( collect_list_nat
% 5.12/5.43 @ ^ [X2: list_nat] :
% 5.12/5.43 ( ( member_list_nat @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8208_set__diff__eq,axiom,
% 5.12/5.43 ( minus_2163939370556025621et_nat
% 5.12/5.43 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.12/5.43 ( collect_set_nat
% 5.12/5.43 @ ^ [X2: set_nat] :
% 5.12/5.43 ( ( member_set_nat @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_set_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8209_set__diff__eq,axiom,
% 5.12/5.43 ( minus_minus_set_int
% 5.12/5.43 = ( ^ [A6: set_int,B6: set_int] :
% 5.12/5.43 ( collect_int
% 5.12/5.43 @ ^ [X2: int] :
% 5.12/5.43 ( ( member_int @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8210_set__diff__eq,axiom,
% 5.12/5.43 ( minus_1356011639430497352at_nat
% 5.12/5.43 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( collec3392354462482085612at_nat
% 5.12/5.43 @ ^ [X2: product_prod_nat_nat] :
% 5.12/5.43 ( ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.12/5.43 & ~ ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8211_set__diff__eq,axiom,
% 5.12/5.43 ( minus_minus_set_nat
% 5.12/5.43 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.12/5.43 ( collect_nat
% 5.12/5.43 @ ^ [X2: nat] :
% 5.12/5.43 ( ( member_nat @ X2 @ A6 )
% 5.12/5.43 & ~ ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_diff_eq
% 5.12/5.43 thf(fact_8212_minus__set__def,axiom,
% 5.12/5.43 ( minus_811609699411566653omplex
% 5.12/5.43 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.12/5.43 ( collect_complex
% 5.12/5.43 @ ( minus_8727706125548526216plex_o
% 5.12/5.43 @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: complex] : ( member_complex @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8213_minus__set__def,axiom,
% 5.12/5.43 ( minus_minus_set_real
% 5.12/5.43 = ( ^ [A6: set_real,B6: set_real] :
% 5.12/5.43 ( collect_real
% 5.12/5.43 @ ( minus_minus_real_o
% 5.12/5.43 @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: real] : ( member_real @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8214_minus__set__def,axiom,
% 5.12/5.43 ( minus_7954133019191499631st_nat
% 5.12/5.43 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.12/5.43 ( collect_list_nat
% 5.12/5.43 @ ( minus_1139252259498527702_nat_o
% 5.12/5.43 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8215_minus__set__def,axiom,
% 5.12/5.43 ( minus_2163939370556025621et_nat
% 5.12/5.43 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.12/5.43 ( collect_set_nat
% 5.12/5.43 @ ( minus_6910147592129066416_nat_o
% 5.12/5.43 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8216_minus__set__def,axiom,
% 5.12/5.43 ( minus_minus_set_int
% 5.12/5.43 = ( ^ [A6: set_int,B6: set_int] :
% 5.12/5.43 ( collect_int
% 5.12/5.43 @ ( minus_minus_int_o
% 5.12/5.43 @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: int] : ( member_int @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8217_minus__set__def,axiom,
% 5.12/5.43 ( minus_1356011639430497352at_nat
% 5.12/5.43 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.12/5.43 ( collec3392354462482085612at_nat
% 5.12/5.43 @ ( minus_2270307095948843157_nat_o
% 5.12/5.43 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8218_minus__set__def,axiom,
% 5.12/5.43 ( minus_minus_set_nat
% 5.12/5.43 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.12/5.43 ( collect_nat
% 5.12/5.43 @ ( minus_minus_nat_o
% 5.12/5.43 @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 5.12/5.43 @ ^ [X2: nat] : ( member_nat @ X2 @ B6 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_set_def
% 5.12/5.43 thf(fact_8219_subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: real,B: real] :
% 5.12/5.43 ( ( ord_less_eq_set_real
% 5.12/5.43 @ ( collect_real
% 5.12/5.43 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 5.12/5.43 @ ( collect_real
% 5.12/5.43 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 5.12/5.43 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_divisors_dvd
% 5.12/5.43 thf(fact_8220_subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: int,B: int] :
% 5.12/5.43 ( ( ord_less_eq_set_int
% 5.12/5.43 @ ( collect_int
% 5.12/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.12/5.43 @ ( collect_int
% 5.12/5.43 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.12/5.43 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_divisors_dvd
% 5.12/5.43 thf(fact_8221_subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: code_integer,B: code_integer] :
% 5.12/5.43 ( ( ord_le7084787975880047091nteger
% 5.12/5.43 @ ( collect_Code_integer
% 5.12/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.12/5.43 @ ( collect_Code_integer
% 5.12/5.43 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.12/5.43 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_divisors_dvd
% 5.12/5.43 thf(fact_8222_subset__divisors__dvd,axiom,
% 5.12/5.43 ! [A: nat,B: nat] :
% 5.12/5.43 ( ( ord_less_eq_set_nat
% 5.12/5.43 @ ( collect_nat
% 5.12/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.12/5.43 @ ( collect_nat
% 5.12/5.43 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.12/5.43 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.12/5.43
% 5.12/5.43 % subset_divisors_dvd
% 5.12/5.43 thf(fact_8223_diff__Suc,axiom,
% 5.12/5.43 ! [M2: nat,N: nat] :
% 5.12/5.43 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 = ( case_nat_nat @ zero_zero_nat
% 5.12/5.43 @ ^ [K3: nat] : K3
% 5.12/5.43 @ ( minus_minus_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % diff_Suc
% 5.12/5.43 thf(fact_8224_nat__less__as__int,axiom,
% 5.12/5.43 ( ord_less_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_less_as_int
% 5.12/5.43 thf(fact_8225_nat__leq__as__int,axiom,
% 5.12/5.43 ( ord_less_eq_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_leq_as_int
% 5.12/5.43 thf(fact_8226_numeral__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.12/5.43 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(3)
% 5.12/5.43 thf(fact_8227_numeral__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.12/5.43 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(3)
% 5.12/5.43 thf(fact_8228_numeral__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.12/5.43 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(3)
% 5.12/5.43 thf(fact_8229_numeral__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.12/5.43 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(3)
% 5.12/5.43 thf(fact_8230_numeral__code_I3_J,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.12/5.43 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % numeral_code(3)
% 5.12/5.43 thf(fact_8231_set__vebt__def,axiom,
% 5.12/5.43 ( vEBT_set_vebt
% 5.12/5.43 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_vebt_def
% 5.12/5.43 thf(fact_8232_nat__plus__as__int,axiom,
% 5.12/5.43 ( plus_plus_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_plus_as_int
% 5.12/5.43 thf(fact_8233_nat__times__as__int,axiom,
% 5.12/5.43 ( times_times_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_times_as_int
% 5.12/5.43 thf(fact_8234_nat__minus__as__int,axiom,
% 5.12/5.43 ( minus_minus_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_minus_as_int
% 5.12/5.43 thf(fact_8235_nat__div__as__int,axiom,
% 5.12/5.43 ( divide_divide_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_div_as_int
% 5.12/5.43 thf(fact_8236_nat__mod__as__int,axiom,
% 5.12/5.43 ( modulo_modulo_nat
% 5.12/5.43 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % nat_mod_as_int
% 5.12/5.43 thf(fact_8237_signed__take__bit__code,axiom,
% 5.12/5.43 ( bit_ri6519982836138164636nteger
% 5.12/5.43 = ( ^ [N4: nat,A3: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A3 ) @ N4 ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A3 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N4 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A3 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % signed_take_bit_code
% 5.12/5.43 thf(fact_8238_signed__take__bit__code,axiom,
% 5.12/5.43 ( bit_ri631733984087533419it_int
% 5.12/5.43 = ( ^ [N4: nat,A3: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A3 ) @ N4 ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A3 ) @ ( bit_se545348938243370406it_int @ ( suc @ N4 ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A3 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % signed_take_bit_code
% 5.12/5.43 thf(fact_8239_take__bit__push__bit,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,A: int] :
% 5.12/5.43 ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.12/5.43 = ( bit_se545348938243370406it_int @ N @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M2 @ N ) @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % take_bit_push_bit
% 5.12/5.43 thf(fact_8240_take__bit__push__bit,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,A: nat] :
% 5.12/5.43 ( ( bit_se2925701944663578781it_nat @ M2 @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.12/5.43 = ( bit_se547839408752420682it_nat @ N @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M2 @ N ) @ A ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % take_bit_push_bit
% 5.12/5.43 thf(fact_8241_diff__nat__eq__if,axiom,
% 5.12/5.43 ! [Z3: int,Z2: int] :
% 5.12/5.43 ( ( ( ord_less_int @ Z3 @ zero_zero_int )
% 5.12/5.43 => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z3 ) )
% 5.12/5.43 = ( nat2 @ Z2 ) ) )
% 5.12/5.43 & ( ~ ( ord_less_int @ Z3 @ zero_zero_int )
% 5.12/5.43 => ( ( minus_minus_nat @ ( nat2 @ Z2 ) @ ( nat2 @ Z3 ) )
% 5.12/5.43 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z2 @ Z3 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z2 @ Z3 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % diff_nat_eq_if
% 5.12/5.43 thf(fact_8242_bit__push__bit__iff__int,axiom,
% 5.12/5.43 ! [M2: nat,K: int,N: nat] :
% 5.12/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K ) @ N )
% 5.12/5.43 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_push_bit_iff_int
% 5.12/5.43 thf(fact_8243_set__decode__def,axiom,
% 5.12/5.43 ( nat_set_decode
% 5.12/5.43 = ( ^ [X2: nat] :
% 5.12/5.43 ( collect_nat
% 5.12/5.43 @ ^ [N4: nat] :
% 5.12/5.43 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_decode_def
% 5.12/5.43 thf(fact_8244_bit__push__bit__iff__nat,axiom,
% 5.12/5.43 ! [M2: nat,Q5: nat,N: nat] :
% 5.12/5.43 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q5 ) @ N )
% 5.12/5.43 = ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 & ( bit_se1148574629649215175it_nat @ Q5 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_push_bit_iff_nat
% 5.12/5.43 thf(fact_8245_pochhammer__code,axiom,
% 5.12/5.43 ( comm_s2602460028002588243omplex
% 5.12/5.43 = ( ^ [A3: complex,N4: nat] :
% 5.12/5.43 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 5.12/5.43 @ ( set_fo1517530859248394432omplex
% 5.12/5.43 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.12/5.43 @ one_one_complex ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_code
% 5.12/5.43 thf(fact_8246_pochhammer__code,axiom,
% 5.12/5.43 ( comm_s7457072308508201937r_real
% 5.12/5.43 = ( ^ [A3: real,N4: nat] :
% 5.12/5.43 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 5.12/5.43 @ ( set_fo3111899725591712190t_real
% 5.12/5.43 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.12/5.43 @ one_one_real ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_code
% 5.12/5.43 thf(fact_8247_pochhammer__code,axiom,
% 5.12/5.43 ( comm_s4028243227959126397er_rat
% 5.12/5.43 = ( ^ [A3: rat,N4: nat] :
% 5.12/5.43 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 5.12/5.43 @ ( set_fo1949268297981939178at_rat
% 5.12/5.43 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.12/5.43 @ one_one_rat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_code
% 5.12/5.43 thf(fact_8248_pochhammer__code,axiom,
% 5.12/5.43 ( comm_s4660882817536571857er_int
% 5.12/5.43 = ( ^ [A3: int,N4: nat] :
% 5.12/5.43 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 5.12/5.43 @ ( set_fo2581907887559384638at_int
% 5.12/5.43 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.12/5.43 @ one_one_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_code
% 5.12/5.43 thf(fact_8249_pochhammer__code,axiom,
% 5.12/5.43 ( comm_s4663373288045622133er_nat
% 5.12/5.43 = ( ^ [A3: nat,N4: nat] :
% 5.12/5.43 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 5.12/5.43 @ ( set_fo2584398358068434914at_nat
% 5.12/5.43 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.12/5.43 @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_code
% 5.12/5.43 thf(fact_8250_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.12/5.43 ( bit_se1146084159140164899it_int
% 5.12/5.43 = ( ^ [A3: int,N4: nat] :
% 5.12/5.43 ( ( bit_se725231765392027082nd_int @ A3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) )
% 5.12/5.43 != zero_zero_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_iff_and_push_bit_not_eq_0
% 5.12/5.43 thf(fact_8251_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.12/5.43 ( bit_se1148574629649215175it_nat
% 5.12/5.43 = ( ^ [A3: nat,N4: nat] :
% 5.12/5.43 ( ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) )
% 5.12/5.43 != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_iff_and_push_bit_not_eq_0
% 5.12/5.43 thf(fact_8252_gbinomial__code,axiom,
% 5.12/5.43 ( gbinomial_complex
% 5.12/5.43 = ( ^ [A3: complex,K3: nat] :
% 5.12/5.43 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.12/5.43 @ ( divide1717551699836669952omplex
% 5.12/5.43 @ ( set_fo1517530859248394432omplex
% 5.12/5.43 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.12/5.43 @ one_one_complex )
% 5.12/5.43 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_code
% 5.12/5.43 thf(fact_8253_gbinomial__code,axiom,
% 5.12/5.43 ( gbinomial_rat
% 5.12/5.43 = ( ^ [A3: rat,K3: nat] :
% 5.12/5.43 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.12/5.43 @ ( divide_divide_rat
% 5.12/5.43 @ ( set_fo1949268297981939178at_rat
% 5.12/5.43 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.12/5.43 @ one_one_rat )
% 5.12/5.43 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_code
% 5.12/5.43 thf(fact_8254_gbinomial__code,axiom,
% 5.12/5.43 ( gbinomial_real
% 5.12/5.43 = ( ^ [A3: real,K3: nat] :
% 5.12/5.43 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.12/5.43 @ ( divide_divide_real
% 5.12/5.43 @ ( set_fo3111899725591712190t_real
% 5.12/5.43 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.12/5.43 @ zero_zero_nat
% 5.12/5.43 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.12/5.43 @ one_one_real )
% 5.12/5.43 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_code
% 5.12/5.43 thf(fact_8255_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.12/5.43 ! [Uy2: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.12/5.43 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V ) @ TreeList @ S ) @ X )
% 5.12/5.43 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.43 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.naive_member.simps(3)
% 5.12/5.43 thf(fact_8256_push__bit__minus__one,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus_one
% 5.12/5.43 thf(fact_8257_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.12/5.43 ! [V: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 5.12/5.43 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd2 ) @ X )
% 5.12/5.43 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.simps(5)
% 5.12/5.43 thf(fact_8258_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.12/5.43 ! [Mi2: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.12/5.43 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 5.12/5.43 = ( ( X = Mi2 )
% 5.12/5.43 | ( X = Ma )
% 5.12/5.43 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.simps(4)
% 5.12/5.43 thf(fact_8259_vebt__member_Osimps_I5_J,axiom,
% 5.12/5.43 ! [Mi2: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.12/5.43 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 5.12/5.43 = ( ( X != Mi2 )
% 5.12/5.43 => ( ( X != Ma )
% 5.12/5.43 => ( ~ ( ord_less_nat @ X @ Mi2 )
% 5.12/5.43 & ( ~ ( ord_less_nat @ X @ Mi2 )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.12/5.43 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_member.simps(5)
% 5.12/5.43 thf(fact_8260_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.43 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.12/5.43 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [S2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.naive_member.elims(3)
% 5.12/5.43 thf(fact_8261_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.43 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [S2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.43 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.naive_member.elims(2)
% 5.12/5.43 thf(fact_8262_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.43 ( ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.12/5.43 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [S2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.naive_member.elims(1)
% 5.12/5.43 thf(fact_8263_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat] :
% 5.12/5.43 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.43 => ~ ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 ) ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vc2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.43 => ~ ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 )
% 5.12/5.43 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.12/5.43 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vd: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.43 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.elims(2)
% 5.12/5.43 thf(fact_8264_xor__nat__unfold,axiom,
% 5.12/5.43 ( bit_se6528837805403552850or_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_unfold
% 5.12/5.43 thf(fact_8265_xor__nat__rec,axiom,
% 5.12/5.43 ( bit_se6528837805403552850or_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.43 ( plus_plus_nat
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.12/5.43 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.12/5.43 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_rec
% 5.12/5.43 thf(fact_8266_xor__one__eq,axiom,
% 5.12/5.43 ! [A: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 5.12/5.43 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n356916108424825756nteger
% 5.12/5.43 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_one_eq
% 5.12/5.43 thf(fact_8267_xor__one__eq,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 5.12/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_one_eq
% 5.12/5.43 thf(fact_8268_xor__one__eq,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 5.12/5.43 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_one_eq
% 5.12/5.43 thf(fact_8269_one__xor__eq,axiom,
% 5.12/5.43 ! [A: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 5.12/5.43 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n356916108424825756nteger
% 5.12/5.43 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_xor_eq
% 5.12/5.43 thf(fact_8270_one__xor__eq,axiom,
% 5.12/5.43 ! [A: nat] :
% 5.12/5.43 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 5.12/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_xor_eq
% 5.12/5.43 thf(fact_8271_one__xor__eq,axiom,
% 5.12/5.43 ! [A: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 5.12/5.43 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % one_xor_eq
% 5.12/5.43 thf(fact_8272_vebt__member_Oelims_I2_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.43 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Summary2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.43 => ~ ( ( Xa != Mi )
% 5.12/5.43 => ( ( Xa != Ma2 )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_member.elims(2)
% 5.12/5.43 thf(fact_8273_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.43 ( ~ ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.43 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.43 => ( ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat] :
% 5.12/5.43 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.43 => ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 ) ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vc2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.43 => ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 )
% 5.12/5.43 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.12/5.43 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vd: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.elims(3)
% 5.12/5.43 thf(fact_8274_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.43 ( ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ( ( ? [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat] :
% 5.12/5.43 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 ) ) ) ) )
% 5.12/5.43 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vc2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( Xa = Mi )
% 5.12/5.43 | ( Xa = Ma2 )
% 5.12/5.43 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.12/5.43 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Vd: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % VEBT_internal.membermima.elims(1)
% 5.12/5.43 thf(fact_8275_bit__horner__sum__bit__iff,axiom,
% 5.12/5.43 ! [Bs: list_o,N: nat] :
% 5.12/5.43 ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.12/5.43 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.12/5.43 & ( nth_o @ Bs @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_horner_sum_bit_iff
% 5.12/5.43 thf(fact_8276_bit__horner__sum__bit__iff,axiom,
% 5.12/5.43 ! [Bs: list_o,N: nat] :
% 5.12/5.43 ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.12/5.43 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.12/5.43 & ( nth_o @ Bs @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit_horner_sum_bit_iff
% 5.12/5.43 thf(fact_8277_vebt__member_Oelims_I1_J,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.43 ( ( ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ! [A4: $o,B3: $o] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.43 => A4 )
% 5.12/5.43 & ( ( Xa != zero_zero_nat )
% 5.12/5.43 => ( ( ( Xa = one_one_nat )
% 5.12/5.43 => B3 )
% 5.12/5.43 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.12/5.43 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ( ( ? [V3: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ( ( ? [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.12/5.43 => Y )
% 5.12/5.43 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.12/5.43 ( ? [Summary2: vEBT_VEBT] :
% 5.12/5.43 ( X
% 5.12/5.43 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( ~ ( ( Xa != Mi )
% 5.12/5.43 => ( ( Xa != Ma2 )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.43 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.43 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.43 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.43 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_member.elims(1)
% 5.12/5.43 thf(fact_8278_of__int__code__if,axiom,
% 5.12/5.43 ( ring_1_of_int_int
% 5.12/5.43 = ( ^ [K3: int] :
% 5.12/5.43 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.12/5.43 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.43 @ ( if_int
% 5.12/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_code_if
% 5.12/5.43 thf(fact_8279_of__int__code__if,axiom,
% 5.12/5.43 ( ring_1_of_int_real
% 5.12/5.43 = ( ^ [K3: int] :
% 5.12/5.43 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.12/5.43 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.43 @ ( if_real
% 5.12/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_code_if
% 5.12/5.43 thf(fact_8280_of__int__code__if,axiom,
% 5.12/5.43 ( ring_17405671764205052669omplex
% 5.12/5.43 = ( ^ [K3: int] :
% 5.12/5.43 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.12/5.43 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.43 @ ( if_complex
% 5.12/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_code_if
% 5.12/5.43 thf(fact_8281_of__int__code__if,axiom,
% 5.12/5.43 ( ring_18347121197199848620nteger
% 5.12/5.43 = ( ^ [K3: int] :
% 5.12/5.43 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.12/5.43 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.43 @ ( if_Code_integer
% 5.12/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_code_if
% 5.12/5.43 thf(fact_8282_of__int__code__if,axiom,
% 5.12/5.43 ( ring_1_of_int_rat
% 5.12/5.43 = ( ^ [K3: int] :
% 5.12/5.43 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.12/5.43 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.43 @ ( if_rat
% 5.12/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.43 = zero_zero_int )
% 5.12/5.43 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.43 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_code_if
% 5.12/5.43 thf(fact_8283_monoseq__arctan__series,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.43 => ( topolo6980174941875973593q_real
% 5.12/5.43 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % monoseq_arctan_series
% 5.12/5.43 thf(fact_8284_pochhammer__times__pochhammer__half,axiom,
% 5.12/5.43 ! [Z2: complex,N: nat] :
% 5.12/5.43 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z2 @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.12/5.43 = ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [K3: nat] : ( plus_plus_complex @ Z2 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_times_pochhammer_half
% 5.12/5.43 thf(fact_8285_pochhammer__times__pochhammer__half,axiom,
% 5.12/5.43 ! [Z2: real,N: nat] :
% 5.12/5.43 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z2 @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [K3: nat] : ( plus_plus_real @ Z2 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_times_pochhammer_half
% 5.12/5.43 thf(fact_8286_pochhammer__times__pochhammer__half,axiom,
% 5.12/5.43 ! [Z2: rat,N: nat] :
% 5.12/5.43 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z2 @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [K3: nat] : ( plus_plus_rat @ Z2 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_times_pochhammer_half
% 5.12/5.43 thf(fact_8287_ln__series,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.43 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.43 => ( ( ln_ln_real @ X )
% 5.12/5.43 = ( suminf_real
% 5.12/5.43 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % ln_series
% 5.12/5.43 thf(fact_8288_xor__nonnegative__int__iff,axiom,
% 5.12/5.43 ! [K: int,L: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.12/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.43 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nonnegative_int_iff
% 5.12/5.43 thf(fact_8289_xor__negative__int__iff,axiom,
% 5.12/5.43 ! [K: int,L: int] :
% 5.12/5.43 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.12/5.43 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.43 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_negative_int_iff
% 5.12/5.43 thf(fact_8290_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > complex] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.43 => ( member_complex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8291_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > int] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( member_int @ ( F @ X3 ) @ ring_1_Ints_int ) )
% 5.12/5.43 => ( member_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ring_1_Ints_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8292_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > complex] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.43 => ( member_complex @ ( groups713298508707869441omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8293_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > int] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( member_int @ ( F @ X3 ) @ ring_1_Ints_int ) )
% 5.12/5.43 => ( member_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ring_1_Ints_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8294_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > complex] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.43 => ( member_complex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8295_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > complex] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.43 => ( member_complex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8296_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > real] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.43 => ( member_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8297_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > real] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.43 => ( member_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8298_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > real] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.43 => ( member_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8299_Ints__prod,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > real] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.43 => ( member_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ints_prod
% 5.12/5.43 thf(fact_8300_of__nat__prod,axiom,
% 5.12/5.43 ! [F: int > nat,A2: set_int] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8301_of__nat__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri8010041392384452111omplex @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [X2: nat] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8302_of__nat__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8303_of__nat__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [X2: nat] : ( semiri681578069525770553at_rat @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8304_of__nat__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8305_of__nat__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_nat_prod
% 5.12/5.43 thf(fact_8306_of__int__prod,axiom,
% 5.12/5.43 ! [F: nat > int,A2: set_nat] :
% 5.12/5.43 ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8307_of__int__prod,axiom,
% 5.12/5.43 ! [F: nat > int,A2: set_nat] :
% 5.12/5.43 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [X2: nat] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8308_of__int__prod,axiom,
% 5.12/5.43 ! [F: nat > int,A2: set_nat] :
% 5.12/5.43 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A2 ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [X2: nat] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8309_of__int__prod,axiom,
% 5.12/5.43 ! [F: int > int,A2: set_int] :
% 5.12/5.43 ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.12/5.43 = ( groups2316167850115554303t_real
% 5.12/5.43 @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8310_of__int__prod,axiom,
% 5.12/5.43 ! [F: int > int,A2: set_int] :
% 5.12/5.43 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.12/5.43 = ( groups1072433553688619179nt_rat
% 5.12/5.43 @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8311_of__int__prod,axiom,
% 5.12/5.43 ! [F: int > int,A2: set_int] :
% 5.12/5.43 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 5.12/5.43 = ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % of_int_prod
% 5.12/5.43 thf(fact_8312_powser__zero,axiom,
% 5.12/5.43 ! [F: nat > complex] :
% 5.12/5.43 ( ( suminf_complex
% 5.12/5.43 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) )
% 5.12/5.43 = ( F @ zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % powser_zero
% 5.12/5.43 thf(fact_8313_powser__zero,axiom,
% 5.12/5.43 ! [F: nat > real] :
% 5.12/5.43 ( ( suminf_real
% 5.12/5.43 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) )
% 5.12/5.43 = ( F @ zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % powser_zero
% 5.12/5.43 thf(fact_8314_prod_Ocl__ivl__Suc,axiom,
% 5.12/5.43 ! [N: nat,M2: nat,G: nat > complex] :
% 5.12/5.43 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = one_one_complex ) )
% 5.12/5.43 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.cl_ivl_Suc
% 5.12/5.43 thf(fact_8315_prod_Ocl__ivl__Suc,axiom,
% 5.12/5.43 ! [N: nat,M2: nat,G: nat > real] :
% 5.12/5.43 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = one_one_real ) )
% 5.12/5.43 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.cl_ivl_Suc
% 5.12/5.43 thf(fact_8316_prod_Ocl__ivl__Suc,axiom,
% 5.12/5.43 ! [N: nat,M2: nat,G: nat > rat] :
% 5.12/5.43 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = one_one_rat ) )
% 5.12/5.43 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.cl_ivl_Suc
% 5.12/5.43 thf(fact_8317_prod_Ocl__ivl__Suc,axiom,
% 5.12/5.43 ! [N: nat,M2: nat,G: nat > nat] :
% 5.12/5.43 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = one_one_nat ) )
% 5.12/5.43 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.cl_ivl_Suc
% 5.12/5.43 thf(fact_8318_prod_Ocl__ivl__Suc,axiom,
% 5.12/5.43 ! [N: nat,M2: nat,G: nat > int] :
% 5.12/5.43 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = one_one_int ) )
% 5.12/5.43 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.cl_ivl_Suc
% 5.12/5.43 thf(fact_8319_XOR__lower,axiom,
% 5.12/5.43 ! [X: int,Y: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % XOR_lower
% 5.12/5.43 thf(fact_8320_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.12/5.43 ! [G: nat > nat,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.shift_bounds_cl_Suc_ivl
% 5.12/5.43 thf(fact_8321_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.12/5.43 ! [G: nat > int,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.shift_bounds_cl_Suc_ivl
% 5.12/5.43 thf(fact_8322_flip__bit__int__def,axiom,
% 5.12/5.43 ( bit_se2159334234014336723it_int
% 5.12/5.43 = ( ^ [N4: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % flip_bit_int_def
% 5.12/5.43 thf(fact_8323_xor__nat__def,axiom,
% 5.12/5.43 ( bit_se6528837805403552850or_nat
% 5.12/5.43 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_nat_def
% 5.12/5.43 thf(fact_8324_prod_OatLeastAtMost__rev,axiom,
% 5.12/5.43 ! [G: nat > nat,N: nat,M2: nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeastAtMost_rev
% 5.12/5.43 thf(fact_8325_prod_OatLeastAtMost__rev,axiom,
% 5.12/5.43 ! [G: nat > int,N: nat,M2: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeastAtMost_rev
% 5.12/5.43 thf(fact_8326_prod_OatLeast0__atMost__Suc,axiom,
% 5.12/5.43 ! [G: nat > real,N: nat] :
% 5.12/5.43 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast0_atMost_Suc
% 5.12/5.43 thf(fact_8327_prod_OatLeast0__atMost__Suc,axiom,
% 5.12/5.43 ! [G: nat > rat,N: nat] :
% 5.12/5.43 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast0_atMost_Suc
% 5.12/5.43 thf(fact_8328_prod_OatLeast0__atMost__Suc,axiom,
% 5.12/5.43 ! [G: nat > nat,N: nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast0_atMost_Suc
% 5.12/5.43 thf(fact_8329_prod_OatLeast0__atMost__Suc,axiom,
% 5.12/5.43 ! [G: nat > int,N: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast0_atMost_Suc
% 5.12/5.43 thf(fact_8330_prod_OatLeast__Suc__atMost,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.43 = ( times_times_real @ ( G @ M2 ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast_Suc_atMost
% 5.12/5.43 thf(fact_8331_prod_OatLeast__Suc__atMost,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.43 = ( times_times_rat @ ( G @ M2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast_Suc_atMost
% 5.12/5.43 thf(fact_8332_prod_OatLeast__Suc__atMost,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.43 = ( times_times_nat @ ( G @ M2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast_Suc_atMost
% 5.12/5.43 thf(fact_8333_prod_OatLeast__Suc__atMost,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.43 = ( times_times_int @ ( G @ M2 ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.atLeast_Suc_atMost
% 5.12/5.43 thf(fact_8334_prod_Onat__ivl__Suc_H,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.nat_ivl_Suc'
% 5.12/5.43 thf(fact_8335_prod_Onat__ivl__Suc_H,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.nat_ivl_Suc'
% 5.12/5.43 thf(fact_8336_prod_Onat__ivl__Suc_H,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.nat_ivl_Suc'
% 5.12/5.43 thf(fact_8337_prod_Onat__ivl__Suc_H,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.nat_ivl_Suc'
% 5.12/5.43 thf(fact_8338_prod_OSuc__reindex__ivl,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_real @ ( G @ M2 )
% 5.12/5.43 @ ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.Suc_reindex_ivl
% 5.12/5.43 thf(fact_8339_prod_OSuc__reindex__ivl,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_rat @ ( G @ M2 )
% 5.12/5.43 @ ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.Suc_reindex_ivl
% 5.12/5.43 thf(fact_8340_prod_OSuc__reindex__ivl,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_nat @ ( G @ M2 )
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.Suc_reindex_ivl
% 5.12/5.43 thf(fact_8341_prod_OSuc__reindex__ivl,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.43 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.43 = ( times_times_int @ ( G @ M2 )
% 5.12/5.43 @ ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.Suc_reindex_ivl
% 5.12/5.43 thf(fact_8342_fact__prod,axiom,
% 5.12/5.43 ( semiri5044797733671781792omplex
% 5.12/5.43 = ( ^ [N4: nat] :
% 5.12/5.43 ( semiri8010041392384452111omplex
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_prod
% 5.12/5.43 thf(fact_8343_fact__prod,axiom,
% 5.12/5.43 ( semiri773545260158071498ct_rat
% 5.12/5.43 = ( ^ [N4: nat] :
% 5.12/5.43 ( semiri681578069525770553at_rat
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_prod
% 5.12/5.43 thf(fact_8344_fact__prod,axiom,
% 5.12/5.43 ( semiri1406184849735516958ct_int
% 5.12/5.43 = ( ^ [N4: nat] :
% 5.12/5.43 ( semiri1314217659103216013at_int
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_prod
% 5.12/5.43 thf(fact_8345_fact__prod,axiom,
% 5.12/5.43 ( semiri1408675320244567234ct_nat
% 5.12/5.43 = ( ^ [N4: nat] :
% 5.12/5.43 ( semiri1316708129612266289at_nat
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_prod
% 5.12/5.43 thf(fact_8346_fact__prod,axiom,
% 5.12/5.43 ( semiri2265585572941072030t_real
% 5.12/5.43 = ( ^ [N4: nat] :
% 5.12/5.43 ( semiri5074537144036343181t_real
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_prod
% 5.12/5.43 thf(fact_8347_prod__atLeastAtMost__code,axiom,
% 5.12/5.43 ! [F: nat > complex,A: nat,B: nat] :
% 5.12/5.43 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.43 = ( set_fo1517530859248394432omplex
% 5.12/5.43 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 5.12/5.43 @ A
% 5.12/5.43 @ B
% 5.12/5.43 @ one_one_complex ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_atLeastAtMost_code
% 5.12/5.43 thf(fact_8348_prod__atLeastAtMost__code,axiom,
% 5.12/5.43 ! [F: nat > real,A: nat,B: nat] :
% 5.12/5.43 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.43 = ( set_fo3111899725591712190t_real
% 5.12/5.43 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 5.12/5.43 @ A
% 5.12/5.43 @ B
% 5.12/5.43 @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_atLeastAtMost_code
% 5.12/5.43 thf(fact_8349_prod__atLeastAtMost__code,axiom,
% 5.12/5.43 ! [F: nat > rat,A: nat,B: nat] :
% 5.12/5.43 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.43 = ( set_fo1949268297981939178at_rat
% 5.12/5.43 @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 5.12/5.43 @ A
% 5.12/5.43 @ B
% 5.12/5.43 @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_atLeastAtMost_code
% 5.12/5.43 thf(fact_8350_prod__atLeastAtMost__code,axiom,
% 5.12/5.43 ! [F: nat > nat,A: nat,B: nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.43 = ( set_fo2584398358068434914at_nat
% 5.12/5.43 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 5.12/5.43 @ A
% 5.12/5.43 @ B
% 5.12/5.43 @ one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_atLeastAtMost_code
% 5.12/5.43 thf(fact_8351_prod__atLeastAtMost__code,axiom,
% 5.12/5.43 ! [F: nat > int,A: nat,B: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.43 = ( set_fo2581907887559384638at_int
% 5.12/5.43 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 5.12/5.43 @ A
% 5.12/5.43 @ B
% 5.12/5.43 @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_atLeastAtMost_code
% 5.12/5.43 thf(fact_8352_prod_Oub__add__nat,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > real,P4: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.43 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.43 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.ub_add_nat
% 5.12/5.43 thf(fact_8353_prod_Oub__add__nat,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > rat,P4: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.43 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.43 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.ub_add_nat
% 5.12/5.43 thf(fact_8354_prod_Oub__add__nat,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > nat,P4: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.43 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.ub_add_nat
% 5.12/5.43 thf(fact_8355_prod_Oub__add__nat,axiom,
% 5.12/5.43 ! [M2: nat,N: nat,G: nat > int,P4: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.43 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.ub_add_nat
% 5.12/5.43 thf(fact_8356_fact__eq__fact__times,axiom,
% 5.12/5.43 ! [N: nat,M2: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.43 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 5.12/5.43 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_eq_fact_times
% 5.12/5.43 thf(fact_8357_monoseq__realpow,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.43 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.43 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % monoseq_realpow
% 5.12/5.43 thf(fact_8358_pochhammer__Suc__prod,axiom,
% 5.12/5.43 ! [A: complex,N: nat] :
% 5.12/5.43 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod
% 5.12/5.43 thf(fact_8359_pochhammer__Suc__prod,axiom,
% 5.12/5.43 ! [A: real,N: nat] :
% 5.12/5.43 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod
% 5.12/5.43 thf(fact_8360_pochhammer__Suc__prod,axiom,
% 5.12/5.43 ! [A: rat,N: nat] :
% 5.12/5.43 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod
% 5.12/5.43 thf(fact_8361_pochhammer__Suc__prod,axiom,
% 5.12/5.43 ! [A: nat,N: nat] :
% 5.12/5.43 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod
% 5.12/5.43 thf(fact_8362_pochhammer__Suc__prod,axiom,
% 5.12/5.43 ! [A: int,N: nat] :
% 5.12/5.43 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod
% 5.12/5.43 thf(fact_8363_pochhammer__prod__rev,axiom,
% 5.12/5.43 ( comm_s2602460028002588243omplex
% 5.12/5.43 = ( ^ [A3: complex,N4: nat] :
% 5.12/5.43 ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N4 @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_prod_rev
% 5.12/5.43 thf(fact_8364_pochhammer__prod__rev,axiom,
% 5.12/5.43 ( comm_s7457072308508201937r_real
% 5.12/5.43 = ( ^ [A3: real,N4: nat] :
% 5.12/5.43 ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N4 @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_prod_rev
% 5.12/5.43 thf(fact_8365_pochhammer__prod__rev,axiom,
% 5.12/5.43 ( comm_s4028243227959126397er_rat
% 5.12/5.43 = ( ^ [A3: rat,N4: nat] :
% 5.12/5.43 ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N4 @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_prod_rev
% 5.12/5.43 thf(fact_8366_pochhammer__prod__rev,axiom,
% 5.12/5.43 ( comm_s4663373288045622133er_nat
% 5.12/5.43 = ( ^ [A3: nat,N4: nat] :
% 5.12/5.43 ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N4 @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_prod_rev
% 5.12/5.43 thf(fact_8367_pochhammer__prod__rev,axiom,
% 5.12/5.43 ( comm_s4660882817536571857er_int
% 5.12/5.43 = ( ^ [A3: int,N4: nat] :
% 5.12/5.43 ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N4 @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_prod_rev
% 5.12/5.43 thf(fact_8368_fact__div__fact,axiom,
% 5.12/5.43 ! [N: nat,M2: nat] :
% 5.12/5.43 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.43 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [X2: nat] : X2
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % fact_div_fact
% 5.12/5.43 thf(fact_8369_XOR__upper,axiom,
% 5.12/5.43 ! [X: int,N: nat,Y: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.43 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.43 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.43 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % XOR_upper
% 5.12/5.43 thf(fact_8370_prod_Oin__pairs,axiom,
% 5.12/5.43 ! [G: nat > real,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.in_pairs
% 5.12/5.43 thf(fact_8371_prod_Oin__pairs,axiom,
% 5.12/5.43 ! [G: nat > rat,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.in_pairs
% 5.12/5.43 thf(fact_8372_prod_Oin__pairs,axiom,
% 5.12/5.43 ! [G: nat > nat,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.in_pairs
% 5.12/5.43 thf(fact_8373_prod_Oin__pairs,axiom,
% 5.12/5.43 ! [G: nat > int,M2: nat,N: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.in_pairs
% 5.12/5.43 thf(fact_8374_pochhammer__Suc__prod__rev,axiom,
% 5.12/5.43 ! [A: complex,N: nat] :
% 5.12/5.43 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod_rev
% 5.12/5.43 thf(fact_8375_pochhammer__Suc__prod__rev,axiom,
% 5.12/5.43 ! [A: real,N: nat] :
% 5.12/5.43 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod_rev
% 5.12/5.43 thf(fact_8376_pochhammer__Suc__prod__rev,axiom,
% 5.12/5.43 ! [A: rat,N: nat] :
% 5.12/5.43 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod_rev
% 5.12/5.43 thf(fact_8377_pochhammer__Suc__prod__rev,axiom,
% 5.12/5.43 ! [A: nat,N: nat] :
% 5.12/5.43 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod_rev
% 5.12/5.43 thf(fact_8378_pochhammer__Suc__prod__rev,axiom,
% 5.12/5.43 ! [A: int,N: nat] :
% 5.12/5.43 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pochhammer_Suc_prod_rev
% 5.12/5.43 thf(fact_8379_gbinomial__Suc,axiom,
% 5.12/5.43 ! [A: complex,K: nat] :
% 5.12/5.43 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.12/5.43 = ( divide1717551699836669952omplex
% 5.12/5.43 @ ( groups6464643781859351333omplex
% 5.12/5.43 @ ^ [I2: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.12/5.43 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_Suc
% 5.12/5.43 thf(fact_8380_gbinomial__Suc,axiom,
% 5.12/5.43 ! [A: rat,K: nat] :
% 5.12/5.43 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.12/5.43 = ( divide_divide_rat
% 5.12/5.43 @ ( groups73079841787564623at_rat
% 5.12/5.43 @ ^ [I2: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.12/5.43 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_Suc
% 5.12/5.43 thf(fact_8381_gbinomial__Suc,axiom,
% 5.12/5.43 ! [A: real,K: nat] :
% 5.12/5.43 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.12/5.43 = ( divide_divide_real
% 5.12/5.43 @ ( groups129246275422532515t_real
% 5.12/5.43 @ ^ [I2: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.12/5.43 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_Suc
% 5.12/5.43 thf(fact_8382_gbinomial__Suc,axiom,
% 5.12/5.43 ! [A: nat,K: nat] :
% 5.12/5.43 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.12/5.43 = ( divide_divide_nat
% 5.12/5.43 @ ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [I2: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.12/5.43 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_Suc
% 5.12/5.43 thf(fact_8383_gbinomial__Suc,axiom,
% 5.12/5.43 ! [A: int,K: nat] :
% 5.12/5.43 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.12/5.43 = ( divide_divide_int
% 5.12/5.43 @ ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [I2: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I2 ) )
% 5.12/5.43 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.12/5.43 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % gbinomial_Suc
% 5.12/5.43 thf(fact_8384_xor__int__rec,axiom,
% 5.12/5.43 ( bit_se6526347334894502574or_int
% 5.12/5.43 = ( ^ [K3: int,L2: int] :
% 5.12/5.43 ( plus_plus_int
% 5.12/5.43 @ ( zero_n2684676970156552555ol_int
% 5.12/5.43 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.12/5.43 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.12/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_int_rec
% 5.12/5.43 thf(fact_8385_pi__series,axiom,
% 5.12/5.43 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.12/5.43 = ( suminf_real
% 5.12/5.43 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % pi_series
% 5.12/5.43 thf(fact_8386_arctan__series,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.43 => ( ( arctan @ X )
% 5.12/5.43 = ( suminf_real
% 5.12/5.43 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % arctan_series
% 5.12/5.43 thf(fact_8387_suminf__geometric,axiom,
% 5.12/5.43 ! [C: real] :
% 5.12/5.43 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.12/5.43 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.12/5.43 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % suminf_geometric
% 5.12/5.43 thf(fact_8388_suminf__geometric,axiom,
% 5.12/5.43 ! [C: complex] :
% 5.12/5.43 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.12/5.43 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.12/5.43 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % suminf_geometric
% 5.12/5.43 thf(fact_8389_prod_Oempty,axiom,
% 5.12/5.43 ! [G: nat > complex] :
% 5.12/5.43 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.12/5.43 = one_one_complex ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8390_prod_Oempty,axiom,
% 5.12/5.43 ! [G: nat > real] :
% 5.12/5.43 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.12/5.43 = one_one_real ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8391_prod_Oempty,axiom,
% 5.12/5.43 ! [G: nat > rat] :
% 5.12/5.43 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.12/5.43 = one_one_rat ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8392_prod_Oempty,axiom,
% 5.12/5.43 ! [G: int > complex] :
% 5.12/5.43 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.12/5.43 = one_one_complex ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8393_prod_Oempty,axiom,
% 5.12/5.43 ! [G: int > real] :
% 5.12/5.43 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.12/5.43 = one_one_real ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8394_prod_Oempty,axiom,
% 5.12/5.43 ! [G: int > rat] :
% 5.12/5.43 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.12/5.43 = one_one_rat ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8395_prod_Oempty,axiom,
% 5.12/5.43 ! [G: int > nat] :
% 5.12/5.43 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.12/5.43 = one_one_nat ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8396_prod_Oempty,axiom,
% 5.12/5.43 ! [G: nat > nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat @ G @ bot_bot_set_nat )
% 5.12/5.43 = one_one_nat ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8397_prod_Oempty,axiom,
% 5.12/5.43 ! [G: nat > int] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ G @ bot_bot_set_nat )
% 5.12/5.43 = one_one_int ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8398_prod_Oempty,axiom,
% 5.12/5.43 ! [G: int > int] :
% 5.12/5.43 ( ( groups1705073143266064639nt_int @ G @ bot_bot_set_int )
% 5.12/5.43 = one_one_int ) ).
% 5.12/5.43
% 5.12/5.43 % prod.empty
% 5.12/5.43 thf(fact_8399_suminf__zero,axiom,
% 5.12/5.43 ( ( suminf_real
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_real )
% 5.12/5.43 = zero_zero_real ) ).
% 5.12/5.43
% 5.12/5.43 % suminf_zero
% 5.12/5.43 thf(fact_8400_suminf__zero,axiom,
% 5.12/5.43 ( ( suminf_nat
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_nat )
% 5.12/5.43 = zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % suminf_zero
% 5.12/5.43 thf(fact_8401_suminf__zero,axiom,
% 5.12/5.43 ( ( suminf_int
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_int )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % suminf_zero
% 5.12/5.43 thf(fact_8402_prod_Oneutral__const,axiom,
% 5.12/5.43 ! [A2: set_nat] :
% 5.12/5.43 ( ( groups708209901874060359at_nat
% 5.12/5.43 @ ^ [Uu3: nat] : one_one_nat
% 5.12/5.43 @ A2 )
% 5.12/5.43 = one_one_nat ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral_const
% 5.12/5.43 thf(fact_8403_prod_Oneutral__const,axiom,
% 5.12/5.43 ! [A2: set_nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [Uu3: nat] : one_one_int
% 5.12/5.43 @ A2 )
% 5.12/5.43 = one_one_int ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral_const
% 5.12/5.43 thf(fact_8404_prod_Oneutral__const,axiom,
% 5.12/5.43 ! [A2: set_int] :
% 5.12/5.43 ( ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [Uu3: int] : one_one_int
% 5.12/5.43 @ A2 )
% 5.12/5.43 = one_one_int ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral_const
% 5.12/5.43 thf(fact_8405_int__prod,axiom,
% 5.12/5.43 ! [F: int > nat,A2: set_int] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % int_prod
% 5.12/5.43 thf(fact_8406_int__prod,axiom,
% 5.12/5.43 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.43 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 5.12/5.43 = ( groups705719431365010083at_int
% 5.12/5.43 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.43 @ A2 ) ) ).
% 5.12/5.43
% 5.12/5.43 % int_prod
% 5.12/5.43 thf(fact_8407_prod__int__eq,axiom,
% 5.12/5.43 ! [I: nat,J2: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J2 ) )
% 5.12/5.43 = ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [X2: int] : X2
% 5.12/5.43 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_int_eq
% 5.12/5.43 thf(fact_8408_prod__int__plus__eq,axiom,
% 5.12/5.43 ! [I: nat,J2: nat] :
% 5.12/5.43 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J2 ) ) )
% 5.12/5.43 = ( groups1705073143266064639nt_int
% 5.12/5.43 @ ^ [X2: int] : X2
% 5.12/5.43 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J2 ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_int_plus_eq
% 5.12/5.43 thf(fact_8409_prod_Oneutral,axiom,
% 5.12/5.43 ! [A2: set_nat,G: nat > nat] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ( G @ X3 )
% 5.12/5.43 = one_one_nat ) )
% 5.12/5.43 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.12/5.43 = one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral
% 5.12/5.43 thf(fact_8410_prod_Oneutral,axiom,
% 5.12/5.43 ! [A2: set_nat,G: nat > int] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ( G @ X3 )
% 5.12/5.43 = one_one_int ) )
% 5.12/5.43 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.12/5.43 = one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral
% 5.12/5.43 thf(fact_8411_prod_Oneutral,axiom,
% 5.12/5.43 ! [A2: set_int,G: int > int] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ( G @ X3 )
% 5.12/5.43 = one_one_int ) )
% 5.12/5.43 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.12/5.43 = one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.neutral
% 5.12/5.43 thf(fact_8412_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: complex > complex,A2: set_complex] :
% 5.12/5.43 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.12/5.43 != one_one_complex )
% 5.12/5.43 => ~ ! [A4: complex] :
% 5.12/5.43 ( ( member_complex @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_complex ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8413_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: real > complex,A2: set_real] :
% 5.12/5.43 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.12/5.43 != one_one_complex )
% 5.12/5.43 => ~ ! [A4: real] :
% 5.12/5.43 ( ( member_real @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_complex ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8414_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: nat > complex,A2: set_nat] :
% 5.12/5.43 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.12/5.43 != one_one_complex )
% 5.12/5.43 => ~ ! [A4: nat] :
% 5.12/5.43 ( ( member_nat @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_complex ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8415_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: int > complex,A2: set_int] :
% 5.12/5.43 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.12/5.43 != one_one_complex )
% 5.12/5.43 => ~ ! [A4: int] :
% 5.12/5.43 ( ( member_int @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_complex ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8416_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: complex > real,A2: set_complex] :
% 5.12/5.43 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.12/5.43 != one_one_real )
% 5.12/5.43 => ~ ! [A4: complex] :
% 5.12/5.43 ( ( member_complex @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_real ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8417_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: real > real,A2: set_real] :
% 5.12/5.43 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.12/5.43 != one_one_real )
% 5.12/5.43 => ~ ! [A4: real] :
% 5.12/5.43 ( ( member_real @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_real ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8418_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: nat > real,A2: set_nat] :
% 5.12/5.43 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.12/5.43 != one_one_real )
% 5.12/5.43 => ~ ! [A4: nat] :
% 5.12/5.43 ( ( member_nat @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_real ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8419_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: int > real,A2: set_int] :
% 5.12/5.43 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.12/5.43 != one_one_real )
% 5.12/5.43 => ~ ! [A4: int] :
% 5.12/5.43 ( ( member_int @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_real ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8420_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: complex > rat,A2: set_complex] :
% 5.12/5.43 ( ( ( groups225925009352817453ex_rat @ G @ A2 )
% 5.12/5.43 != one_one_rat )
% 5.12/5.43 => ~ ! [A4: complex] :
% 5.12/5.43 ( ( member_complex @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_rat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8421_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.43 ! [G: real > rat,A2: set_real] :
% 5.12/5.43 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.12/5.43 != one_one_rat )
% 5.12/5.43 => ~ ! [A4: real] :
% 5.12/5.43 ( ( member_real @ A4 @ A2 )
% 5.12/5.43 => ( ( G @ A4 )
% 5.12/5.43 = one_one_rat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod.not_neutral_contains_not_neutral
% 5.12/5.43 thf(fact_8422_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.12/5.43 ( ! [I3: complex] :
% 5.12/5.43 ( ( member_complex @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8423_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > real,G: real > real] :
% 5.12/5.43 ( ! [I3: real] :
% 5.12/5.43 ( ( member_real @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8424_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.12/5.43 ( ! [I3: nat] :
% 5.12/5.43 ( ( member_nat @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8425_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > real,G: int > real] :
% 5.12/5.43 ( ! [I3: int] :
% 5.12/5.43 ( ( member_int @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8426_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.12/5.43 ( ! [I3: complex] :
% 5.12/5.43 ( ( member_complex @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8427_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.12/5.43 ( ! [I3: real] :
% 5.12/5.43 ( ( member_real @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8428_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.12/5.43 ( ! [I3: nat] :
% 5.12/5.43 ( ( member_nat @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8429_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.12/5.43 ( ! [I3: int] :
% 5.12/5.43 ( ( member_int @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8430_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.12/5.43 ( ! [I3: complex] :
% 5.12/5.43 ( ( member_complex @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8431_prod__mono,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.12/5.43 ( ! [I3: real] :
% 5.12/5.43 ( ( member_real @ I3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.12/5.43 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_mono
% 5.12/5.43 thf(fact_8432_prod__nonneg,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > nat] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_nonneg
% 5.12/5.43 thf(fact_8433_prod__nonneg,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > int] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_nonneg
% 5.12/5.43 thf(fact_8434_prod__nonneg,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > int] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_nonneg
% 5.12/5.43 thf(fact_8435_prod__pos,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > nat] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_pos
% 5.12/5.43 thf(fact_8436_prod__pos,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > int] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_pos
% 5.12/5.43 thf(fact_8437_prod__pos,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > int] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_pos
% 5.12/5.43 thf(fact_8438_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > real] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8439_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > real] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8440_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > real] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8441_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > real] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8442_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > rat] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8443_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > rat] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8444_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > rat] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8445_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > rat] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8446_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > nat] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8447_prod__ge__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > nat] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_ge_1
% 5.12/5.43 thf(fact_8448_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > real] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8449_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > real] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8450_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > real] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8451_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > real] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.12/5.43 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8452_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > rat] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8453_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > rat] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8454_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_nat,F: nat > rat] :
% 5.12/5.43 ( ! [X3: nat] :
% 5.12/5.43 ( ( member_nat @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8455_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_int,F: int > rat] :
% 5.12/5.43 ( ! [X3: int] :
% 5.12/5.43 ( ( member_int @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.12/5.43 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8456_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_complex,F: complex > nat] :
% 5.12/5.43 ( ! [X3: complex] :
% 5.12/5.43 ( ( member_complex @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8457_prod__le__1,axiom,
% 5.12/5.43 ! [A2: set_real,F: real > nat] :
% 5.12/5.43 ( ! [X3: real] :
% 5.12/5.43 ( ( member_real @ X3 @ A2 )
% 5.12/5.43 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.12/5.43 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.12/5.43 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % prod_le_1
% 5.12/5.43 thf(fact_8458_bij__betw__nth__root__unity,axiom,
% 5.12/5.43 ! [C: complex,N: nat] :
% 5.12/5.43 ( ( C != zero_zero_complex )
% 5.12/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.43 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.12/5.43 @ ( collect_complex
% 5.12/5.43 @ ^ [Z6: complex] :
% 5.12/5.43 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.43 = one_one_complex ) )
% 5.12/5.43 @ ( collect_complex
% 5.12/5.43 @ ^ [Z6: complex] :
% 5.12/5.43 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.43 = C ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % bij_betw_nth_root_unity
% 5.12/5.43 thf(fact_8459_summable__arctan__series,axiom,
% 5.12/5.43 ! [X: real] :
% 5.12/5.43 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.43 => ( summable_real
% 5.12/5.43 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_arctan_series
% 5.12/5.43 thf(fact_8460_xor__int__unfold,axiom,
% 5.12/5.43 ( bit_se6526347334894502574or_int
% 5.12/5.43 = ( ^ [K3: int,L2: int] :
% 5.12/5.43 ( if_int
% 5.12/5.43 @ ( K3
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.12/5.43 @ ( if_int
% 5.12/5.43 @ ( L2
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.12/5.43 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % xor_int_unfold
% 5.12/5.43 thf(fact_8461_vebt__buildup_Oelims,axiom,
% 5.12/5.43 ! [X: nat,Y: vEBT_VEBT] :
% 5.12/5.43 ( ( ( vEBT_vebt_buildup @ X )
% 5.12/5.43 = Y )
% 5.12/5.43 => ( ( ( X = zero_zero_nat )
% 5.12/5.43 => ( Y
% 5.12/5.43 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.12/5.43 => ( ( ( X
% 5.12/5.43 = ( suc @ zero_zero_nat ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.12/5.43 => ~ ! [Va: nat] :
% 5.12/5.43 ( ( X
% 5.12/5.43 = ( suc @ ( suc @ Va ) ) )
% 5.12/5.43 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( 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 ) ) ) ) ) ) )
% 5.12/5.43 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.12/5.43 => ( Y
% 5.12/5.43 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % vebt_buildup.elims
% 5.12/5.43 thf(fact_8462_intind,axiom,
% 5.12/5.43 ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( P @ X )
% 5.12/5.43 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % intind
% 5.12/5.43 thf(fact_8463_intind,axiom,
% 5.12/5.43 ! [I: nat,N: nat,P: int > $o,X: int] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( P @ X )
% 5.12/5.43 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % intind
% 5.12/5.43 thf(fact_8464_intind,axiom,
% 5.12/5.43 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( P @ X )
% 5.12/5.43 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % intind
% 5.12/5.43 thf(fact_8465_replicate__eq__replicate,axiom,
% 5.12/5.43 ! [M2: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.12/5.43 ( ( ( replicate_VEBT_VEBT @ M2 @ X )
% 5.12/5.43 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.12/5.43 = ( ( M2 = N )
% 5.12/5.43 & ( ( M2 != zero_zero_nat )
% 5.12/5.43 => ( X = Y ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % replicate_eq_replicate
% 5.12/5.43 thf(fact_8466_length__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: vEBT_VEBT] :
% 5.12/5.43 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.12/5.43 = N ) ).
% 5.12/5.43
% 5.12/5.43 % length_replicate
% 5.12/5.43 thf(fact_8467_length__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: $o] :
% 5.12/5.43 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 5.12/5.43 = N ) ).
% 5.12/5.43
% 5.12/5.43 % length_replicate
% 5.12/5.43 thf(fact_8468_length__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: nat] :
% 5.12/5.43 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 5.12/5.43 = N ) ).
% 5.12/5.43
% 5.12/5.43 % length_replicate
% 5.12/5.43 thf(fact_8469_length__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: int] :
% 5.12/5.43 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 5.12/5.43 = N ) ).
% 5.12/5.43
% 5.12/5.43 % length_replicate
% 5.12/5.43 thf(fact_8470_summable__single,axiom,
% 5.12/5.43 ! [I: nat,F: nat > real] :
% 5.12/5.43 ( summable_real
% 5.12/5.43 @ ^ [R: nat] : ( if_real @ ( R = I ) @ ( F @ R ) @ zero_zero_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_single
% 5.12/5.43 thf(fact_8471_summable__single,axiom,
% 5.12/5.43 ! [I: nat,F: nat > nat] :
% 5.12/5.43 ( summable_nat
% 5.12/5.43 @ ^ [R: nat] : ( if_nat @ ( R = I ) @ ( F @ R ) @ zero_zero_nat ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_single
% 5.12/5.43 thf(fact_8472_summable__single,axiom,
% 5.12/5.43 ! [I: nat,F: nat > int] :
% 5.12/5.43 ( summable_int
% 5.12/5.43 @ ^ [R: nat] : ( if_int @ ( R = I ) @ ( F @ R ) @ zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_single
% 5.12/5.43 thf(fact_8473_summable__zero,axiom,
% 5.12/5.43 ( summable_real
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_real ) ).
% 5.12/5.43
% 5.12/5.43 % summable_zero
% 5.12/5.43 thf(fact_8474_summable__zero,axiom,
% 5.12/5.43 ( summable_nat
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_nat ) ).
% 5.12/5.43
% 5.12/5.43 % summable_zero
% 5.12/5.43 thf(fact_8475_summable__zero,axiom,
% 5.12/5.43 ( summable_int
% 5.12/5.43 @ ^ [N4: nat] : zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % summable_zero
% 5.12/5.43 thf(fact_8476_bit_Oconj__cancel__left,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % bit.conj_cancel_left
% 5.12/5.43 thf(fact_8477_bit_Oconj__cancel__right,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se725231765392027082nd_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % bit.conj_cancel_right
% 5.12/5.43 thf(fact_8478_in__set__replicate,axiom,
% 5.12/5.43 ! [X: complex,N: nat,Y: complex] :
% 5.12/5.43 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8479_in__set__replicate,axiom,
% 5.12/5.43 ! [X: real,N: nat,Y: real] :
% 5.12/5.43 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8480_in__set__replicate,axiom,
% 5.12/5.43 ! [X: set_nat,N: nat,Y: set_nat] :
% 5.12/5.43 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8481_in__set__replicate,axiom,
% 5.12/5.43 ! [X: int,N: nat,Y: int] :
% 5.12/5.43 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8482_in__set__replicate,axiom,
% 5.12/5.43 ! [X: nat,N: nat,Y: nat] :
% 5.12/5.43 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8483_in__set__replicate,axiom,
% 5.12/5.43 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.12/5.43 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 5.12/5.43 = ( ( X = Y )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % in_set_replicate
% 5.12/5.43 thf(fact_8484_Bex__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: int,P: int > $o] :
% 5.12/5.43 ( ( ? [X2: int] :
% 5.12/5.43 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.12/5.43 & ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Bex_set_replicate
% 5.12/5.43 thf(fact_8485_Bex__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: nat,P: nat > $o] :
% 5.12/5.43 ( ( ? [X2: nat] :
% 5.12/5.43 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.12/5.43 & ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Bex_set_replicate
% 5.12/5.43 thf(fact_8486_Bex__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.12/5.43 ( ( ? [X2: vEBT_VEBT] :
% 5.12/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.12/5.43 & ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 & ( N != zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Bex_set_replicate
% 5.12/5.43 thf(fact_8487_Ball__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: int,P: int > $o] :
% 5.12/5.43 ( ( ! [X2: int] :
% 5.12/5.43 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.12/5.43 => ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ball_set_replicate
% 5.12/5.43 thf(fact_8488_Ball__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: nat,P: nat > $o] :
% 5.12/5.43 ( ( ! [X2: nat] :
% 5.12/5.43 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.12/5.43 => ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ball_set_replicate
% 5.12/5.43 thf(fact_8489_Ball__set__replicate,axiom,
% 5.12/5.43 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.12/5.43 ( ( ! [X2: vEBT_VEBT] :
% 5.12/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.12/5.43 => ( P @ X2 ) ) )
% 5.12/5.43 = ( ( P @ A )
% 5.12/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % Ball_set_replicate
% 5.12/5.43 thf(fact_8490_nth__replicate,axiom,
% 5.12/5.43 ! [I: nat,N: nat,X: nat] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I )
% 5.12/5.43 = X ) ) ).
% 5.12/5.43
% 5.12/5.43 % nth_replicate
% 5.12/5.43 thf(fact_8491_nth__replicate,axiom,
% 5.12/5.43 ! [I: nat,N: nat,X: int] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( nth_int @ ( replicate_int @ N @ X ) @ I )
% 5.12/5.43 = X ) ) ).
% 5.12/5.43
% 5.12/5.43 % nth_replicate
% 5.12/5.43 thf(fact_8492_nth__replicate,axiom,
% 5.12/5.43 ! [I: nat,N: nat,X: vEBT_VEBT] :
% 5.12/5.43 ( ( ord_less_nat @ I @ N )
% 5.12/5.43 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I )
% 5.12/5.43 = X ) ) ).
% 5.12/5.43
% 5.12/5.43 % nth_replicate
% 5.12/5.43 thf(fact_8493_summable__cmult__iff,axiom,
% 5.12/5.43 ! [C: real,F: nat > real] :
% 5.12/5.43 ( ( summable_real
% 5.12/5.43 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) ) )
% 5.12/5.43 = ( ( C = zero_zero_real )
% 5.12/5.43 | ( summable_real @ F ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_cmult_iff
% 5.12/5.43 thf(fact_8494_summable__divide__iff,axiom,
% 5.12/5.43 ! [F: nat > complex,C: complex] :
% 5.12/5.43 ( ( summable_complex
% 5.12/5.43 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C ) )
% 5.12/5.43 = ( ( C = zero_zero_complex )
% 5.12/5.43 | ( summable_complex @ F ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_divide_iff
% 5.12/5.43 thf(fact_8495_summable__divide__iff,axiom,
% 5.12/5.43 ! [F: nat > real,C: real] :
% 5.12/5.43 ( ( summable_real
% 5.12/5.43 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C ) )
% 5.12/5.43 = ( ( C = zero_zero_real )
% 5.12/5.43 | ( summable_real @ F ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_divide_iff
% 5.12/5.43 thf(fact_8496_bit_Ocompl__zero,axiom,
% 5.12/5.43 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.compl_zero
% 5.12/5.43 thf(fact_8497_bit_Ocompl__zero,axiom,
% 5.12/5.43 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.compl_zero
% 5.12/5.43 thf(fact_8498_bit_Ocompl__one,axiom,
% 5.12/5.43 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 = zero_z3403309356797280102nteger ) ).
% 5.12/5.43
% 5.12/5.43 % bit.compl_one
% 5.12/5.43 thf(fact_8499_bit_Ocompl__one,axiom,
% 5.12/5.43 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = zero_zero_int ) ).
% 5.12/5.43
% 5.12/5.43 % bit.compl_one
% 5.12/5.43 thf(fact_8500_bit_Oxor__one__left,axiom,
% 5.12/5.43 ! [X: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.12/5.43 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_one_left
% 5.12/5.43 thf(fact_8501_bit_Oxor__one__left,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.12/5.43 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_one_left
% 5.12/5.43 thf(fact_8502_bit_Oxor__one__right,axiom,
% 5.12/5.43 ! [X: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_one_right
% 5.12/5.43 thf(fact_8503_bit_Oxor__one__right,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_one_right
% 5.12/5.43 thf(fact_8504_bit_Oxor__cancel__left,axiom,
% 5.12/5.43 ! [X: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_cancel_left
% 5.12/5.43 thf(fact_8505_bit_Oxor__cancel__left,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_cancel_left
% 5.12/5.43 thf(fact_8506_bit_Oxor__cancel__right,axiom,
% 5.12/5.43 ! [X: code_integer] :
% 5.12/5.43 ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_cancel_right
% 5.12/5.43 thf(fact_8507_bit_Oxor__cancel__right,axiom,
% 5.12/5.43 ! [X: int] :
% 5.12/5.43 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.12/5.43 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % bit.xor_cancel_right
% 5.12/5.43 thf(fact_8508_not__nonnegative__int__iff,axiom,
% 5.12/5.43 ! [K: int] :
% 5.12/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.12/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_nonnegative_int_iff
% 5.12/5.43 thf(fact_8509_not__negative__int__iff,axiom,
% 5.12/5.43 ! [K: int] :
% 5.12/5.43 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.12/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_negative_int_iff
% 5.12/5.43 thf(fact_8510_minus__not__numeral__eq,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.12/5.43 = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_not_numeral_eq
% 5.12/5.43 thf(fact_8511_minus__not__numeral__eq,axiom,
% 5.12/5.43 ! [N: num] :
% 5.12/5.43 ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.43 = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % minus_not_numeral_eq
% 5.12/5.43 thf(fact_8512_set__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: vEBT_VEBT] :
% 5.12/5.43 ( ( N != zero_zero_nat )
% 5.12/5.43 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.12/5.43 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_replicate
% 5.12/5.43 thf(fact_8513_set__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: nat] :
% 5.12/5.43 ( ( N != zero_zero_nat )
% 5.12/5.43 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.12/5.43 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_replicate
% 5.12/5.43 thf(fact_8514_set__replicate,axiom,
% 5.12/5.43 ! [N: nat,X: int] :
% 5.12/5.43 ( ( N != zero_zero_nat )
% 5.12/5.43 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.12/5.43 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % set_replicate
% 5.12/5.43 thf(fact_8515_push__bit__minus__one__eq__not__mask,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.12/5.43 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus_one_eq_not_mask
% 5.12/5.43 thf(fact_8516_push__bit__minus__one__eq__not__mask,axiom,
% 5.12/5.43 ! [N: nat] :
% 5.12/5.43 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.43 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % push_bit_minus_one_eq_not_mask
% 5.12/5.43 thf(fact_8517_summable__geometric__iff,axiom,
% 5.12/5.43 ! [C: real] :
% 5.12/5.43 ( ( summable_real @ ( power_power_real @ C ) )
% 5.12/5.43 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_geometric_iff
% 5.12/5.43 thf(fact_8518_summable__geometric__iff,axiom,
% 5.12/5.43 ! [C: complex] :
% 5.12/5.43 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.12/5.43 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.12/5.43
% 5.12/5.43 % summable_geometric_iff
% 5.12/5.43 thf(fact_8519_not__one__eq,axiom,
% 5.12/5.43 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 5.12/5.43 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_one_eq
% 5.12/5.43 thf(fact_8520_not__one__eq,axiom,
% 5.12/5.43 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 5.12/5.43 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.43
% 5.12/5.43 % not_one_eq
% 5.12/5.43 thf(fact_8521_summable__minus__iff,axiom,
% 5.12/5.43 ! [F: nat > real] :
% 5.12/5.43 ( ( summable_real
% 5.12/5.43 @ ^ [N4: nat] : ( uminus_uminus_real @ ( F @ N4 ) ) )
% 5.12/5.44 = ( summable_real @ F ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_minus_iff
% 5.12/5.44 thf(fact_8522_summable__minus__iff,axiom,
% 5.12/5.44 ! [F: nat > complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( uminus1482373934393186551omplex @ ( F @ N4 ) ) )
% 5.12/5.44 = ( summable_complex @ F ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_minus_iff
% 5.12/5.44 thf(fact_8523_summable__minus,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( uminus_uminus_real @ ( F @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_minus
% 5.12/5.44 thf(fact_8524_summable__minus,axiom,
% 5.12/5.44 ! [F: nat > complex] :
% 5.12/5.44 ( ( summable_complex @ F )
% 5.12/5.44 => ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( uminus1482373934393186551omplex @ ( F @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_minus
% 5.12/5.44 thf(fact_8525_summable__diff,axiom,
% 5.12/5.44 ! [F: nat > real,G: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ( summable_real @ G )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_diff
% 5.12/5.44 thf(fact_8526_summable__const__iff,axiom,
% 5.12/5.44 ! [C: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [Uu3: nat] : C )
% 5.12/5.44 = ( C = zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_const_iff
% 5.12/5.44 thf(fact_8527_summable__divide,axiom,
% 5.12/5.44 ! [F: nat > complex,C: complex] :
% 5.12/5.44 ( ( summable_complex @ F )
% 5.12/5.44 => ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_divide
% 5.12/5.44 thf(fact_8528_summable__divide,axiom,
% 5.12/5.44 ! [F: nat > real,C: real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_divide
% 5.12/5.44 thf(fact_8529_summable__Suc__iff,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) ) )
% 5.12/5.44 = ( summable_real @ F ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_Suc_iff
% 5.12/5.44 thf(fact_8530_powser__insidea,axiom,
% 5.12/5.44 ! [F: nat > real,X: real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X @ N4 ) ) )
% 5.12/5.44 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_insidea
% 5.12/5.44 thf(fact_8531_powser__insidea,axiom,
% 5.12/5.44 ! [F: nat > complex,X: complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ X @ N4 ) ) )
% 5.12/5.44 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_insidea
% 5.12/5.44 thf(fact_8532_not__diff__distrib,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 5.12/5.44 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_diff_distrib
% 5.12/5.44 thf(fact_8533_not__add__distrib,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 5.12/5.44 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_add_distrib
% 5.12/5.44 thf(fact_8534_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_complex,N: nat,X: complex] :
% 5.12/5.44 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: complex] :
% 5.12/5.44 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_complex @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8535_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_real,N: nat,X: real] :
% 5.12/5.44 ( ( ( size_size_list_real @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: real] :
% 5.12/5.44 ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_real @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8536_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_set_nat,N: nat,X: set_nat] :
% 5.12/5.44 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: set_nat] :
% 5.12/5.44 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8537_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.12/5.44 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: vEBT_VEBT] :
% 5.12/5.44 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8538_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_o,N: nat,X: $o] :
% 5.12/5.44 ( ( ( size_size_list_o @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: $o] :
% 5.12/5.44 ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_o @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8539_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_nat,N: nat,X: nat] :
% 5.12/5.44 ( ( ( size_size_list_nat @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: nat] :
% 5.12/5.44 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_nat @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8540_replicate__eqI,axiom,
% 5.12/5.44 ! [Xs: list_int,N: nat,X: int] :
% 5.12/5.44 ( ( ( size_size_list_int @ Xs )
% 5.12/5.44 = N )
% 5.12/5.44 => ( ! [Y3: int] :
% 5.12/5.44 ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 5.12/5.44 => ( Y3 = X ) )
% 5.12/5.44 => ( Xs
% 5.12/5.44 = ( replicate_int @ N @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_eqI
% 5.12/5.44 thf(fact_8541_replicate__length__same,axiom,
% 5.12/5.44 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.12/5.44 ( ! [X3: vEBT_VEBT] :
% 5.12/5.44 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.12/5.44 => ( X3 = X ) )
% 5.12/5.44 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X )
% 5.12/5.44 = Xs ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_length_same
% 5.12/5.44 thf(fact_8542_replicate__length__same,axiom,
% 5.12/5.44 ! [Xs: list_o,X: $o] :
% 5.12/5.44 ( ! [X3: $o] :
% 5.12/5.44 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.12/5.44 => ( X3 = X ) )
% 5.12/5.44 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X )
% 5.12/5.44 = Xs ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_length_same
% 5.12/5.44 thf(fact_8543_replicate__length__same,axiom,
% 5.12/5.44 ! [Xs: list_nat,X: nat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.12/5.44 => ( X3 = X ) )
% 5.12/5.44 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X )
% 5.12/5.44 = Xs ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_length_same
% 5.12/5.44 thf(fact_8544_replicate__length__same,axiom,
% 5.12/5.44 ! [Xs: list_int,X: int] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.12/5.44 => ( X3 = X ) )
% 5.12/5.44 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X )
% 5.12/5.44 = Xs ) ) ).
% 5.12/5.44
% 5.12/5.44 % replicate_length_same
% 5.12/5.44 thf(fact_8545_summable__mult__D,axiom,
% 5.12/5.44 ! [C: real,F: nat > real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) ) )
% 5.12/5.44 => ( ( C != zero_zero_real )
% 5.12/5.44 => ( summable_real @ F ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_mult_D
% 5.12/5.44 thf(fact_8546_summable__zero__power,axiom,
% 5.12/5.44 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power
% 5.12/5.44 thf(fact_8547_summable__zero__power,axiom,
% 5.12/5.44 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power
% 5.12/5.44 thf(fact_8548_summable__zero__power,axiom,
% 5.12/5.44 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power
% 5.12/5.44 thf(fact_8549_suminf__diff,axiom,
% 5.12/5.44 ! [F: nat > real,G: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ( summable_real @ G )
% 5.12/5.44 => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.12/5.44 = ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_diff
% 5.12/5.44 thf(fact_8550_suminf__divide,axiom,
% 5.12/5.44 ! [F: nat > complex,C: complex] :
% 5.12/5.44 ( ( summable_complex @ F )
% 5.12/5.44 => ( ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C ) )
% 5.12/5.44 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_divide
% 5.12/5.44 thf(fact_8551_suminf__divide,axiom,
% 5.12/5.44 ! [F: nat > real,C: real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C ) )
% 5.12/5.44 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_divide
% 5.12/5.44 thf(fact_8552_suminf__minus,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( uminus_uminus_real @ ( F @ N4 ) ) )
% 5.12/5.44 = ( uminus_uminus_real @ ( suminf_real @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_minus
% 5.12/5.44 thf(fact_8553_suminf__minus,axiom,
% 5.12/5.44 ! [F: nat > complex] :
% 5.12/5.44 ( ( summable_complex @ F )
% 5.12/5.44 => ( ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( uminus1482373934393186551omplex @ ( F @ N4 ) ) )
% 5.12/5.44 = ( uminus1482373934393186551omplex @ ( suminf_complex @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_minus
% 5.12/5.44 thf(fact_8554_suminf__eq__zero__iff,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ( suminf_real @ F )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 = ( ! [N4: nat] :
% 5.12/5.44 ( ( F @ N4 )
% 5.12/5.44 = zero_zero_real ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_eq_zero_iff
% 5.12/5.44 thf(fact_8555_suminf__eq__zero__iff,axiom,
% 5.12/5.44 ! [F: nat > nat] :
% 5.12/5.44 ( ( summable_nat @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ( suminf_nat @ F )
% 5.12/5.44 = zero_zero_nat )
% 5.12/5.44 = ( ! [N4: nat] :
% 5.12/5.44 ( ( F @ N4 )
% 5.12/5.44 = zero_zero_nat ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_eq_zero_iff
% 5.12/5.44 thf(fact_8556_suminf__eq__zero__iff,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( ( summable_int @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ( suminf_int @ F )
% 5.12/5.44 = zero_zero_int )
% 5.12/5.44 = ( ! [N4: nat] :
% 5.12/5.44 ( ( F @ N4 )
% 5.12/5.44 = zero_zero_int ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_eq_zero_iff
% 5.12/5.44 thf(fact_8557_suminf__nonneg,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_nonneg
% 5.12/5.44 thf(fact_8558_suminf__nonneg,axiom,
% 5.12/5.44 ! [F: nat > nat] :
% 5.12/5.44 ( ( summable_nat @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_nonneg
% 5.12/5.44 thf(fact_8559_suminf__nonneg,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( ( summable_int @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_nonneg
% 5.12/5.44 thf(fact_8560_suminf__pos,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos
% 5.12/5.44 thf(fact_8561_suminf__pos,axiom,
% 5.12/5.44 ! [F: nat > nat] :
% 5.12/5.44 ( ( summable_nat @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos
% 5.12/5.44 thf(fact_8562_suminf__pos,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( ( summable_int @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N2 ) )
% 5.12/5.44 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos
% 5.12/5.44 thf(fact_8563_minus__eq__not__plus__1,axiom,
% 5.12/5.44 ( uminus1351360451143612070nteger
% 5.12/5.44 = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_eq_not_plus_1
% 5.12/5.44 thf(fact_8564_minus__eq__not__plus__1,axiom,
% 5.12/5.44 ( uminus_uminus_int
% 5.12/5.44 = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_eq_not_plus_1
% 5.12/5.44 thf(fact_8565_not__eq__complement,axiom,
% 5.12/5.44 ( bit_ri7632146776885996613nteger
% 5.12/5.44 = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_eq_complement
% 5.12/5.44 thf(fact_8566_not__eq__complement,axiom,
% 5.12/5.44 ( bit_ri7919022796975470100ot_int
% 5.12/5.44 = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_eq_complement
% 5.12/5.44 thf(fact_8567_minus__eq__not__minus__1,axiom,
% 5.12/5.44 ( uminus1351360451143612070nteger
% 5.12/5.44 = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_eq_not_minus_1
% 5.12/5.44 thf(fact_8568_minus__eq__not__minus__1,axiom,
% 5.12/5.44 ( uminus_uminus_int
% 5.12/5.44 = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_eq_not_minus_1
% 5.12/5.44 thf(fact_8569_summable__0__powser,axiom,
% 5.12/5.44 ! [F: nat > complex] :
% 5.12/5.44 ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_0_powser
% 5.12/5.44 thf(fact_8570_summable__0__powser,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_0_powser
% 5.12/5.44 thf(fact_8571_summable__zero__power_H,axiom,
% 5.12/5.44 ! [F: nat > complex] :
% 5.12/5.44 ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power'
% 5.12/5.44 thf(fact_8572_summable__zero__power_H,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power'
% 5.12/5.44 thf(fact_8573_summable__zero__power_H,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( summable_int
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_int @ ( F @ N4 ) @ ( power_power_int @ zero_zero_int @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_zero_power'
% 5.12/5.44 thf(fact_8574_powser__split__head_I3_J,axiom,
% 5.12/5.44 ! [F: nat > complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z2 @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(3)
% 5.12/5.44 thf(fact_8575_powser__split__head_I3_J,axiom,
% 5.12/5.44 ! [F: nat > real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z2 @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(3)
% 5.12/5.44 thf(fact_8576_summable__powser__split__head,axiom,
% 5.12/5.44 ! [F: nat > complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 = ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_powser_split_head
% 5.12/5.44 thf(fact_8577_summable__powser__split__head,axiom,
% 5.12/5.44 ! [F: nat > real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 = ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_powser_split_head
% 5.12/5.44 thf(fact_8578_not__int__def,axiom,
% 5.12/5.44 ( bit_ri7919022796975470100ot_int
% 5.12/5.44 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_int_def
% 5.12/5.44 thf(fact_8579_and__not__numerals_I1_J,axiom,
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(1)
% 5.12/5.44 thf(fact_8580_disjunctive__diff,axiom,
% 5.12/5.44 ! [B: int,A: int] :
% 5.12/5.44 ( ! [N2: nat] :
% 5.12/5.44 ( ( bit_se1146084159140164899it_int @ B @ N2 )
% 5.12/5.44 => ( bit_se1146084159140164899it_int @ A @ N2 ) )
% 5.12/5.44 => ( ( minus_minus_int @ A @ B )
% 5.12/5.44 = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % disjunctive_diff
% 5.12/5.44 thf(fact_8581_take__bit__not__eq__mask__diff,axiom,
% 5.12/5.44 ! [N: nat,A: int] :
% 5.12/5.44 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.12/5.44 = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % take_bit_not_eq_mask_diff
% 5.12/5.44 thf(fact_8582_minus__numeral__inc__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 5.12/5.44 = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_numeral_inc_eq
% 5.12/5.44 thf(fact_8583_minus__numeral__inc__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_numeral_inc_eq
% 5.12/5.44 thf(fact_8584_suminf__pos__iff,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.12/5.44 = ( ? [I2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos_iff
% 5.12/5.44 thf(fact_8585_suminf__pos__iff,axiom,
% 5.12/5.44 ! [F: nat > nat] :
% 5.12/5.44 ( ( summable_nat @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.12/5.44 = ( ? [I2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos_iff
% 5.12/5.44 thf(fact_8586_suminf__pos__iff,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( ( summable_int @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.12/5.44 = ( ? [I2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I2 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos_iff
% 5.12/5.44 thf(fact_8587_suminf__pos2,axiom,
% 5.12/5.44 ! [F: nat > real,I: nat] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.12/5.44 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos2
% 5.12/5.44 thf(fact_8588_suminf__pos2,axiom,
% 5.12/5.44 ! [F: nat > nat,I: nat] :
% 5.12/5.44 ( ( summable_nat @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.12/5.44 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos2
% 5.12/5.44 thf(fact_8589_suminf__pos2,axiom,
% 5.12/5.44 ! [F: nat > int,I: nat] :
% 5.12/5.44 ( ( summable_int @ F )
% 5.12/5.44 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 5.12/5.44 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.12/5.44 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_pos2
% 5.12/5.44 thf(fact_8590_not__int__div__2,axiom,
% 5.12/5.44 ! [K: int] :
% 5.12/5.44 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_int_div_2
% 5.12/5.44 thf(fact_8591_powser__inside,axiom,
% 5.12/5.44 ! [F: nat > real,X: real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X @ N4 ) ) )
% 5.12/5.44 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_inside
% 5.12/5.44 thf(fact_8592_powser__inside,axiom,
% 5.12/5.44 ! [F: nat > complex,X: complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ X @ N4 ) ) )
% 5.12/5.44 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.12/5.44 => ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_inside
% 5.12/5.44 thf(fact_8593_and__not__numerals_I2_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = one_one_int ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(2)
% 5.12/5.44 thf(fact_8594_and__not__numerals_I4_J,axiom,
% 5.12/5.44 ! [M2: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(4)
% 5.12/5.44 thf(fact_8595_not__numeral__Bit0__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 5.12/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_numeral_Bit0_eq
% 5.12/5.44 thf(fact_8596_not__numeral__Bit0__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_numeral_Bit0_eq
% 5.12/5.44 thf(fact_8597_summable__geometric,axiom,
% 5.12/5.44 ! [C: real] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.12/5.44 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_geometric
% 5.12/5.44 thf(fact_8598_summable__geometric,axiom,
% 5.12/5.44 ! [C: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.12/5.44 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_geometric
% 5.12/5.44 thf(fact_8599_complete__algebra__summable__geometric,axiom,
% 5.12/5.44 ! [X: real] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.12/5.44 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complete_algebra_summable_geometric
% 5.12/5.44 thf(fact_8600_complete__algebra__summable__geometric,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.12/5.44 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complete_algebra_summable_geometric
% 5.12/5.44 thf(fact_8601_suminf__split__head,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) ) )
% 5.12/5.44 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % suminf_split_head
% 5.12/5.44 thf(fact_8602_summable__exp,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N4 ) ) @ ( power_power_complex @ X @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_exp
% 5.12/5.44 thf(fact_8603_summable__exp,axiom,
% 5.12/5.44 ! [X: real] :
% 5.12/5.44 ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N4 ) ) @ ( power_power_real @ X @ N4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_exp
% 5.12/5.44 thf(fact_8604_set__replicate__Suc,axiom,
% 5.12/5.44 ! [N: nat,X: vEBT_VEBT] :
% 5.12/5.44 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 5.12/5.44 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_Suc
% 5.12/5.44 thf(fact_8605_set__replicate__Suc,axiom,
% 5.12/5.44 ! [N: nat,X: nat] :
% 5.12/5.44 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 5.12/5.44 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_Suc
% 5.12/5.44 thf(fact_8606_set__replicate__Suc,axiom,
% 5.12/5.44 ! [N: nat,X: int] :
% 5.12/5.44 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 5.12/5.44 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_Suc
% 5.12/5.44 thf(fact_8607_set__replicate__conv__if,axiom,
% 5.12/5.44 ! [N: nat,X: vEBT_VEBT] :
% 5.12/5.44 ( ( ( N = zero_zero_nat )
% 5.12/5.44 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.12/5.44 = bot_bo8194388402131092736T_VEBT ) )
% 5.12/5.44 & ( ( N != zero_zero_nat )
% 5.12/5.44 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.12/5.44 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_conv_if
% 5.12/5.44 thf(fact_8608_set__replicate__conv__if,axiom,
% 5.12/5.44 ! [N: nat,X: nat] :
% 5.12/5.44 ( ( ( N = zero_zero_nat )
% 5.12/5.44 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.12/5.44 = bot_bot_set_nat ) )
% 5.12/5.44 & ( ( N != zero_zero_nat )
% 5.12/5.44 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.12/5.44 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_conv_if
% 5.12/5.44 thf(fact_8609_set__replicate__conv__if,axiom,
% 5.12/5.44 ! [N: nat,X: int] :
% 5.12/5.44 ( ( ( N = zero_zero_nat )
% 5.12/5.44 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.12/5.44 = bot_bot_set_int ) )
% 5.12/5.44 & ( ( N != zero_zero_nat )
% 5.12/5.44 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.12/5.44 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_replicate_conv_if
% 5.12/5.44 thf(fact_8610_bit__minus__int__iff,axiom,
% 5.12/5.44 ! [K: int,N: nat] :
% 5.12/5.44 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.12/5.44 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % bit_minus_int_iff
% 5.12/5.44 thf(fact_8611_not__numeral__BitM__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N ) ) )
% 5.12/5.44 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_numeral_BitM_eq
% 5.12/5.44 thf(fact_8612_not__numeral__BitM__eq,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_numeral_BitM_eq
% 5.12/5.44 thf(fact_8613_take__bit__not__mask__eq__0,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) )
% 5.12/5.44 = zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % take_bit_not_mask_eq_0
% 5.12/5.44 thf(fact_8614_unset__bit__eq__and__not,axiom,
% 5.12/5.44 ( bit_se4203085406695923979it_int
% 5.12/5.44 = ( ^ [N4: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % unset_bit_eq_and_not
% 5.12/5.44 thf(fact_8615_unset__bit__int__def,axiom,
% 5.12/5.44 ( bit_se4203085406695923979it_int
% 5.12/5.44 = ( ^ [N4: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % unset_bit_int_def
% 5.12/5.44 thf(fact_8616_and__not__numerals_I7_J,axiom,
% 5.12/5.44 ! [M2: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(7)
% 5.12/5.44 thf(fact_8617_and__not__numerals_I3_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.44 = zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(3)
% 5.12/5.44 thf(fact_8618_powser__split__head_I1_J,axiom,
% 5.12/5.44 ! [F: nat > complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.12/5.44 @ ( times_times_complex
% 5.12/5.44 @ ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 @ Z2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(1)
% 5.12/5.44 thf(fact_8619_powser__split__head_I1_J,axiom,
% 5.12/5.44 ! [F: nat > real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.12/5.44 @ ( times_times_real
% 5.12/5.44 @ ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 @ Z2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(1)
% 5.12/5.44 thf(fact_8620_powser__split__head_I2_J,axiom,
% 5.12/5.44 ! [F: nat > complex,Z2: complex] :
% 5.12/5.44 ( ( summable_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( ( times_times_complex
% 5.12/5.44 @ ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 @ Z2 )
% 5.12/5.44 = ( minus_minus_complex
% 5.12/5.44 @ ( suminf_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z2 @ N4 ) ) )
% 5.12/5.44 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(2)
% 5.12/5.44 thf(fact_8621_powser__split__head_I2_J,axiom,
% 5.12/5.44 ! [F: nat > real,Z2: real] :
% 5.12/5.44 ( ( summable_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 => ( ( times_times_real
% 5.12/5.44 @ ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 @ Z2 )
% 5.12/5.44 = ( minus_minus_real
% 5.12/5.44 @ ( suminf_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z2 @ N4 ) ) )
% 5.12/5.44 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_split_head(2)
% 5.12/5.44 thf(fact_8622_summable__power__series,axiom,
% 5.12/5.44 ! [F: nat > real,Z2: real] :
% 5.12/5.44 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.12/5.44 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.12/5.44 => ( ( ord_less_eq_real @ zero_zero_real @ Z2 )
% 5.12/5.44 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.12/5.44 => ( summable_real
% 5.12/5.44 @ ^ [I2: nat] : ( times_times_real @ ( F @ I2 ) @ ( power_power_real @ Z2 @ I2 ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_power_series
% 5.12/5.44 thf(fact_8623_bit__not__iff__eq,axiom,
% 5.12/5.44 ! [A: int,N: nat] :
% 5.12/5.44 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N )
% 5.12/5.44 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.12/5.44 != zero_zero_int )
% 5.12/5.44 & ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bit_not_iff_eq
% 5.12/5.44 thf(fact_8624_minus__exp__eq__not__mask,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.44 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_exp_eq_not_mask
% 5.12/5.44 thf(fact_8625_minus__exp__eq__not__mask,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_exp_eq_not_mask
% 5.12/5.44 thf(fact_8626_summable__ratio__test,axiom,
% 5.12/5.44 ! [C: real,N5: nat,F: nat > real] :
% 5.12/5.44 ( ( ord_less_real @ C @ one_one_real )
% 5.12/5.44 => ( ! [N2: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ N5 @ N2 )
% 5.12/5.44 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) )
% 5.12/5.44 => ( summable_real @ F ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_ratio_test
% 5.12/5.44 thf(fact_8627_summable__ratio__test,axiom,
% 5.12/5.44 ! [C: real,N5: nat,F: nat > complex] :
% 5.12/5.44 ( ( ord_less_real @ C @ one_one_real )
% 5.12/5.44 => ( ! [N2: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ N5 @ N2 )
% 5.12/5.44 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) )
% 5.12/5.44 => ( summable_complex @ F ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % summable_ratio_test
% 5.12/5.44 thf(fact_8628_and__not__numerals_I8_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % and_not_numerals(8)
% 5.12/5.44 thf(fact_8629_not__int__rec,axiom,
% 5.12/5.44 ( bit_ri7919022796975470100ot_int
% 5.12/5.44 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % not_int_rec
% 5.12/5.44 thf(fact_8630_vebt__buildup_Osimps_I3_J,axiom,
% 5.12/5.44 ! [Va2: nat] :
% 5.12/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.12/5.44 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.12/5.44 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.12/5.44 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % vebt_buildup.simps(3)
% 5.12/5.44 thf(fact_8631_sin__paired,axiom,
% 5.12/5.44 ! [X: real] :
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.12/5.44 @ ( sin_real @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % sin_paired
% 5.12/5.44 thf(fact_8632_vebt__member_Opelims_I3_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ~ ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.12/5.44 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.12/5.44 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.12/5.44 => ( ! [V3: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa ) ) )
% 5.12/5.44 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) )
% 5.12/5.44 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.12/5.44 => ( ( Xa != Mi )
% 5.12/5.44 => ( ( Xa != Ma2 )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % vebt_member.pelims(3)
% 5.12/5.44 thf(fact_8633_vebt__member_Opelims_I1_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.44 ( ( ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [V3: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) ) )
% 5.12/5.44 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( Xa != Mi )
% 5.12/5.44 => ( ( Xa != Ma2 )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % vebt_member.pelims(1)
% 5.12/5.44 thf(fact_8634_sum__gp,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,X: complex] :
% 5.12/5.44 ( ( ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_complex ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( ( X = one_one_complex )
% 5.12/5.44 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.12/5.44 & ( ( X != one_one_complex )
% 5.12/5.44 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp
% 5.12/5.44 thf(fact_8635_sum__gp,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,X: rat] :
% 5.12/5.44 ( ( ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_rat ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( ( X = one_one_rat )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.12/5.44 & ( ( X != one_one_rat )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp
% 5.12/5.44 thf(fact_8636_sum__gp,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,X: real] :
% 5.12/5.44 ( ( ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_real ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ N @ M2 )
% 5.12/5.44 => ( ( ( X = one_one_real )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 5.12/5.44 & ( ( X != one_one_real )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp
% 5.12/5.44 thf(fact_8637_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > int] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( member_int @ ( F @ X3 ) @ ring_1_Ints_int ) )
% 5.12/5.44 => ( member_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ring_1_Ints_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8638_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > complex] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.44 => ( member_complex @ ( groups5754745047067104278omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8639_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > int] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( member_int @ ( F @ X3 ) @ ring_1_Ints_int ) )
% 5.12/5.44 => ( member_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ring_1_Ints_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8640_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > complex] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.44 => ( member_complex @ ( groups2073611262835488442omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8641_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > int] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( member_int @ ( F @ X3 ) @ ring_1_Ints_int ) )
% 5.12/5.44 => ( member_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ring_1_Ints_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8642_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > complex] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.44 => ( member_complex @ ( groups3049146728041665814omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8643_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > real] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.44 => ( member_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8644_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > real] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.44 => ( member_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8645_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > real] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( member_real @ ( F @ X3 ) @ ring_1_Ints_real ) )
% 5.12/5.44 => ( member_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ring_1_Ints_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8646_Ints__sum,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > complex] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( member_complex @ ( F @ X3 ) @ ring_1_Ints_complex ) )
% 5.12/5.44 => ( member_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ring_1_Ints_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % Ints_sum
% 5.12/5.44 thf(fact_8647_sum_Oneutral__const,axiom,
% 5.12/5.44 ! [A2: set_nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [Uu3: nat] : zero_zero_nat
% 5.12/5.44 @ A2 )
% 5.12/5.44 = zero_zero_nat ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral_const
% 5.12/5.44 thf(fact_8648_sum_Oneutral__const,axiom,
% 5.12/5.44 ! [A2: set_complex] :
% 5.12/5.44 ( ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [Uu3: complex] : zero_zero_complex
% 5.12/5.44 @ A2 )
% 5.12/5.44 = zero_zero_complex ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral_const
% 5.12/5.44 thf(fact_8649_sum_Oneutral__const,axiom,
% 5.12/5.44 ! [A2: set_int] :
% 5.12/5.44 ( ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [Uu3: int] : zero_zero_int
% 5.12/5.44 @ A2 )
% 5.12/5.44 = zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral_const
% 5.12/5.44 thf(fact_8650_sum_Oneutral__const,axiom,
% 5.12/5.44 ! [A2: set_nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [Uu3: nat] : zero_zero_real
% 5.12/5.44 @ A2 )
% 5.12/5.44 = zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral_const
% 5.12/5.44 thf(fact_8651_of__nat__sum,axiom,
% 5.12/5.44 ! [F: complex > nat,A2: set_complex] :
% 5.12/5.44 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8652_of__nat__sum,axiom,
% 5.12/5.44 ! [F: int > nat,A2: set_int] :
% 5.12/5.44 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8653_of__nat__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri8010041392384452111omplex @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups2073611262835488442omplex
% 5.12/5.44 @ ^ [X2: nat] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8654_of__nat__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [X2: nat] : ( semiri681578069525770553at_rat @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8655_of__nat__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8656_of__nat__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8657_of__nat__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_nat_sum
% 5.12/5.44 thf(fact_8658_of__int__sum,axiom,
% 5.12/5.44 ! [F: complex > int,A2: set_complex] :
% 5.12/5.44 ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A2 ) )
% 5.12/5.44 = ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : ( ring_17405671764205052669omplex @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_int_sum
% 5.12/5.44 thf(fact_8659_of__int__sum,axiom,
% 5.12/5.44 ! [F: nat > int,A2: set_nat] :
% 5.12/5.44 ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A2 ) )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [X2: nat] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_int_sum
% 5.12/5.44 thf(fact_8660_of__int__sum,axiom,
% 5.12/5.44 ! [F: int > int,A2: set_int] :
% 5.12/5.44 ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.12/5.44 = ( groups8778361861064173332t_real
% 5.12/5.44 @ ^ [X2: int] : ( ring_1_of_int_real @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_int_sum
% 5.12/5.44 thf(fact_8661_of__int__sum,axiom,
% 5.12/5.44 ! [F: int > int,A2: set_int] :
% 5.12/5.44 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.12/5.44 = ( groups3906332499630173760nt_rat
% 5.12/5.44 @ ^ [X2: int] : ( ring_1_of_int_rat @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_int_sum
% 5.12/5.44 thf(fact_8662_of__int__sum,axiom,
% 5.12/5.44 ! [F: int > int,A2: set_int] :
% 5.12/5.44 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.12/5.44 = ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : ( ring_1_of_int_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % of_int_sum
% 5.12/5.44 thf(fact_8663_sums__zero,axiom,
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : zero_zero_real
% 5.12/5.44 @ zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % sums_zero
% 5.12/5.44 thf(fact_8664_sums__zero,axiom,
% 5.12/5.44 ( sums_nat
% 5.12/5.44 @ ^ [N4: nat] : zero_zero_nat
% 5.12/5.44 @ zero_zero_nat ) ).
% 5.12/5.44
% 5.12/5.44 % sums_zero
% 5.12/5.44 thf(fact_8665_sums__zero,axiom,
% 5.12/5.44 ( sums_int
% 5.12/5.44 @ ^ [N4: nat] : zero_zero_int
% 5.12/5.44 @ zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % sums_zero
% 5.12/5.44 thf(fact_8666_sum_Oempty,axiom,
% 5.12/5.44 ! [G: nat > rat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 5.12/5.44 = zero_zero_rat ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8667_sum_Oempty,axiom,
% 5.12/5.44 ! [G: nat > int] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 5.12/5.44 = zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8668_sum_Oempty,axiom,
% 5.12/5.44 ! [G: int > real] :
% 5.12/5.44 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 5.12/5.44 = zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8669_sum_Oempty,axiom,
% 5.12/5.44 ! [G: int > rat] :
% 5.12/5.44 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 5.12/5.44 = zero_zero_rat ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8670_sum_Oempty,axiom,
% 5.12/5.44 ! [G: int > nat] :
% 5.12/5.44 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 5.12/5.44 = zero_zero_nat ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8671_sum_Oempty,axiom,
% 5.12/5.44 ! [G: nat > nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ G @ bot_bot_set_nat )
% 5.12/5.44 = zero_zero_nat ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8672_sum_Oempty,axiom,
% 5.12/5.44 ! [G: complex > complex] :
% 5.12/5.44 ( ( groups7754918857620584856omplex @ G @ bot_bot_set_complex )
% 5.12/5.44 = zero_zero_complex ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8673_sum_Oempty,axiom,
% 5.12/5.44 ! [G: int > int] :
% 5.12/5.44 ( ( groups4538972089207619220nt_int @ G @ bot_bot_set_int )
% 5.12/5.44 = zero_zero_int ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8674_sum_Oempty,axiom,
% 5.12/5.44 ! [G: nat > real] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ G @ bot_bot_set_nat )
% 5.12/5.44 = zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % sum.empty
% 5.12/5.44 thf(fact_8675_sum__abs__ge__zero,axiom,
% 5.12/5.44 ! [F: int > int,A2: set_int] :
% 5.12/5.44 ( ord_less_eq_int @ zero_zero_int
% 5.12/5.44 @ ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [I2: int] : ( abs_abs_int @ ( F @ I2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_abs_ge_zero
% 5.12/5.44 thf(fact_8676_sum__abs__ge__zero,axiom,
% 5.12/5.44 ! [F: nat > real,A2: set_nat] :
% 5.12/5.44 ( ord_less_eq_real @ zero_zero_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( abs_abs_real @ ( F @ I2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_abs_ge_zero
% 5.12/5.44 thf(fact_8677_powser__sums__zero__iff,axiom,
% 5.12/5.44 ! [A: nat > complex,X: complex] :
% 5.12/5.44 ( ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.12/5.44 @ X )
% 5.12/5.44 = ( ( A @ zero_zero_nat )
% 5.12/5.44 = X ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_zero_iff
% 5.12/5.44 thf(fact_8678_powser__sums__zero__iff,axiom,
% 5.12/5.44 ! [A: nat > real,X: real] :
% 5.12/5.44 ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.12/5.44 @ X )
% 5.12/5.44 = ( ( A @ zero_zero_nat )
% 5.12/5.44 = X ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_zero_iff
% 5.12/5.44 thf(fact_8679_sum_Ocl__ivl__Suc,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,G: nat > rat] :
% 5.12/5.44 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = zero_zero_rat ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.cl_ivl_Suc
% 5.12/5.44 thf(fact_8680_sum_Ocl__ivl__Suc,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,G: nat > int] :
% 5.12/5.44 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = zero_zero_int ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.cl_ivl_Suc
% 5.12/5.44 thf(fact_8681_sum_Ocl__ivl__Suc,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,G: nat > nat] :
% 5.12/5.44 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = zero_zero_nat ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.cl_ivl_Suc
% 5.12/5.44 thf(fact_8682_sum_Ocl__ivl__Suc,axiom,
% 5.12/5.44 ! [N: nat,M2: nat,G: nat > real] :
% 5.12/5.44 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = zero_zero_real ) )
% 5.12/5.44 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.cl_ivl_Suc
% 5.12/5.44 thf(fact_8683_sums__divide,axiom,
% 5.12/5.44 ! [F: nat > complex,A: complex,C: complex] :
% 5.12/5.44 ( ( sums_complex @ F @ A )
% 5.12/5.44 => ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C )
% 5.12/5.44 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_divide
% 5.12/5.44 thf(fact_8684_sums__divide,axiom,
% 5.12/5.44 ! [F: nat > real,A: real,C: real] :
% 5.12/5.44 ( ( sums_real @ F @ A )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C )
% 5.12/5.44 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_divide
% 5.12/5.44 thf(fact_8685_sums__single,axiom,
% 5.12/5.44 ! [I: nat,F: nat > real] :
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [R: nat] : ( if_real @ ( R = I ) @ ( F @ R ) @ zero_zero_real )
% 5.12/5.44 @ ( F @ I ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_single
% 5.12/5.44 thf(fact_8686_sums__single,axiom,
% 5.12/5.44 ! [I: nat,F: nat > nat] :
% 5.12/5.44 ( sums_nat
% 5.12/5.44 @ ^ [R: nat] : ( if_nat @ ( R = I ) @ ( F @ R ) @ zero_zero_nat )
% 5.12/5.44 @ ( F @ I ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_single
% 5.12/5.44 thf(fact_8687_sums__single,axiom,
% 5.12/5.44 ! [I: nat,F: nat > int] :
% 5.12/5.44 ( sums_int
% 5.12/5.44 @ ^ [R: nat] : ( if_int @ ( R = I ) @ ( F @ R ) @ zero_zero_int )
% 5.12/5.44 @ ( F @ I ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_single
% 5.12/5.44 thf(fact_8688_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: complex > real,A2: set_complex] :
% 5.12/5.44 ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.12/5.44 != zero_zero_real )
% 5.12/5.44 => ~ ! [A4: complex] :
% 5.12/5.44 ( ( member_complex @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8689_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: real > real,A2: set_real] :
% 5.12/5.44 ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.12/5.44 != zero_zero_real )
% 5.12/5.44 => ~ ! [A4: real] :
% 5.12/5.44 ( ( member_real @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8690_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: int > real,A2: set_int] :
% 5.12/5.44 ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.12/5.44 != zero_zero_real )
% 5.12/5.44 => ~ ! [A4: int] :
% 5.12/5.44 ( ( member_int @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8691_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: complex > rat,A2: set_complex] :
% 5.12/5.44 ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.12/5.44 != zero_zero_rat )
% 5.12/5.44 => ~ ! [A4: complex] :
% 5.12/5.44 ( ( member_complex @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8692_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: real > rat,A2: set_real] :
% 5.12/5.44 ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.12/5.44 != zero_zero_rat )
% 5.12/5.44 => ~ ! [A4: real] :
% 5.12/5.44 ( ( member_real @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8693_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: nat > rat,A2: set_nat] :
% 5.12/5.44 ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.12/5.44 != zero_zero_rat )
% 5.12/5.44 => ~ ! [A4: nat] :
% 5.12/5.44 ( ( member_nat @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8694_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: int > rat,A2: set_int] :
% 5.12/5.44 ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.12/5.44 != zero_zero_rat )
% 5.12/5.44 => ~ ! [A4: int] :
% 5.12/5.44 ( ( member_int @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8695_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: complex > nat,A2: set_complex] :
% 5.12/5.44 ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.12/5.44 != zero_zero_nat )
% 5.12/5.44 => ~ ! [A4: complex] :
% 5.12/5.44 ( ( member_complex @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8696_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: real > nat,A2: set_real] :
% 5.12/5.44 ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.12/5.44 != zero_zero_nat )
% 5.12/5.44 => ~ ! [A4: real] :
% 5.12/5.44 ( ( member_real @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8697_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.12/5.44 ! [G: int > nat,A2: set_int] :
% 5.12/5.44 ( ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.12/5.44 != zero_zero_nat )
% 5.12/5.44 => ~ ! [A4: int] :
% 5.12/5.44 ( ( member_int @ A4 @ A2 )
% 5.12/5.44 => ( ( G @ A4 )
% 5.12/5.44 = zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.not_neutral_contains_not_neutral
% 5.12/5.44 thf(fact_8698_sum_Oneutral,axiom,
% 5.12/5.44 ! [A2: set_nat,G: nat > nat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( ( G @ X3 )
% 5.12/5.44 = zero_zero_nat ) )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 5.12/5.44 = zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral
% 5.12/5.44 thf(fact_8699_sum_Oneutral,axiom,
% 5.12/5.44 ! [A2: set_complex,G: complex > complex] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ( G @ X3 )
% 5.12/5.44 = zero_zero_complex ) )
% 5.12/5.44 => ( ( groups7754918857620584856omplex @ G @ A2 )
% 5.12/5.44 = zero_zero_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral
% 5.12/5.44 thf(fact_8700_sum_Oneutral,axiom,
% 5.12/5.44 ! [A2: set_int,G: int > int] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ( G @ X3 )
% 5.12/5.44 = zero_zero_int ) )
% 5.12/5.44 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.12/5.44 = zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral
% 5.12/5.44 thf(fact_8701_sum_Oneutral,axiom,
% 5.12/5.44 ! [A2: set_nat,G: nat > real] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( ( G @ X3 )
% 5.12/5.44 = zero_zero_real ) )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ A2 )
% 5.12/5.44 = zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.neutral
% 5.12/5.44 thf(fact_8702_sums__0,axiom,
% 5.12/5.44 ! [F: nat > real] :
% 5.12/5.44 ( ! [N2: nat] :
% 5.12/5.44 ( ( F @ N2 )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 => ( sums_real @ F @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_0
% 5.12/5.44 thf(fact_8703_sums__0,axiom,
% 5.12/5.44 ! [F: nat > nat] :
% 5.12/5.44 ( ! [N2: nat] :
% 5.12/5.44 ( ( F @ N2 )
% 5.12/5.44 = zero_zero_nat )
% 5.12/5.44 => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_0
% 5.12/5.44 thf(fact_8704_sums__0,axiom,
% 5.12/5.44 ! [F: nat > int] :
% 5.12/5.44 ( ! [N2: nat] :
% 5.12/5.44 ( ( F @ N2 )
% 5.12/5.44 = zero_zero_int )
% 5.12/5.44 => ( sums_int @ F @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_0
% 5.12/5.44 thf(fact_8705_sums__diff,axiom,
% 5.12/5.44 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.12/5.44 ( ( sums_real @ F @ A )
% 5.12/5.44 => ( ( sums_real @ G @ B )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.12/5.44 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_diff
% 5.12/5.44 thf(fact_8706_sums__minus,axiom,
% 5.12/5.44 ! [F: nat > real,A: real] :
% 5.12/5.44 ( ( sums_real @ F @ A )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( uminus_uminus_real @ ( F @ N4 ) )
% 5.12/5.44 @ ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_minus
% 5.12/5.44 thf(fact_8707_sums__minus,axiom,
% 5.12/5.44 ! [F: nat > complex,A: complex] :
% 5.12/5.44 ( ( sums_complex @ F @ A )
% 5.12/5.44 => ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( uminus1482373934393186551omplex @ ( F @ N4 ) )
% 5.12/5.44 @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_minus
% 5.12/5.44 thf(fact_8708_sum__subtractf,axiom,
% 5.12/5.44 ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 5.12/5.44 ( ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : ( minus_minus_complex @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf
% 5.12/5.44 thf(fact_8709_sum__subtractf,axiom,
% 5.12/5.44 ! [F: int > int,G: int > int,A2: set_int] :
% 5.12/5.44 ( ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : ( minus_minus_int @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf
% 5.12/5.44 thf(fact_8710_sum__subtractf,axiom,
% 5.12/5.44 ! [F: nat > real,G: nat > real,A2: set_nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [X2: nat] : ( minus_minus_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf
% 5.12/5.44 thf(fact_8711_sum__divide__distrib,axiom,
% 5.12/5.44 ! [F: complex > complex,A2: set_complex,R4: complex] :
% 5.12/5.44 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R4 )
% 5.12/5.44 = ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [N4: complex] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ R4 )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_divide_distrib
% 5.12/5.44 thf(fact_8712_sum__divide__distrib,axiom,
% 5.12/5.44 ! [F: nat > real,A2: set_nat,R4: real] :
% 5.12/5.44 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R4 )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ R4 )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_divide_distrib
% 5.12/5.44 thf(fact_8713_sum__negf,axiom,
% 5.12/5.44 ! [F: complex > complex,A2: set_complex] :
% 5.12/5.44 ( ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : ( uminus1482373934393186551omplex @ ( F @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( uminus1482373934393186551omplex @ ( groups7754918857620584856omplex @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_negf
% 5.12/5.44 thf(fact_8714_sum__negf,axiom,
% 5.12/5.44 ! [F: int > int,A2: set_int] :
% 5.12/5.44 ( ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : ( uminus_uminus_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_negf
% 5.12/5.44 thf(fact_8715_sum__negf,axiom,
% 5.12/5.44 ! [F: nat > real,A2: set_nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [X2: nat] : ( uminus_uminus_real @ ( F @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( uminus_uminus_real @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_negf
% 5.12/5.44 thf(fact_8716_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > real] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8717_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > real] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8718_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > real] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8719_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > rat] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8720_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > rat] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8721_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > rat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8722_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > rat] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8723_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > nat] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8724_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > nat] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8725_sum__nonneg,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > nat] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonneg
% 5.12/5.44 thf(fact_8726_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > real] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.12/5.44 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8727_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > real] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.12/5.44 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8728_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > real] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.12/5.44 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8729_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > rat] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.12/5.44 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8730_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > rat] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.12/5.44 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8731_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > rat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.12/5.44 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8732_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > rat] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.12/5.44 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8733_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_complex,F: complex > nat] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.12/5.44 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8734_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_real,F: real > nat] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.12/5.44 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8735_sum__nonpos,axiom,
% 5.12/5.44 ! [A2: set_int,F: int > nat] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.12/5.44 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nonpos
% 5.12/5.44 thf(fact_8736_sum__cong__Suc,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.12/5.44 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.12/5.44 => ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.12/5.44 => ( ( F @ ( suc @ X3 ) )
% 5.12/5.44 = ( G @ ( suc @ X3 ) ) ) )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.12/5.44 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_cong_Suc
% 5.12/5.44 thf(fact_8737_sum__cong__Suc,axiom,
% 5.12/5.44 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.12/5.44 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.12/5.44 => ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.12/5.44 => ( ( F @ ( suc @ X3 ) )
% 5.12/5.44 = ( G @ ( suc @ X3 ) ) ) )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.12/5.44 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_cong_Suc
% 5.12/5.44 thf(fact_8738_sums__mult2__iff,axiom,
% 5.12/5.44 ! [C: real,F: nat > real,D: real] :
% 5.12/5.44 ( ( C != zero_zero_real )
% 5.12/5.44 => ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ C )
% 5.12/5.44 @ ( times_times_real @ D @ C ) )
% 5.12/5.44 = ( sums_real @ F @ D ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_mult2_iff
% 5.12/5.44 thf(fact_8739_sums__mult__iff,axiom,
% 5.12/5.44 ! [C: real,F: nat > real,D: real] :
% 5.12/5.44 ( ( C != zero_zero_real )
% 5.12/5.44 => ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) )
% 5.12/5.44 @ ( times_times_real @ C @ D ) )
% 5.12/5.44 = ( sums_real @ F @ D ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_mult_iff
% 5.12/5.44 thf(fact_8740_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.12/5.44 ! [G: nat > nat,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.shift_bounds_cl_Suc_ivl
% 5.12/5.44 thf(fact_8741_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.12/5.44 ! [G: nat > real,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.shift_bounds_cl_Suc_ivl
% 5.12/5.44 thf(fact_8742_sums__mult__D,axiom,
% 5.12/5.44 ! [C: complex,F: nat > complex,A: complex] :
% 5.12/5.44 ( ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ C @ ( F @ N4 ) )
% 5.12/5.44 @ A )
% 5.12/5.44 => ( ( C != zero_zero_complex )
% 5.12/5.44 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_mult_D
% 5.12/5.44 thf(fact_8743_sums__mult__D,axiom,
% 5.12/5.44 ! [C: real,F: nat > real,A: real] :
% 5.12/5.44 ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) )
% 5.12/5.44 @ A )
% 5.12/5.44 => ( ( C != zero_zero_real )
% 5.12/5.44 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_mult_D
% 5.12/5.44 thf(fact_8744_sums__Suc__imp,axiom,
% 5.12/5.44 ! [F: nat > real,S: real] :
% 5.12/5.44 ( ( ( F @ zero_zero_nat )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 => ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.12/5.44 @ S )
% 5.12/5.44 => ( sums_real @ F @ S ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_Suc_imp
% 5.12/5.44 thf(fact_8745_sums__Suc,axiom,
% 5.12/5.44 ! [F: nat > real,L: real] :
% 5.12/5.44 ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.12/5.44 @ L )
% 5.12/5.44 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_Suc
% 5.12/5.44 thf(fact_8746_sums__Suc,axiom,
% 5.12/5.44 ! [F: nat > nat,L: nat] :
% 5.12/5.44 ( ( sums_nat
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.12/5.44 @ L )
% 5.12/5.44 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_Suc
% 5.12/5.44 thf(fact_8747_sums__Suc,axiom,
% 5.12/5.44 ! [F: nat > int,L: int] :
% 5.12/5.44 ( ( sums_int
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.12/5.44 @ L )
% 5.12/5.44 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_Suc
% 5.12/5.44 thf(fact_8748_sums__Suc__iff,axiom,
% 5.12/5.44 ! [F: nat > real,S: real] :
% 5.12/5.44 ( ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) )
% 5.12/5.44 @ S )
% 5.12/5.44 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_Suc_iff
% 5.12/5.44 thf(fact_8749_sums__zero__iff__shift,axiom,
% 5.12/5.44 ! [N: nat,F: nat > real,S: real] :
% 5.12/5.44 ( ! [I3: nat] :
% 5.12/5.44 ( ( ord_less_nat @ I3 @ N )
% 5.12/5.44 => ( ( F @ I3 )
% 5.12/5.44 = zero_zero_real ) )
% 5.12/5.44 => ( ( sums_real
% 5.12/5.44 @ ^ [I2: nat] : ( F @ ( plus_plus_nat @ I2 @ N ) )
% 5.12/5.44 @ S )
% 5.12/5.44 = ( sums_real @ F @ S ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_zero_iff_shift
% 5.12/5.44 thf(fact_8750_sum_OatLeastAtMost__rev,axiom,
% 5.12/5.44 ! [G: nat > nat,N: nat,M2: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeastAtMost_rev
% 5.12/5.44 thf(fact_8751_sum_OatLeastAtMost__rev,axiom,
% 5.12/5.44 ! [G: nat > real,N: nat,M2: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeastAtMost_rev
% 5.12/5.44 thf(fact_8752_powser__sums__if,axiom,
% 5.12/5.44 ! [M2: nat,Z2: complex] :
% 5.12/5.44 ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( if_complex @ ( N4 = M2 ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z2 @ N4 ) )
% 5.12/5.44 @ ( power_power_complex @ Z2 @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_if
% 5.12/5.44 thf(fact_8753_powser__sums__if,axiom,
% 5.12/5.44 ! [M2: nat,Z2: real] :
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( if_real @ ( N4 = M2 ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z2 @ N4 ) )
% 5.12/5.44 @ ( power_power_real @ Z2 @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_if
% 5.12/5.44 thf(fact_8754_powser__sums__if,axiom,
% 5.12/5.44 ! [M2: nat,Z2: int] :
% 5.12/5.44 ( sums_int
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_int @ ( if_int @ ( N4 = M2 ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z2 @ N4 ) )
% 5.12/5.44 @ ( power_power_int @ Z2 @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_if
% 5.12/5.44 thf(fact_8755_powser__sums__zero,axiom,
% 5.12/5.44 ! [A: nat > complex] :
% 5.12/5.44 ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 5.12/5.44 @ ( A @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_zero
% 5.12/5.44 thf(fact_8756_powser__sums__zero,axiom,
% 5.12/5.44 ! [A: nat > real] :
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 5.12/5.44 @ ( A @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % powser_sums_zero
% 5.12/5.44 thf(fact_8757_sum__shift__lb__Suc0__0,axiom,
% 5.12/5.44 ! [F: nat > rat,K: nat] :
% 5.12/5.44 ( ( ( F @ zero_zero_nat )
% 5.12/5.44 = zero_zero_rat )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.12/5.44 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_shift_lb_Suc0_0
% 5.12/5.44 thf(fact_8758_sum__shift__lb__Suc0__0,axiom,
% 5.12/5.44 ! [F: nat > int,K: nat] :
% 5.12/5.44 ( ( ( F @ zero_zero_nat )
% 5.12/5.44 = zero_zero_int )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.12/5.44 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_shift_lb_Suc0_0
% 5.12/5.44 thf(fact_8759_sum__shift__lb__Suc0__0,axiom,
% 5.12/5.44 ! [F: nat > nat,K: nat] :
% 5.12/5.44 ( ( ( F @ zero_zero_nat )
% 5.12/5.44 = zero_zero_nat )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_shift_lb_Suc0_0
% 5.12/5.44 thf(fact_8760_sum__shift__lb__Suc0__0,axiom,
% 5.12/5.44 ! [F: nat > real,K: nat] :
% 5.12/5.44 ( ( ( F @ zero_zero_nat )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.12/5.44 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_shift_lb_Suc0_0
% 5.12/5.44 thf(fact_8761_sum_OatLeast0__atMost__Suc,axiom,
% 5.12/5.44 ! [G: nat > rat,N: nat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast0_atMost_Suc
% 5.12/5.44 thf(fact_8762_sum_OatLeast0__atMost__Suc,axiom,
% 5.12/5.44 ! [G: nat > int,N: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast0_atMost_Suc
% 5.12/5.44 thf(fact_8763_sum_OatLeast0__atMost__Suc,axiom,
% 5.12/5.44 ! [G: nat > nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast0_atMost_Suc
% 5.12/5.44 thf(fact_8764_sum_OatLeast0__atMost__Suc,axiom,
% 5.12/5.44 ! [G: nat > real,N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast0_atMost_Suc
% 5.12/5.44 thf(fact_8765_sum_OatLeast__Suc__atMost,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( plus_plus_rat @ ( G @ M2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast_Suc_atMost
% 5.12/5.44 thf(fact_8766_sum_OatLeast__Suc__atMost,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( plus_plus_int @ ( G @ M2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast_Suc_atMost
% 5.12/5.44 thf(fact_8767_sum_OatLeast__Suc__atMost,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( plus_plus_nat @ ( G @ M2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast_Suc_atMost
% 5.12/5.44 thf(fact_8768_sum_OatLeast__Suc__atMost,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( plus_plus_real @ ( G @ M2 ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.atLeast_Suc_atMost
% 5.12/5.44 thf(fact_8769_sum_Onat__ivl__Suc_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.nat_ivl_Suc'
% 5.12/5.44 thf(fact_8770_sum_Onat__ivl__Suc_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.nat_ivl_Suc'
% 5.12/5.44 thf(fact_8771_sum_Onat__ivl__Suc_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.nat_ivl_Suc'
% 5.12/5.44 thf(fact_8772_sum_Onat__ivl__Suc_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.nat_ivl_Suc'
% 5.12/5.44 thf(fact_8773_sum_OSuc__reindex__ivl,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( G @ M2 )
% 5.12/5.44 @ ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.Suc_reindex_ivl
% 5.12/5.44 thf(fact_8774_sum_OSuc__reindex__ivl,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_int @ ( G @ M2 )
% 5.12/5.44 @ ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.Suc_reindex_ivl
% 5.12/5.44 thf(fact_8775_sum_OSuc__reindex__ivl,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_nat @ ( G @ M2 )
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.Suc_reindex_ivl
% 5.12/5.44 thf(fact_8776_sum_OSuc__reindex__ivl,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( G @ M2 )
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.Suc_reindex_ivl
% 5.12/5.44 thf(fact_8777_sum__Suc__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [I2: nat] : ( minus_minus_rat @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_Suc_diff
% 5.12/5.44 thf(fact_8778_sum__Suc__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [I2: nat] : ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_Suc_diff
% 5.12/5.44 thf(fact_8779_sum__Suc__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 => ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( minus_minus_real @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_Suc_diff
% 5.12/5.44 thf(fact_8780_sum__atLeastAtMost__code,axiom,
% 5.12/5.44 ! [F: nat > rat,A: nat,B: nat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.44 = ( set_fo1949268297981939178at_rat
% 5.12/5.44 @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 5.12/5.44 @ A
% 5.12/5.44 @ B
% 5.12/5.44 @ zero_zero_rat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_atLeastAtMost_code
% 5.12/5.44 thf(fact_8781_sum__atLeastAtMost__code,axiom,
% 5.12/5.44 ! [F: nat > int,A: nat,B: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.44 = ( set_fo2581907887559384638at_int
% 5.12/5.44 @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 5.12/5.44 @ A
% 5.12/5.44 @ B
% 5.12/5.44 @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_atLeastAtMost_code
% 5.12/5.44 thf(fact_8782_sum__atLeastAtMost__code,axiom,
% 5.12/5.44 ! [F: nat > nat,A: nat,B: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.44 = ( set_fo2584398358068434914at_nat
% 5.12/5.44 @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 5.12/5.44 @ A
% 5.12/5.44 @ B
% 5.12/5.44 @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_atLeastAtMost_code
% 5.12/5.44 thf(fact_8783_sum__atLeastAtMost__code,axiom,
% 5.12/5.44 ! [F: nat > real,A: nat,B: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.44 = ( set_fo3111899725591712190t_real
% 5.12/5.44 @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 5.12/5.44 @ A
% 5.12/5.44 @ B
% 5.12/5.44 @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_atLeastAtMost_code
% 5.12/5.44 thf(fact_8784_sum_Oub__add__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > rat,P4: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.ub_add_nat
% 5.12/5.44 thf(fact_8785_sum_Oub__add__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > int,P4: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.44 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.44 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.ub_add_nat
% 5.12/5.44 thf(fact_8786_sum_Oub__add__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > nat,P4: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.44 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.ub_add_nat
% 5.12/5.44 thf(fact_8787_sum_Oub__add__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,G: nat > real,P4: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P4 ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.ub_add_nat
% 5.12/5.44 thf(fact_8788_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.12/5.44 ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 5.12/5.44 = one_one_Code_integer )
% 5.12/5.44 => ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_le3102999989581377725nteger
% 5.12/5.44 @ ( abs_abs_Code_integer
% 5.12/5.44 @ ( minus_8373710615458151222nteger
% 5.12/5.44 @ ( groups6621422865394947399nteger
% 5.12/5.44 @ ^ [I2: complex] : ( times_3573771949741848930nteger @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8789_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.12/5.44 ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 5.12/5.44 = one_one_Code_integer )
% 5.12/5.44 => ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_le3102999989581377725nteger
% 5.12/5.44 @ ( abs_abs_Code_integer
% 5.12/5.44 @ ( minus_8373710615458151222nteger
% 5.12/5.44 @ ( groups7713935264441627589nteger
% 5.12/5.44 @ ^ [I2: real] : ( times_3573771949741848930nteger @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8790_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.12/5.44 ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.12/5.44 = one_one_Code_integer )
% 5.12/5.44 => ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_le3102999989581377725nteger
% 5.12/5.44 @ ( abs_abs_Code_integer
% 5.12/5.44 @ ( minus_8373710615458151222nteger
% 5.12/5.44 @ ( groups7501900531339628137nteger
% 5.12/5.44 @ ^ [I2: nat] : ( times_3573771949741848930nteger @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8791_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.12/5.44 ( ! [I3: int] :
% 5.12/5.44 ( ( member_int @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.12/5.44 = one_one_Code_integer )
% 5.12/5.44 => ( ! [I3: int] :
% 5.12/5.44 ( ( member_int @ I3 @ I5 )
% 5.12/5.44 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_le3102999989581377725nteger
% 5.12/5.44 @ ( abs_abs_Code_integer
% 5.12/5.44 @ ( minus_8373710615458151222nteger
% 5.12/5.44 @ ( groups7873554091576472773nteger
% 5.12/5.44 @ ^ [I2: int] : ( times_3573771949741848930nteger @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8792_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.12/5.44 ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 5.12/5.44 = one_one_real )
% 5.12/5.44 => ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_real
% 5.12/5.44 @ ( abs_abs_real
% 5.12/5.44 @ ( minus_minus_real
% 5.12/5.44 @ ( groups5808333547571424918x_real
% 5.12/5.44 @ ^ [I2: complex] : ( times_times_real @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8793_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.12/5.44 ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 5.12/5.44 = one_one_real )
% 5.12/5.44 => ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_real
% 5.12/5.44 @ ( abs_abs_real
% 5.12/5.44 @ ( minus_minus_real
% 5.12/5.44 @ ( groups8097168146408367636l_real
% 5.12/5.44 @ ^ [I2: real] : ( times_times_real @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8794_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.12/5.44 ( ! [I3: int] :
% 5.12/5.44 ( ( member_int @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 5.12/5.44 = one_one_real )
% 5.12/5.44 => ( ! [I3: int] :
% 5.12/5.44 ( ( member_int @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_real
% 5.12/5.44 @ ( abs_abs_real
% 5.12/5.44 @ ( minus_minus_real
% 5.12/5.44 @ ( groups8778361861064173332t_real
% 5.12/5.44 @ ^ [I2: int] : ( times_times_real @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8795_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.12/5.44 ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups5058264527183730370ex_rat @ X @ I5 )
% 5.12/5.44 = one_one_rat )
% 5.12/5.44 => ( ! [I3: complex] :
% 5.12/5.44 ( ( member_complex @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_rat
% 5.12/5.44 @ ( abs_abs_rat
% 5.12/5.44 @ ( minus_minus_rat
% 5.12/5.44 @ ( groups5058264527183730370ex_rat
% 5.12/5.44 @ ^ [I2: complex] : ( times_times_rat @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8796_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.12/5.44 ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 5.12/5.44 = one_one_rat )
% 5.12/5.44 => ( ! [I3: real] :
% 5.12/5.44 ( ( member_real @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_rat
% 5.12/5.44 @ ( abs_abs_rat
% 5.12/5.44 @ ( minus_minus_rat
% 5.12/5.44 @ ( groups1300246762558778688al_rat
% 5.12/5.44 @ ^ [I2: real] : ( times_times_rat @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8797_convex__sum__bound__le,axiom,
% 5.12/5.44 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.12/5.44 ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.12/5.44 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.12/5.44 = one_one_rat )
% 5.12/5.44 => ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.12/5.44 => ( ord_less_eq_rat
% 5.12/5.44 @ ( abs_abs_rat
% 5.12/5.44 @ ( minus_minus_rat
% 5.12/5.44 @ ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [I2: nat] : ( times_times_rat @ ( A @ I2 ) @ ( X @ I2 ) )
% 5.12/5.44 @ I5 )
% 5.12/5.44 @ B ) )
% 5.12/5.44 @ Delta ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % convex_sum_bound_le
% 5.12/5.44 thf(fact_8798_sum__natinterval__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > rat] :
% 5.12/5.44 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_rat @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_natinterval_diff
% 5.12/5.44 thf(fact_8799_sum__natinterval__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > int] :
% 5.12/5.44 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_int @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_natinterval_diff
% 5.12/5.44 thf(fact_8800_sum__natinterval__diff,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > real] :
% 5.12/5.44 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( minus_minus_real @ ( F @ M2 ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = zero_zero_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_natinterval_diff
% 5.12/5.44 thf(fact_8801_sum__telescope_H_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.12/5.44 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_telescope''
% 5.12/5.44 thf(fact_8802_sum__telescope_H_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.12/5.44 = ( minus_minus_int @ ( F @ N ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_telescope''
% 5.12/5.44 thf(fact_8803_sum__telescope_H_H,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,F: nat > real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 5.12/5.44 = ( minus_minus_real @ ( F @ N ) @ ( F @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_telescope''
% 5.12/5.44 thf(fact_8804_geometric__sums,axiom,
% 5.12/5.44 ! [C: real] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.12/5.44 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % geometric_sums
% 5.12/5.44 thf(fact_8805_geometric__sums,axiom,
% 5.12/5.44 ! [C: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.12/5.44 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % geometric_sums
% 5.12/5.44 thf(fact_8806_power__half__series,axiom,
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 5.12/5.44 @ one_one_real ) ).
% 5.12/5.44
% 5.12/5.44 % power_half_series
% 5.12/5.44 thf(fact_8807_mask__eq__sum__exp,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.12/5.44 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % mask_eq_sum_exp
% 5.12/5.44 thf(fact_8808_mask__eq__sum__exp,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.12/5.44 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % mask_eq_sum_exp
% 5.12/5.44 thf(fact_8809_sum__gp__multiplied,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,X: complex] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_multiplied
% 5.12/5.44 thf(fact_8810_sum__gp__multiplied,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,X: rat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_multiplied
% 5.12/5.44 thf(fact_8811_sum__gp__multiplied,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,X: int] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_multiplied
% 5.12/5.44 thf(fact_8812_sum__gp__multiplied,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,X: real] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_multiplied
% 5.12/5.44 thf(fact_8813_sum_Oin__pairs,axiom,
% 5.12/5.44 ! [G: nat > rat,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.44 = ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.in_pairs
% 5.12/5.44 thf(fact_8814_sum_Oin__pairs,axiom,
% 5.12/5.44 ! [G: nat > int,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.44 = ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.in_pairs
% 5.12/5.44 thf(fact_8815_sum_Oin__pairs,axiom,
% 5.12/5.44 ! [G: nat > nat,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.in_pairs
% 5.12/5.44 thf(fact_8816_sum_Oin__pairs,axiom,
% 5.12/5.44 ! [G: nat > real,M2: nat,N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.12/5.44 = ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum.in_pairs
% 5.12/5.44 thf(fact_8817_sums__if_H,axiom,
% 5.12/5.44 ! [G: nat > real,X: real] :
% 5.12/5.44 ( ( sums_real @ G @ X )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.44 @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_if'
% 5.12/5.44 thf(fact_8818_sums__if,axiom,
% 5.12/5.44 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 5.12/5.44 ( ( sums_real @ G @ X )
% 5.12/5.44 => ( ( sums_real @ F @ Y )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( F @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.44 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sums_if
% 5.12/5.44 thf(fact_8819_mask__eq__sum__exp__nat,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % mask_eq_sum_exp_nat
% 5.12/5.44 thf(fact_8820_gauss__sum__nat,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [X2: nat] : X2
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gauss_sum_nat
% 5.12/5.44 thf(fact_8821_gbinomial__sum__up__index,axiom,
% 5.12/5.44 ! [K: nat,N: nat] :
% 5.12/5.44 ( ( groups2073611262835488442omplex
% 5.12/5.44 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gbinomial_sum_up_index
% 5.12/5.44 thf(fact_8822_gbinomial__sum__up__index,axiom,
% 5.12/5.44 ! [K: nat,N: nat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gbinomial_sum_up_index
% 5.12/5.44 thf(fact_8823_gbinomial__sum__up__index,axiom,
% 5.12/5.44 ! [K: nat,N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gbinomial_sum_up_index
% 5.12/5.44 thf(fact_8824_double__arith__series,axiom,
% 5.12/5.44 ! [A: complex,D: complex,N: nat] :
% 5.12/5.44 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.12/5.44 @ ( groups2073611262835488442omplex
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_arith_series
% 5.12/5.44 thf(fact_8825_double__arith__series,axiom,
% 5.12/5.44 ! [A: rat,D: rat,N: nat] :
% 5.12/5.44 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.12/5.44 @ ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_arith_series
% 5.12/5.44 thf(fact_8826_double__arith__series,axiom,
% 5.12/5.44 ! [A: int,D: int,N: nat] :
% 5.12/5.44 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.12/5.44 @ ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_arith_series
% 5.12/5.44 thf(fact_8827_double__arith__series,axiom,
% 5.12/5.44 ! [A: nat,D: nat,N: nat] :
% 5.12/5.44 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_arith_series
% 5.12/5.44 thf(fact_8828_double__arith__series,axiom,
% 5.12/5.44 ! [A: real,D: real,N: nat] :
% 5.12/5.44 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_arith_series
% 5.12/5.44 thf(fact_8829_double__gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum
% 5.12/5.44 thf(fact_8830_double__gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum
% 5.12/5.44 thf(fact_8831_double__gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum
% 5.12/5.44 thf(fact_8832_double__gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum
% 5.12/5.44 thf(fact_8833_double__gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum
% 5.12/5.44 thf(fact_8834_arith__series__nat,axiom,
% 5.12/5.44 ! [A: nat,D: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arith_series_nat
% 5.12/5.44 thf(fact_8835_Sum__Icc__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [X2: nat] : X2
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Sum_Icc_nat
% 5.12/5.44 thf(fact_8836_gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gauss_sum
% 5.12/5.44 thf(fact_8837_gauss__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gauss_sum
% 5.12/5.44 thf(fact_8838_arith__series,axiom,
% 5.12/5.44 ! [A: int,D: int,N: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arith_series
% 5.12/5.44 thf(fact_8839_arith__series,axiom,
% 5.12/5.44 ! [A: nat,D: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ D ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( 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 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arith_series
% 5.12/5.44 thf(fact_8840_double__gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.12/5.44 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8841_double__gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.12/5.44 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8842_double__gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.12/5.44 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8843_double__gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.12/5.44 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8844_double__gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.12/5.44 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % double_gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8845_sum__gp__offset,axiom,
% 5.12/5.44 ! [X: complex,M2: nat,N: nat] :
% 5.12/5.44 ( ( ( X = one_one_complex )
% 5.12/5.44 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.12/5.44 & ( ( X != one_one_complex )
% 5.12/5.44 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_offset
% 5.12/5.44 thf(fact_8846_sum__gp__offset,axiom,
% 5.12/5.44 ! [X: rat,M2: nat,N: nat] :
% 5.12/5.44 ( ( ( X = one_one_rat )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.12/5.44 & ( ( X != one_one_rat )
% 5.12/5.44 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_offset
% 5.12/5.44 thf(fact_8847_sum__gp__offset,axiom,
% 5.12/5.44 ! [X: real,M2: nat,N: nat] :
% 5.12/5.44 ( ( ( X = one_one_real )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.12/5.44 & ( ( X != one_one_real )
% 5.12/5.44 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_gp_offset
% 5.12/5.44 thf(fact_8848_cos__paired,axiom,
% 5.12/5.44 ! [X: real] :
% 5.12/5.44 ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.44 @ ( cos_real @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % cos_paired
% 5.12/5.44 thf(fact_8849_gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.12/5.44 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8850_gauss__sum__from__Suc__0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gauss_sum_from_Suc_0
% 5.12/5.44 thf(fact_8851_gchoose__row__sum__weighted,axiom,
% 5.12/5.44 ! [R4: complex,M2: nat] :
% 5.12/5.44 ( ( groups2073611262835488442omplex
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R4 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R4 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.12/5.44 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M2 ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R4 @ ( suc @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gchoose_row_sum_weighted
% 5.12/5.44 thf(fact_8852_gchoose__row__sum__weighted,axiom,
% 5.12/5.44 ! [R4: rat,M2: nat] :
% 5.12/5.44 ( ( groups2906978787729119204at_rat
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R4 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.12/5.44 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M2 ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R4 @ ( suc @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gchoose_row_sum_weighted
% 5.12/5.44 thf(fact_8853_gchoose__row__sum__weighted,axiom,
% 5.12/5.44 ! [R4: real,M2: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R4 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.12/5.44 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 5.12/5.44 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R4 @ ( suc @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gchoose_row_sum_weighted
% 5.12/5.44 thf(fact_8854_vebt__member_Opelims_I2_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ( vEBT_vebt_member @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.12/5.44 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( Xa != Mi )
% 5.12/5.44 => ( ( Xa != Ma2 )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Xa @ Mi )
% 5.12/5.44 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.12/5.44 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % vebt_member.pelims(2)
% 5.12/5.44 thf(fact_8855_geometric__deriv__sums,axiom,
% 5.12/5.44 ! [Z2: real] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z2 ) @ one_one_real )
% 5.12/5.44 => ( sums_real
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) @ ( power_power_real @ Z2 @ N4 ) )
% 5.12/5.44 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % geometric_deriv_sums
% 5.12/5.44 thf(fact_8856_geometric__deriv__sums,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z2 ) @ one_one_real )
% 5.12/5.44 => ( sums_complex
% 5.12/5.44 @ ^ [N4: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N4 ) ) @ ( power_power_complex @ Z2 @ N4 ) )
% 5.12/5.44 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % geometric_deriv_sums
% 5.12/5.44 thf(fact_8857_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.44 ( ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.12/5.44 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.naive_member.pelims(1)
% 5.12/5.44 thf(fact_8858_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.12/5.44 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.naive_member.pelims(2)
% 5.12/5.44 thf(fact_8859_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [A4: $o,B3: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.12/5.44 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => A4 )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( ( ( Xa = one_one_nat )
% 5.12/5.44 => B3 )
% 5.12/5.44 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.12/5.44 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.12/5.44 => ~ ! [Uy: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa ) )
% 5.12/5.44 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.naive_member.pelims(3)
% 5.12/5.44 thf(fact_8860_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ~ ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 5.12/5.44 => ( ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) @ Xa ) ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.12/5.44 => ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 ) ) ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) @ Xa ) )
% 5.12/5.44 => ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 )
% 5.12/5.44 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.12/5.44 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) )
% 5.12/5.44 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.membermima.pelims(3)
% 5.12/5.44 thf(fact_8861_int__sum,axiom,
% 5.12/5.44 ! [F: int > nat,A2: set_int] :
% 5.12/5.44 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_sum
% 5.12/5.44 thf(fact_8862_int__sum,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat] :
% 5.12/5.44 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.12/5.44 = ( groups3539618377306564664at_int
% 5.12/5.44 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.12/5.44 @ A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_sum
% 5.12/5.44 thf(fact_8863_sum__subtractf__nat,axiom,
% 5.12/5.44 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.12/5.44 ( ! [X3: complex] :
% 5.12/5.44 ( ( member_complex @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ( groups5693394587270226106ex_nat
% 5.12/5.44 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf_nat
% 5.12/5.44 thf(fact_8864_sum__subtractf__nat,axiom,
% 5.12/5.44 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.12/5.44 ( ! [X3: real] :
% 5.12/5.44 ( ( member_real @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ( groups1935376822645274424al_nat
% 5.12/5.44 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf_nat
% 5.12/5.44 thf(fact_8865_sum__subtractf__nat,axiom,
% 5.12/5.44 ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.12/5.44 ( ! [X3: set_nat] :
% 5.12/5.44 ( ( member_set_nat @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ( groups8294997508430121362at_nat
% 5.12/5.44 @ ^ [X2: set_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf_nat
% 5.12/5.44 thf(fact_8866_sum__subtractf__nat,axiom,
% 5.12/5.44 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.12/5.44 ( ! [X3: int] :
% 5.12/5.44 ( ( member_int @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ( groups4541462559716669496nt_nat
% 5.12/5.44 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf_nat
% 5.12/5.44 thf(fact_8867_sum__subtractf__nat,axiom,
% 5.12/5.44 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.44 @ A2 )
% 5.12/5.44 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_subtractf_nat
% 5.12/5.44 thf(fact_8868_sum__SucD,axiom,
% 5.12/5.44 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.12/5.44 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.12/5.44 = ( suc @ N ) )
% 5.12/5.44 => ? [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ A2 )
% 5.12/5.44 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_SucD
% 5.12/5.44 thf(fact_8869_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: complex,A2: set_complex,F: complex > nat] :
% 5.12/5.44 ( ( ( member_complex @ A @ A2 )
% 5.12/5.44 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member_complex @ A @ A2 )
% 5.12/5.44 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.12/5.44 = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8870_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: real,A2: set_real,F: real > nat] :
% 5.12/5.44 ( ( ( member_real @ A @ A2 )
% 5.12/5.44 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member_real @ A @ A2 )
% 5.12/5.44 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.12/5.44 = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8871_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 5.12/5.44 ( ( ( member_set_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member_set_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.12/5.44 = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8872_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: int,A2: set_int,F: int > nat] :
% 5.12/5.44 ( ( ( member_int @ A @ A2 )
% 5.12/5.44 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member_int @ A @ A2 )
% 5.12/5.44 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.12/5.44 = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8873_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.12/5.44 ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 5.12/5.44 = ( groups977919841031483927at_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8874_sum__diff1__nat,axiom,
% 5.12/5.44 ! [A: nat,A2: set_nat,F: nat > nat] :
% 5.12/5.44 ( ( ( member_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.12/5.44 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.12/5.44 & ( ~ ( member_nat @ A @ A2 )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_diff1_nat
% 5.12/5.44 thf(fact_8875_sum__nth__roots,axiom,
% 5.12/5.44 ! [N: nat,C: complex] :
% 5.12/5.44 ( ( ord_less_nat @ one_one_nat @ N )
% 5.12/5.44 => ( ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : X2
% 5.12/5.44 @ ( collect_complex
% 5.12/5.44 @ ^ [Z6: complex] :
% 5.12/5.44 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.44 = C ) ) )
% 5.12/5.44 = zero_zero_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_nth_roots
% 5.12/5.44 thf(fact_8876_norm__prod__diff,axiom,
% 5.12/5.44 ! [I5: set_nat,Z2: nat > complex,W: nat > complex] :
% 5.12/5.44 ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z2 @ I3 ) ) @ one_one_real ) )
% 5.12/5.44 => ( ! [I3: nat] :
% 5.12/5.44 ( ( member_nat @ I3 @ I5 )
% 5.12/5.44 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I3 ) ) @ one_one_real ) )
% 5.12/5.44 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z2 @ I5 ) @ ( groups6464643781859351333omplex @ W @ I5 ) ) )
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z2 @ I2 ) @ ( W @ I2 ) ) )
% 5.12/5.44 @ I5 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % norm_prod_diff
% 5.12/5.44 thf(fact_8877_sum__roots__unity,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( ord_less_nat @ one_one_nat @ N )
% 5.12/5.44 => ( ( groups7754918857620584856omplex
% 5.12/5.44 @ ^ [X2: complex] : X2
% 5.12/5.44 @ ( collect_complex
% 5.12/5.44 @ ^ [Z6: complex] :
% 5.12/5.44 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.44 = one_one_complex ) ) )
% 5.12/5.44 = zero_zero_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_roots_unity
% 5.12/5.44 thf(fact_8878_Sum__Icc__int,axiom,
% 5.12/5.44 ! [M2: int,N: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ M2 @ N )
% 5.12/5.44 => ( ( groups4538972089207619220nt_int
% 5.12/5.44 @ ^ [X2: int] : X2
% 5.12/5.44 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Sum_Icc_int
% 5.12/5.44 thf(fact_8879_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.44 ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 ) ) ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) @ Xa ) )
% 5.12/5.44 => ~ ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 )
% 5.12/5.44 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.12/5.44 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) )
% 5.12/5.44 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.membermima.pelims(2)
% 5.12/5.44 thf(fact_8880_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.12/5.44 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.44 ( ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.44 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) )
% 5.12/5.44 => ( ~ Y
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 5.12/5.44 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( Xa = Mi )
% 5.12/5.44 | ( Xa = Ma2 )
% 5.12/5.44 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc2 ) @ Xa ) ) ) )
% 5.12/5.44 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.12/5.44 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.44 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.12/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT_internal.membermima.pelims(1)
% 5.12/5.44 thf(fact_8881_Maclaurin__minus__cos__expansion,axiom,
% 5.12/5.44 ! [N: nat,X: real] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.44 => ? [T3: real] :
% 5.12/5.44 ( ( ord_less_real @ X @ T3 )
% 5.12/5.44 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.12/5.44 & ( ( cos_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_minus_cos_expansion
% 5.12/5.44 thf(fact_8882_Maclaurin__cos__expansion2,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ? [T3: real] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.12/5.44 & ( ord_less_real @ T3 @ X )
% 5.12/5.44 & ( ( cos_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_cos_expansion2
% 5.12/5.44 thf(fact_8883_Maclaurin__sin__expansion3,axiom,
% 5.12/5.44 ! [N: nat,X: real] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.44 => ? [T3: real] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.12/5.44 & ( ord_less_real @ T3 @ X )
% 5.12/5.44 & ( ( sin_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_sin_expansion3
% 5.12/5.44 thf(fact_8884_Maclaurin__sin__expansion4,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.44 => ? [T3: real] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.12/5.44 & ( ord_less_eq_real @ T3 @ X )
% 5.12/5.44 & ( ( sin_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_sin_expansion4
% 5.12/5.44 thf(fact_8885_lessThan__0,axiom,
% 5.12/5.44 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.12/5.44 = bot_bot_set_nat ) ).
% 5.12/5.44
% 5.12/5.44 % lessThan_0
% 5.12/5.44 thf(fact_8886_sumr__cos__zero__one,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ zero_zero_real @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.12/5.44 = one_one_real ) ).
% 5.12/5.44
% 5.12/5.44 % sumr_cos_zero_one
% 5.12/5.44 thf(fact_8887_lessThan__Suc,axiom,
% 5.12/5.44 ! [K: nat] :
% 5.12/5.44 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.12/5.44 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % lessThan_Suc
% 5.12/5.44 thf(fact_8888_lessThan__empty__iff,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( ( set_ord_lessThan_nat @ N )
% 5.12/5.44 = bot_bot_set_nat )
% 5.12/5.44 = ( N = zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % lessThan_empty_iff
% 5.12/5.44 thf(fact_8889_Maclaurin__lemma,axiom,
% 5.12/5.44 ! [H: real,F: real > real,J2: nat > real,N: nat] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ H )
% 5.12/5.44 => ? [B7: real] :
% 5.12/5.44 ( ( F @ H )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( J2 @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ B7 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_lemma
% 5.12/5.44 thf(fact_8890_sum__split__even__odd,axiom,
% 5.12/5.44 ! [F: nat > real,G: nat > real,N: nat] :
% 5.12/5.44 ( ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ ( F @ I2 ) @ ( G @ I2 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ one_one_nat ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_split_even_odd
% 5.12/5.44 thf(fact_8891_Maclaurin__exp__le,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ? [T3: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.44 & ( ( exp_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_exp_le
% 5.12/5.44 thf(fact_8892_Maclaurin__sin__bound,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ( ord_less_eq_real
% 5.12/5.44 @ ( abs_abs_real
% 5.12/5.44 @ ( minus_minus_real @ ( sin_real @ X )
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.12/5.44 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_sin_bound
% 5.12/5.44 thf(fact_8893_sum__pos__lt__pair,axiom,
% 5.12/5.44 ! [F: nat > real,K: nat] :
% 5.12/5.44 ( ( summable_real @ F )
% 5.12/5.44 => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 5.12/5.44 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_pos_lt_pair
% 5.12/5.44 thf(fact_8894_Maclaurin__exp__lt,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ( ( X != zero_zero_real )
% 5.12/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ? [T3: real] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.12/5.44 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.44 & ( ( exp_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_exp_lt
% 5.12/5.44 thf(fact_8895_Maclaurin__sin__expansion,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ? [T3: real] :
% 5.12/5.44 ( ( sin_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_sin_expansion
% 5.12/5.44 thf(fact_8896_Maclaurin__sin__expansion2,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ? [T3: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.44 & ( ( sin_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_sin_expansion2
% 5.12/5.44 thf(fact_8897_Maclaurin__cos__expansion,axiom,
% 5.12/5.44 ! [X: real,N: nat] :
% 5.12/5.44 ? [T3: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.44 & ( ( cos_real @ X )
% 5.12/5.44 = ( plus_plus_real
% 5.12/5.44 @ ( groups6591440286371151544t_real
% 5.12/5.44 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.44 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Maclaurin_cos_expansion
% 5.12/5.44 thf(fact_8898_bij__betw__roots__unity,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ( bij_betw_nat_complex
% 5.12/5.44 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.12/5.44 @ ( set_ord_lessThan_nat @ N )
% 5.12/5.44 @ ( collect_complex
% 5.12/5.44 @ ^ [Z6: complex] :
% 5.12/5.44 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.44 = one_one_complex ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bij_betw_roots_unity
% 5.12/5.44 thf(fact_8899_atMost__0,axiom,
% 5.12/5.44 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.12/5.44 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % atMost_0
% 5.12/5.44 thf(fact_8900_atMost__atLeast0,axiom,
% 5.12/5.44 ( set_ord_atMost_nat
% 5.12/5.44 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % atMost_atLeast0
% 5.12/5.44 thf(fact_8901_lessThan__Suc__atMost,axiom,
% 5.12/5.44 ! [K: nat] :
% 5.12/5.44 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.12/5.44 = ( set_ord_atMost_nat @ K ) ) ).
% 5.12/5.44
% 5.12/5.44 % lessThan_Suc_atMost
% 5.12/5.44 thf(fact_8902_atMost__Suc,axiom,
% 5.12/5.44 ! [K: nat] :
% 5.12/5.44 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.12/5.44 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % atMost_Suc
% 5.12/5.44 thf(fact_8903_sum__choose__upper,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( binomial @ K3 @ M2 )
% 5.12/5.44 @ ( set_ord_atMost_nat @ N ) )
% 5.12/5.44 = ( binomial @ ( suc @ N ) @ ( suc @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_choose_upper
% 5.12/5.44 thf(fact_8904_diffs__sin__coeff,axiom,
% 5.12/5.44 ( ( diffs_real @ sin_coeff )
% 5.12/5.44 = cos_coeff ) ).
% 5.12/5.44
% 5.12/5.44 % diffs_sin_coeff
% 5.12/5.44 thf(fact_8905_sum__choose__lower,axiom,
% 5.12/5.44 ! [R4: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R4 @ K3 ) @ K3 )
% 5.12/5.44 @ ( set_ord_atMost_nat @ N ) )
% 5.12/5.44 = ( binomial @ ( suc @ ( plus_plus_nat @ R4 @ N ) ) @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_choose_lower
% 5.12/5.44 thf(fact_8906_choose__rising__sum_I1_J,axiom,
% 5.12/5.44 ! [N: nat,M2: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.12/5.44 @ ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.44 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % choose_rising_sum(1)
% 5.12/5.44 thf(fact_8907_choose__rising__sum_I2_J,axiom,
% 5.12/5.44 ! [N: nat,M2: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.12/5.44 @ ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.44 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % choose_rising_sum(2)
% 5.12/5.44 thf(fact_8908_diffs__cos__coeff,axiom,
% 5.12/5.44 ( ( diffs_real @ cos_coeff )
% 5.12/5.44 = ( ^ [N4: nat] : ( uminus_uminus_real @ ( sin_coeff @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % diffs_cos_coeff
% 5.12/5.44 thf(fact_8909_atLeast1__atMost__eq__remove0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.44 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeast1_atMost_eq_remove0
% 5.12/5.44 thf(fact_8910_sum__choose__diagonal,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M2 @ K3 ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.44 = ( binomial @ ( suc @ N ) @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_choose_diagonal
% 5.12/5.44 thf(fact_8911_vandermonde,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,R4: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M2 @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R4 @ K3 ) ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ R4 ) )
% 5.12/5.44 = ( binomial @ ( plus_plus_nat @ M2 @ N ) @ R4 ) ) ).
% 5.12/5.44
% 5.12/5.44 % vandermonde
% 5.12/5.44 thf(fact_8912_binomial,axiom,
% 5.12/5.44 ! [A: nat,B: nat,N: nat] :
% 5.12/5.44 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % binomial
% 5.12/5.44 thf(fact_8913_polynomial__product__nat,axiom,
% 5.12/5.44 ! [M2: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.12/5.44 ( ! [I3: nat] :
% 5.12/5.44 ( ( ord_less_nat @ M2 @ I3 )
% 5.12/5.44 => ( ( A @ I3 )
% 5.12/5.44 = zero_zero_nat ) )
% 5.12/5.44 => ( ! [J: nat] :
% 5.12/5.44 ( ( ord_less_nat @ N @ J )
% 5.12/5.44 => ( ( B @ J )
% 5.12/5.44 = zero_zero_nat ) )
% 5.12/5.44 => ( ( times_times_nat
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( power_power_nat @ X @ I2 ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ N ) ) )
% 5.12/5.44 = ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [R: nat] :
% 5.12/5.44 ( times_times_nat
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ R ) )
% 5.12/5.44 @ ( power_power_nat @ X @ R ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % polynomial_product_nat
% 5.12/5.44 thf(fact_8914_binomial__r__part__sum,axiom,
% 5.12/5.44 ! [M2: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % binomial_r_part_sum
% 5.12/5.44 thf(fact_8915_choose__linear__sum,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 5.12/5.44 @ ( set_ord_atMost_nat @ N ) )
% 5.12/5.44 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % choose_linear_sum
% 5.12/5.44 thf(fact_8916_Arg__def,axiom,
% 5.12/5.44 ( arg
% 5.12/5.44 = ( ^ [Z6: complex] :
% 5.12/5.44 ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 5.12/5.44 @ ( fChoice_real
% 5.12/5.44 @ ^ [A3: real] :
% 5.12/5.44 ( ( ( sgn_sgn_complex @ Z6 )
% 5.12/5.44 = ( cis @ A3 ) )
% 5.12/5.44 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.12/5.44 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Arg_def
% 5.12/5.44 thf(fact_8917_vebt__buildup_Opelims,axiom,
% 5.12/5.44 ! [X: nat,Y: vEBT_VEBT] :
% 5.12/5.44 ( ( ( vEBT_vebt_buildup @ X )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.12/5.44 => ( ( ( X = zero_zero_nat )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.44 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.12/5.44 => ( ( ( X
% 5.12/5.44 = ( suc @ zero_zero_nat ) )
% 5.12/5.44 => ( ( Y
% 5.12/5.44 = ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.44 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.12/5.44 => ~ ! [Va: nat] :
% 5.12/5.44 ( ( X
% 5.12/5.44 = ( suc @ ( suc @ Va ) ) )
% 5.12/5.44 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( 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 ) ) ) ) ) ) )
% 5.12/5.44 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( 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 ) ) ) ) ) ) ) ) )
% 5.12/5.44 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % vebt_buildup.pelims
% 5.12/5.44 thf(fact_8918_arctan__def,axiom,
% 5.12/5.44 ( arctan
% 5.12/5.44 = ( ^ [Y6: real] :
% 5.12/5.44 ( the_real
% 5.12/5.44 @ ^ [X2: real] :
% 5.12/5.44 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.12/5.44 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.44 & ( ( tan_real @ X2 )
% 5.12/5.44 = Y6 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arctan_def
% 5.12/5.44 thf(fact_8919_ln__real__def,axiom,
% 5.12/5.44 ( ln_ln_real
% 5.12/5.44 = ( ^ [X2: real] :
% 5.12/5.44 ( the_real
% 5.12/5.44 @ ^ [U2: real] :
% 5.12/5.44 ( ( exp_real @ U2 )
% 5.12/5.44 = X2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % ln_real_def
% 5.12/5.44 thf(fact_8920_ln__neg__is__const,axiom,
% 5.12/5.44 ! [X: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.12/5.44 => ( ( ln_ln_real @ X )
% 5.12/5.44 = ( the_real
% 5.12/5.44 @ ^ [X2: real] : $false ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % ln_neg_is_const
% 5.12/5.44 thf(fact_8921_arccos__def,axiom,
% 5.12/5.44 ( arccos
% 5.12/5.44 = ( ^ [Y6: real] :
% 5.12/5.44 ( the_real
% 5.12/5.44 @ ^ [X2: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.12/5.44 & ( ord_less_eq_real @ X2 @ pi )
% 5.12/5.44 & ( ( cos_real @ X2 )
% 5.12/5.44 = Y6 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arccos_def
% 5.12/5.44 thf(fact_8922_divmod__step__nat__def,axiom,
% 5.12/5.44 ( unique5026877609467782581ep_nat
% 5.12/5.44 = ( ^ [L2: num] :
% 5.12/5.44 ( produc2626176000494625587at_nat
% 5.12/5.44 @ ^ [Q4: nat,R: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_step_nat_def
% 5.12/5.44 thf(fact_8923_divmod__step__int__def,axiom,
% 5.12/5.44 ( unique5024387138958732305ep_int
% 5.12/5.44 = ( ^ [L2: num] :
% 5.12/5.44 ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [Q4: int,R: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_step_int_def
% 5.12/5.44 thf(fact_8924_pi__half,axiom,
% 5.12/5.44 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.44 = ( the_real
% 5.12/5.44 @ ^ [X2: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.12/5.44 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.44 & ( ( cos_real @ X2 )
% 5.12/5.44 = zero_zero_real ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % pi_half
% 5.12/5.44 thf(fact_8925_pi__def,axiom,
% 5.12/5.44 ( pi
% 5.12/5.44 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.12/5.44 @ ( the_real
% 5.12/5.44 @ ^ [X2: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.12/5.44 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.12/5.44 & ( ( cos_real @ X2 )
% 5.12/5.44 = zero_zero_real ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % pi_def
% 5.12/5.44 thf(fact_8926_arcsin__def,axiom,
% 5.12/5.44 ( arcsin
% 5.12/5.44 = ( ^ [Y6: real] :
% 5.12/5.44 ( the_real
% 5.12/5.44 @ ^ [X2: real] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.12/5.44 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.44 & ( ( sin_real @ X2 )
% 5.12/5.44 = Y6 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % arcsin_def
% 5.12/5.44 thf(fact_8927_divmod__nat__if,axiom,
% 5.12/5.44 ( divmod_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.44 ( if_Pro6206227464963214023at_nat
% 5.12/5.44 @ ( ( N4 = zero_zero_nat )
% 5.12/5.44 | ( ord_less_nat @ M5 @ N4 ) )
% 5.12/5.44 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 5.12/5.44 @ ( produc2626176000494625587at_nat
% 5.12/5.44 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.12/5.44 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_nat_if
% 5.12/5.44 thf(fact_8928_set__encode__def,axiom,
% 5.12/5.44 ( nat_set_encode
% 5.12/5.44 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_def
% 5.12/5.44 thf(fact_8929_Sum__Ico__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [X2: nat] : X2
% 5.12/5.44 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Sum_Ico_nat
% 5.12/5.44 thf(fact_8930_VEBT_Osize_I3_J,axiom,
% 5.12/5.44 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.12/5.44 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.12/5.44 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT.size(3)
% 5.12/5.44 thf(fact_8931_set__decode__inverse,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 5.12/5.44 = N ) ).
% 5.12/5.44
% 5.12/5.44 % set_decode_inverse
% 5.12/5.44 thf(fact_8932_set__encode__empty,axiom,
% 5.12/5.44 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.12/5.44 = zero_zero_nat ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_empty
% 5.12/5.44 thf(fact_8933_atLeastLessThan__singleton,axiom,
% 5.12/5.44 ! [M2: nat] :
% 5.12/5.44 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 5.12/5.44 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeastLessThan_singleton
% 5.12/5.44 thf(fact_8934_all__nat__less__eq,axiom,
% 5.12/5.44 ! [N: nat,P: nat > $o] :
% 5.12/5.44 ( ( ! [M5: nat] :
% 5.12/5.44 ( ( ord_less_nat @ M5 @ N )
% 5.12/5.44 => ( P @ M5 ) ) )
% 5.12/5.44 = ( ! [X2: nat] :
% 5.12/5.44 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 => ( P @ X2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % all_nat_less_eq
% 5.12/5.44 thf(fact_8935_ex__nat__less__eq,axiom,
% 5.12/5.44 ! [N: nat,P: nat > $o] :
% 5.12/5.44 ( ( ? [M5: nat] :
% 5.12/5.44 ( ( ord_less_nat @ M5 @ N )
% 5.12/5.44 & ( P @ M5 ) ) )
% 5.12/5.44 = ( ? [X2: nat] :
% 5.12/5.44 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 & ( P @ X2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % ex_nat_less_eq
% 5.12/5.44 thf(fact_8936_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.12/5.44 ! [L: nat,U: nat] :
% 5.12/5.44 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.12/5.44 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeastLessThanSuc_atLeastAtMost
% 5.12/5.44 thf(fact_8937_lessThan__atLeast0,axiom,
% 5.12/5.44 ( set_ord_lessThan_nat
% 5.12/5.44 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % lessThan_atLeast0
% 5.12/5.44 thf(fact_8938_atLeastLessThan0,axiom,
% 5.12/5.44 ! [M2: nat] :
% 5.12/5.44 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 5.12/5.44 = bot_bot_set_nat ) ).
% 5.12/5.44
% 5.12/5.44 % atLeastLessThan0
% 5.12/5.44 thf(fact_8939_atLeast0__lessThan__Suc,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.12/5.44 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeast0_lessThan_Suc
% 5.12/5.44 thf(fact_8940_atLeastLessThanSuc,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.44 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 = bot_bot_set_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeastLessThanSuc
% 5.12/5.44 thf(fact_8941_prod__Suc__Suc__fact,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.12/5.44 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % prod_Suc_Suc_fact
% 5.12/5.44 thf(fact_8942_prod__Suc__fact,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % prod_Suc_fact
% 5.12/5.44 thf(fact_8943_atLeast1__lessThan__eq__remove0,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.44 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeast1_lessThan_eq_remove0
% 5.12/5.44 thf(fact_8944_divmod__nat__def,axiom,
% 5.12/5.44 ( divmod_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M5 @ N4 ) @ ( modulo_modulo_nat @ M5 @ N4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_nat_def
% 5.12/5.44 thf(fact_8945_sum__power2,axiom,
% 5.12/5.44 ! [K: nat] :
% 5.12/5.44 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.12/5.44 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % sum_power2
% 5.12/5.44 thf(fact_8946_VEBT_Osize__gen_I1_J,axiom,
% 5.12/5.44 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.12/5.44 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.12/5.44 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % VEBT.size_gen(1)
% 5.12/5.44 thf(fact_8947_Chebyshev__sum__upper__nat,axiom,
% 5.12/5.44 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.12/5.44 ( ! [I3: nat,J: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ I3 @ J )
% 5.12/5.44 => ( ( ord_less_nat @ J @ N )
% 5.12/5.44 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J ) ) ) )
% 5.12/5.44 => ( ! [I3: nat,J: nat] :
% 5.12/5.44 ( ( ord_less_eq_nat @ I3 @ J )
% 5.12/5.44 => ( ( ord_less_nat @ J @ N )
% 5.12/5.44 => ( ord_less_eq_nat @ ( B @ J ) @ ( B @ I3 ) ) ) )
% 5.12/5.44 => ( ord_less_eq_nat
% 5.12/5.44 @ ( times_times_nat @ N
% 5.12/5.44 @ ( groups3542108847815614940at_nat
% 5.12/5.44 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( B @ I2 ) )
% 5.12/5.44 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.12/5.44 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Chebyshev_sum_upper_nat
% 5.12/5.44 thf(fact_8948_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.12/5.44 ! [L: int,U: int] :
% 5.12/5.44 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.12/5.44 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.12/5.44
% 5.12/5.44 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.12/5.44 thf(fact_8949_set__encode__insert,axiom,
% 5.12/5.44 ! [A2: set_nat,N: nat] :
% 5.12/5.44 ( ( finite_finite_nat @ A2 )
% 5.12/5.44 => ( ~ ( member_nat @ N @ A2 )
% 5.12/5.44 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.12/5.44 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_insert
% 5.12/5.44 thf(fact_8950_int__of__nat__def,axiom,
% 5.12/5.44 code_T6385005292777649522of_nat = semiri1314217659103216013at_int ).
% 5.12/5.44
% 5.12/5.44 % int_of_nat_def
% 5.12/5.44 thf(fact_8951_divmod__step__integer__def,axiom,
% 5.12/5.44 ( unique4921790084139445826nteger
% 5.12/5.44 = ( ^ [L2: num] :
% 5.12/5.44 ( produc6916734918728496179nteger
% 5.12/5.44 @ ^ [Q4: code_integer,R: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_step_integer_def
% 5.12/5.44 thf(fact_8952_set__encode__inverse,axiom,
% 5.12/5.44 ! [A2: set_nat] :
% 5.12/5.44 ( ( finite_finite_nat @ A2 )
% 5.12/5.44 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 5.12/5.44 = A2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_inverse
% 5.12/5.44 thf(fact_8953_set__encode__eq,axiom,
% 5.12/5.44 ! [A2: set_nat,B5: set_nat] :
% 5.12/5.44 ( ( finite_finite_nat @ A2 )
% 5.12/5.44 => ( ( finite_finite_nat @ B5 )
% 5.12/5.44 => ( ( ( nat_set_encode @ A2 )
% 5.12/5.44 = ( nat_set_encode @ B5 ) )
% 5.12/5.44 = ( A2 = B5 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_eq
% 5.12/5.44 thf(fact_8954_minus__integer__code_I1_J,axiom,
% 5.12/5.44 ! [K: code_integer] :
% 5.12/5.44 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.12/5.44 = K ) ).
% 5.12/5.44
% 5.12/5.44 % minus_integer_code(1)
% 5.12/5.44 thf(fact_8955_minus__integer__code_I2_J,axiom,
% 5.12/5.44 ! [L: code_integer] :
% 5.12/5.44 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 5.12/5.44 = ( uminus1351360451143612070nteger @ L ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_integer_code(2)
% 5.12/5.44 thf(fact_8956_divmod__integer_H__def,axiom,
% 5.12/5.44 ( unique3479559517661332726nteger
% 5.12/5.44 = ( ^ [M5: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_integer'_def
% 5.12/5.44 thf(fact_8957_bounded__nat__set__is__finite,axiom,
% 5.12/5.44 ! [N5: set_nat,N: nat] :
% 5.12/5.44 ( ! [X3: nat] :
% 5.12/5.44 ( ( member_nat @ X3 @ N5 )
% 5.12/5.44 => ( ord_less_nat @ X3 @ N ) )
% 5.12/5.44 => ( finite_finite_nat @ N5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % bounded_nat_set_is_finite
% 5.12/5.44 thf(fact_8958_finite__nat__set__iff__bounded,axiom,
% 5.12/5.44 ( finite_finite_nat
% 5.12/5.44 = ( ^ [N7: set_nat] :
% 5.12/5.44 ? [M5: nat] :
% 5.12/5.44 ! [X2: nat] :
% 5.12/5.44 ( ( member_nat @ X2 @ N7 )
% 5.12/5.44 => ( ord_less_nat @ X2 @ M5 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_nat_set_iff_bounded
% 5.12/5.44 thf(fact_8959_sgn__integer__code,axiom,
% 5.12/5.44 ( sgn_sgn_Code_integer
% 5.12/5.44 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sgn_integer_code
% 5.12/5.44 thf(fact_8960_finite__set__decode,axiom,
% 5.12/5.44 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_set_decode
% 5.12/5.44 thf(fact_8961_finite__M__bounded__by__nat,axiom,
% 5.12/5.44 ! [P: nat > $o,I: nat] :
% 5.12/5.44 ( finite_finite_nat
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [K3: nat] :
% 5.12/5.44 ( ( P @ K3 )
% 5.12/5.44 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_M_bounded_by_nat
% 5.12/5.44 thf(fact_8962_set__encode__inf,axiom,
% 5.12/5.44 ! [A2: set_nat] :
% 5.12/5.44 ( ~ ( finite_finite_nat @ A2 )
% 5.12/5.44 => ( ( nat_set_encode @ A2 )
% 5.12/5.44 = zero_zero_nat ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_encode_inf
% 5.12/5.44 thf(fact_8963_zero__natural_Orsp,axiom,
% 5.12/5.44 zero_zero_nat = zero_zero_nat ).
% 5.12/5.44
% 5.12/5.44 % zero_natural.rsp
% 5.12/5.44 thf(fact_8964_zero__integer_Orsp,axiom,
% 5.12/5.44 zero_zero_int = zero_zero_int ).
% 5.12/5.44
% 5.12/5.44 % zero_integer.rsp
% 5.12/5.44 thf(fact_8965_one__integer_Orsp,axiom,
% 5.12/5.44 one_one_int = one_one_int ).
% 5.12/5.44
% 5.12/5.44 % one_integer.rsp
% 5.12/5.44 thf(fact_8966_one__natural_Orsp,axiom,
% 5.12/5.44 one_one_nat = one_one_nat ).
% 5.12/5.44
% 5.12/5.44 % one_natural.rsp
% 5.12/5.44 thf(fact_8967_finite__divisors__nat,axiom,
% 5.12/5.44 ! [M2: nat] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.44 => ( finite_finite_nat
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_divisors_nat
% 5.12/5.44 thf(fact_8968_subset__eq__atLeast0__atMost__finite,axiom,
% 5.12/5.44 ! [N5: set_nat,N: nat] :
% 5.12/5.44 ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 => ( finite_finite_nat @ N5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % subset_eq_atLeast0_atMost_finite
% 5.12/5.44 thf(fact_8969_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.12/5.44 ! [N5: set_nat,N: nat] :
% 5.12/5.44 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.12/5.44 => ( finite_finite_nat @ N5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % subset_eq_atLeast0_lessThan_finite
% 5.12/5.44 thf(fact_8970_even__set__encode__iff,axiom,
% 5.12/5.44 ! [A2: set_nat] :
% 5.12/5.44 ( ( finite_finite_nat @ A2 )
% 5.12/5.44 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.12/5.44 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % even_set_encode_iff
% 5.12/5.44 thf(fact_8971_finite__Collect__less__nat,axiom,
% 5.12/5.44 ! [K: nat] :
% 5.12/5.44 ( finite_finite_nat
% 5.12/5.44 @ ( collect_nat
% 5.12/5.44 @ ^ [N4: nat] : ( ord_less_nat @ N4 @ K ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_Collect_less_nat
% 5.12/5.44 thf(fact_8972_finite__interval__int1,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( finite_finite_int
% 5.12/5.44 @ ( collect_int
% 5.12/5.44 @ ^ [I2: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ A @ I2 )
% 5.12/5.44 & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_interval_int1
% 5.12/5.44 thf(fact_8973_finite__interval__int4,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( finite_finite_int
% 5.12/5.44 @ ( collect_int
% 5.12/5.44 @ ^ [I2: int] :
% 5.12/5.44 ( ( ord_less_int @ A @ I2 )
% 5.12/5.44 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_interval_int4
% 5.12/5.44 thf(fact_8974_finite__interval__int2,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( finite_finite_int
% 5.12/5.44 @ ( collect_int
% 5.12/5.44 @ ^ [I2: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ A @ I2 )
% 5.12/5.44 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_interval_int2
% 5.12/5.44 thf(fact_8975_finite__interval__int3,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( finite_finite_int
% 5.12/5.44 @ ( collect_int
% 5.12/5.44 @ ^ [I2: int] :
% 5.12/5.44 ( ( ord_less_int @ A @ I2 )
% 5.12/5.44 & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_interval_int3
% 5.12/5.44 thf(fact_8976_finite__nth__roots,axiom,
% 5.12/5.44 ! [N: nat,C: complex] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.44 => ( finite3207457112153483333omplex
% 5.12/5.44 @ ( collect_complex
% 5.12/5.44 @ ^ [Z6: complex] :
% 5.12/5.44 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.44 = C ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_nth_roots
% 5.12/5.44 thf(fact_8977_uminus__integer__code_I1_J,axiom,
% 5.12/5.44 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.12/5.44 = zero_z3403309356797280102nteger ) ).
% 5.12/5.44
% 5.12/5.44 % uminus_integer_code(1)
% 5.12/5.44 thf(fact_8978_abs__integer__code,axiom,
% 5.12/5.44 ( abs_abs_Code_integer
% 5.12/5.44 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % abs_integer_code
% 5.12/5.44 thf(fact_8979_finite__atLeastZeroLessThan__int,axiom,
% 5.12/5.44 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_atLeastZeroLessThan_int
% 5.12/5.44 thf(fact_8980_finite__divisors__int,axiom,
% 5.12/5.44 ! [I: int] :
% 5.12/5.44 ( ( I != zero_zero_int )
% 5.12/5.44 => ( finite_finite_int
% 5.12/5.44 @ ( collect_int
% 5.12/5.44 @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % finite_divisors_int
% 5.12/5.44 thf(fact_8981_integer__of__int__code,axiom,
% 5.12/5.44 ( code_integer_of_int
% 5.12/5.44 = ( ^ [K3: int] :
% 5.12/5.44 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.12/5.44 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.12/5.44 @ ( if_Code_integer
% 5.12/5.44 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.12/5.44 = zero_zero_int )
% 5.12/5.44 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.12/5.44 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % integer_of_int_code
% 5.12/5.44 thf(fact_8982_int__ge__less__than2__def,axiom,
% 5.12/5.44 ( int_ge_less_than2
% 5.12/5.44 = ( ^ [D4: int] :
% 5.12/5.44 ( collec213857154873943460nt_int
% 5.12/5.44 @ ( produc4947309494688390418_int_o
% 5.12/5.44 @ ^ [Z7: int,Z6: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ D4 @ Z6 )
% 5.12/5.44 & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_ge_less_than2_def
% 5.12/5.44 thf(fact_8983_int__ge__less__than__def,axiom,
% 5.12/5.44 ( int_ge_less_than
% 5.12/5.44 = ( ^ [D4: int] :
% 5.12/5.44 ( collec213857154873943460nt_int
% 5.12/5.44 @ ( produc4947309494688390418_int_o
% 5.12/5.44 @ ^ [Z7: int,Z6: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ D4 @ Z7 )
% 5.12/5.44 & ( ord_less_int @ Z7 @ Z6 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_ge_less_than_def
% 5.12/5.44 thf(fact_8984_zero__integer__def,axiom,
% 5.12/5.44 ( zero_z3403309356797280102nteger
% 5.12/5.44 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % zero_integer_def
% 5.12/5.44 thf(fact_8985_less__integer_Oabs__eq,axiom,
% 5.12/5.44 ! [Xa: int,X: int] :
% 5.12/5.44 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.12/5.44 = ( ord_less_int @ Xa @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % less_integer.abs_eq
% 5.12/5.44 thf(fact_8986_uminus__integer_Oabs__eq,axiom,
% 5.12/5.44 ! [X: int] :
% 5.12/5.44 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 5.12/5.44 = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % uminus_integer.abs_eq
% 5.12/5.44 thf(fact_8987_one__integer__def,axiom,
% 5.12/5.44 ( one_one_Code_integer
% 5.12/5.44 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % one_integer_def
% 5.12/5.44 thf(fact_8988_minus__integer_Oabs__eq,axiom,
% 5.12/5.44 ! [Xa: int,X: int] :
% 5.12/5.44 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.12/5.44 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_integer.abs_eq
% 5.12/5.44 thf(fact_8989_divide__integer_Oabs__eq,axiom,
% 5.12/5.44 ! [Xa: int,X: int] :
% 5.12/5.44 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.12/5.44 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divide_integer.abs_eq
% 5.12/5.44 thf(fact_8990_infinite__int__iff__unbounded,axiom,
% 5.12/5.44 ! [S3: set_int] :
% 5.12/5.44 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.12/5.44 = ( ! [M5: int] :
% 5.12/5.44 ? [N4: int] :
% 5.12/5.44 ( ( ord_less_int @ M5 @ ( abs_abs_int @ N4 ) )
% 5.12/5.44 & ( member_int @ N4 @ S3 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % infinite_int_iff_unbounded
% 5.12/5.44 thf(fact_8991_unbounded__k__infinite,axiom,
% 5.12/5.44 ! [K: nat,S3: set_nat] :
% 5.12/5.44 ( ! [M3: nat] :
% 5.12/5.44 ( ( ord_less_nat @ K @ M3 )
% 5.12/5.44 => ? [N6: nat] :
% 5.12/5.44 ( ( ord_less_nat @ M3 @ N6 )
% 5.12/5.44 & ( member_nat @ N6 @ S3 ) ) )
% 5.12/5.44 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.12/5.44
% 5.12/5.44 % unbounded_k_infinite
% 5.12/5.44 thf(fact_8992_infinite__nat__iff__unbounded,axiom,
% 5.12/5.44 ! [S3: set_nat] :
% 5.12/5.44 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.12/5.44 = ( ! [M5: nat] :
% 5.12/5.44 ? [N4: nat] :
% 5.12/5.44 ( ( ord_less_nat @ M5 @ N4 )
% 5.12/5.44 & ( member_nat @ N4 @ S3 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % infinite_nat_iff_unbounded
% 5.12/5.44 thf(fact_8993_integer__of__num_I3_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.12/5.44 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.12/5.44
% 5.12/5.44 % integer_of_num(3)
% 5.12/5.44 thf(fact_8994_bit__cut__integer__def,axiom,
% 5.12/5.44 ( code_bit_cut_integer
% 5.12/5.44 = ( ^ [K3: code_integer] :
% 5.12/5.44 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.12/5.44 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bit_cut_integer_def
% 5.12/5.44 thf(fact_8995_divmod__integer__def,axiom,
% 5.12/5.44 ( code_divmod_integer
% 5.12/5.44 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L2 ) @ ( modulo364778990260209775nteger @ K3 @ L2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_integer_def
% 5.12/5.44 thf(fact_8996_csqrt_Osimps_I1_J,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( re @ ( csqrt @ Z2 ) )
% 5.12/5.44 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % csqrt.simps(1)
% 5.12/5.44 thf(fact_8997_Re__divide__of__nat,axiom,
% 5.12/5.44 ! [Z2: complex,N: nat] :
% 5.12/5.44 ( ( re @ ( divide1717551699836669952omplex @ Z2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ Z2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_divide_of_nat
% 5.12/5.44 thf(fact_8998_Re__divide__of__real,axiom,
% 5.12/5.44 ! [Z2: complex,R4: real] :
% 5.12/5.44 ( ( re @ ( divide1717551699836669952omplex @ Z2 @ ( real_V4546457046886955230omplex @ R4 ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ Z2 ) @ R4 ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_divide_of_real
% 5.12/5.44 thf(fact_8999_Re__sgn,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( re @ ( sgn_sgn_complex @ Z2 ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_sgn
% 5.12/5.44 thf(fact_9000_Re__divide__numeral,axiom,
% 5.12/5.44 ! [Z2: complex,W: num] :
% 5.12/5.44 ( ( re @ ( divide1717551699836669952omplex @ Z2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ Z2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_divide_numeral
% 5.12/5.44 thf(fact_9001_one__complex_Osimps_I1_J,axiom,
% 5.12/5.44 ( ( re @ one_one_complex )
% 5.12/5.44 = one_one_real ) ).
% 5.12/5.44
% 5.12/5.44 % one_complex.simps(1)
% 5.12/5.44 thf(fact_9002_uminus__complex_Osimps_I1_J,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( re @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.44 = ( uminus_uminus_real @ ( re @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % uminus_complex.simps(1)
% 5.12/5.44 thf(fact_9003_minus__complex_Osimps_I1_J,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.44 = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_complex.simps(1)
% 5.12/5.44 thf(fact_9004_integer__of__num__triv_I1_J,axiom,
% 5.12/5.44 ( ( code_integer_of_num @ one )
% 5.12/5.44 = one_one_Code_integer ) ).
% 5.12/5.44
% 5.12/5.44 % integer_of_num_triv(1)
% 5.12/5.44 thf(fact_9005_cmod__plus__Re__le__0__iff,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ zero_zero_real )
% 5.12/5.44 = ( ( re @ Z2 )
% 5.12/5.44 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % cmod_plus_Re_le_0_iff
% 5.12/5.44 thf(fact_9006_bit__cut__integer__code,axiom,
% 5.12/5.44 ( code_bit_cut_integer
% 5.12/5.44 = ( ^ [K3: code_integer] :
% 5.12/5.44 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.12/5.44 @ ( produc9125791028180074456eger_o
% 5.12/5.44 @ ^ [R: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.12/5.44 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bit_cut_integer_code
% 5.12/5.44 thf(fact_9007_csqrt_Ocode,axiom,
% 5.12/5.44 ( csqrt
% 5.12/5.44 = ( ^ [Z6: complex] :
% 5.12/5.44 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.44 @ ( times_times_real
% 5.12/5.44 @ ( if_real
% 5.12/5.44 @ ( ( im @ Z6 )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 @ one_one_real
% 5.12/5.44 @ ( sgn_sgn_real @ ( im @ Z6 ) ) )
% 5.12/5.44 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % csqrt.code
% 5.12/5.44 thf(fact_9008_csqrt_Osimps_I2_J,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( im @ ( csqrt @ Z2 ) )
% 5.12/5.44 = ( times_times_real
% 5.12/5.44 @ ( if_real
% 5.12/5.44 @ ( ( im @ Z2 )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 @ one_one_real
% 5.12/5.44 @ ( sgn_sgn_real @ ( im @ Z2 ) ) )
% 5.12/5.44 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % csqrt.simps(2)
% 5.12/5.44 thf(fact_9009_Complex__divide,axiom,
% 5.12/5.44 ( divide1717551699836669952omplex
% 5.12/5.44 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Complex_divide
% 5.12/5.44 thf(fact_9010_Im__divide__of__real,axiom,
% 5.12/5.44 ! [Z2: complex,R4: real] :
% 5.12/5.44 ( ( im @ ( divide1717551699836669952omplex @ Z2 @ ( real_V4546457046886955230omplex @ R4 ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( im @ Z2 ) @ R4 ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_divide_of_real
% 5.12/5.44 thf(fact_9011_Im__sgn,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( im @ ( sgn_sgn_complex @ Z2 ) )
% 5.12/5.44 = ( divide_divide_real @ ( im @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_sgn
% 5.12/5.44 thf(fact_9012_Re__i__times,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( re @ ( times_times_complex @ imaginary_unit @ Z2 ) )
% 5.12/5.44 = ( uminus_uminus_real @ ( im @ Z2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_i_times
% 5.12/5.44 thf(fact_9013_Im__divide__numeral,axiom,
% 5.12/5.44 ! [Z2: complex,W: num] :
% 5.12/5.44 ( ( im @ ( divide1717551699836669952omplex @ Z2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( im @ Z2 ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_divide_numeral
% 5.12/5.44 thf(fact_9014_Im__divide__of__nat,axiom,
% 5.12/5.44 ! [Z2: complex,N: nat] :
% 5.12/5.44 ( ( im @ ( divide1717551699836669952omplex @ Z2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.12/5.44 = ( divide_divide_real @ ( im @ Z2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_divide_of_nat
% 5.12/5.44 thf(fact_9015_csqrt__minus,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.12/5.44 | ( ( ( im @ X )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.12/5.44 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.44 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % csqrt_minus
% 5.12/5.44 thf(fact_9016_imaginary__unit_Osimps_I2_J,axiom,
% 5.12/5.44 ( ( im @ imaginary_unit )
% 5.12/5.44 = one_one_real ) ).
% 5.12/5.44
% 5.12/5.44 % imaginary_unit.simps(2)
% 5.12/5.44 thf(fact_9017_one__complex_Osimps_I2_J,axiom,
% 5.12/5.44 ( ( im @ one_one_complex )
% 5.12/5.44 = zero_zero_real ) ).
% 5.12/5.44
% 5.12/5.44 % one_complex.simps(2)
% 5.12/5.44 thf(fact_9018_uminus__complex_Osimps_I2_J,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( im @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.44 = ( uminus_uminus_real @ ( im @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % uminus_complex.simps(2)
% 5.12/5.44 thf(fact_9019_minus__complex_Osimps_I2_J,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.44 = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_complex.simps(2)
% 5.12/5.44 thf(fact_9020_times__complex_Osimps_I1_J,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.12/5.44 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % times_complex.simps(1)
% 5.12/5.44 thf(fact_9021_uminus__complex_Ocode,axiom,
% 5.12/5.44 ( uminus1482373934393186551omplex
% 5.12/5.44 = ( ^ [X2: complex] : ( complex2 @ ( uminus_uminus_real @ ( re @ X2 ) ) @ ( uminus_uminus_real @ ( im @ X2 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % uminus_complex.code
% 5.12/5.44 thf(fact_9022_minus__complex_Ocode,axiom,
% 5.12/5.44 ( minus_minus_complex
% 5.12/5.44 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % minus_complex.code
% 5.12/5.44 thf(fact_9023_times__complex_Ocode,axiom,
% 5.12/5.44 ( times_times_complex
% 5.12/5.44 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % times_complex.code
% 5.12/5.44 thf(fact_9024_Re__power2,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.44 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_power2
% 5.12/5.44 thf(fact_9025_divmod__abs__def,axiom,
% 5.12/5.44 ( code_divmod_abs
% 5.12/5.44 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_abs_def
% 5.12/5.44 thf(fact_9026_inverse__complex_Osimps_I1_J,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % inverse_complex.simps(1)
% 5.12/5.44 thf(fact_9027_Re__divide,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.12/5.44 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_divide
% 5.12/5.44 thf(fact_9028_inverse__complex_Osimps_I2_J,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.12/5.44 = ( 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 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % inverse_complex.simps(2)
% 5.12/5.44 thf(fact_9029_Im__divide,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.12/5.44 = ( 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 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_divide
% 5.12/5.44 thf(fact_9030_complex__unit__circle,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( Z2 != zero_zero_complex )
% 5.12/5.44 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z2 ) @ ( real_V1022390504157884413omplex @ Z2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.44 = one_one_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_unit_circle
% 5.12/5.44 thf(fact_9031_inverse__complex_Ocode,axiom,
% 5.12/5.44 ( invers8013647133539491842omplex
% 5.12/5.44 = ( ^ [X2: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % inverse_complex.code
% 5.12/5.44 thf(fact_9032_divmod__integer__code,axiom,
% 5.12/5.44 ( code_divmod_integer
% 5.12/5.44 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.12/5.44 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.12/5.44 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.12/5.44 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.12/5.44 @ ( produc6916734918728496179nteger
% 5.12/5.44 @ ^ [R: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 5.12/5.44 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 5.12/5.44 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.12/5.44 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.12/5.44 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.12/5.44 @ ( produc6916734918728496179nteger
% 5.12/5.44 @ ^ [R: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 5.12/5.44 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divmod_integer_code
% 5.12/5.44 thf(fact_9033_Im__Reals__divide,axiom,
% 5.12/5.44 ! [R4: complex,Z2: complex] :
% 5.12/5.44 ( ( member_complex @ R4 @ real_V2521375963428798218omplex )
% 5.12/5.44 => ( ( im @ ( divide1717551699836669952omplex @ R4 @ Z2 ) )
% 5.12/5.44 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R4 ) ) @ ( im @ Z2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_Reals_divide
% 5.12/5.44 thf(fact_9034_Re__Reals__divide,axiom,
% 5.12/5.44 ! [R4: complex,Z2: complex] :
% 5.12/5.44 ( ( member_complex @ R4 @ real_V2521375963428798218omplex )
% 5.12/5.44 => ( ( re @ ( divide1717551699836669952omplex @ R4 @ Z2 ) )
% 5.12/5.44 = ( divide_divide_real @ ( times_times_real @ ( re @ R4 ) @ ( re @ Z2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_Reals_divide
% 5.12/5.44 thf(fact_9035_complex__diff__cnj,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( minus_minus_complex @ Z2 @ ( cnj @ Z2 ) )
% 5.12/5.44 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z2 ) ) ) @ imaginary_unit ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_diff_cnj
% 5.12/5.44 thf(fact_9036_complex__cnj__divide,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( cnj @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.12/5.44 = ( divide1717551699836669952omplex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_divide
% 5.12/5.44 thf(fact_9037_complex__cnj__one,axiom,
% 5.12/5.44 ( ( cnj @ one_one_complex )
% 5.12/5.44 = one_one_complex ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_one
% 5.12/5.44 thf(fact_9038_complex__cnj__one__iff,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( ( cnj @ Z2 )
% 5.12/5.44 = one_one_complex )
% 5.12/5.44 = ( Z2 = one_one_complex ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_one_iff
% 5.12/5.44 thf(fact_9039_complex__cnj__minus,axiom,
% 5.12/5.44 ! [X: complex] :
% 5.12/5.44 ( ( cnj @ ( uminus1482373934393186551omplex @ X ) )
% 5.12/5.44 = ( uminus1482373934393186551omplex @ ( cnj @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_minus
% 5.12/5.44 thf(fact_9040_complex__cnj__diff,axiom,
% 5.12/5.44 ! [X: complex,Y: complex] :
% 5.12/5.44 ( ( cnj @ ( minus_minus_complex @ X @ Y ) )
% 5.12/5.44 = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_diff
% 5.12/5.44 thf(fact_9041_complex__cnj__i,axiom,
% 5.12/5.44 ( ( cnj @ imaginary_unit )
% 5.12/5.44 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_i
% 5.12/5.44 thf(fact_9042_complex__cnj__neg__numeral,axiom,
% 5.12/5.44 ! [W: num] :
% 5.12/5.44 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.12/5.44 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj_neg_numeral
% 5.12/5.44 thf(fact_9043_Re__divide__Reals,axiom,
% 5.12/5.44 ! [R4: complex,Z2: complex] :
% 5.12/5.44 ( ( member_complex @ R4 @ real_V2521375963428798218omplex )
% 5.12/5.44 => ( ( re @ ( divide1717551699836669952omplex @ Z2 @ R4 ) )
% 5.12/5.44 = ( divide_divide_real @ ( re @ Z2 ) @ ( re @ R4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_divide_Reals
% 5.12/5.44 thf(fact_9044_Im__divide__Reals,axiom,
% 5.12/5.44 ! [R4: complex,Z2: complex] :
% 5.12/5.44 ( ( member_complex @ R4 @ real_V2521375963428798218omplex )
% 5.12/5.44 => ( ( im @ ( divide1717551699836669952omplex @ Z2 @ R4 ) )
% 5.12/5.44 = ( divide_divide_real @ ( im @ Z2 ) @ ( re @ R4 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_divide_Reals
% 5.12/5.44 thf(fact_9045_cnj_Osimps_I2_J,axiom,
% 5.12/5.44 ! [Z2: complex] :
% 5.12/5.44 ( ( im @ ( cnj @ Z2 ) )
% 5.12/5.44 = ( uminus_uminus_real @ ( im @ Z2 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % cnj.simps(2)
% 5.12/5.44 thf(fact_9046_complex__cnj,axiom,
% 5.12/5.44 ! [A: real,B: real] :
% 5.12/5.44 ( ( cnj @ ( complex2 @ A @ B ) )
% 5.12/5.44 = ( complex2 @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_cnj
% 5.12/5.44 thf(fact_9047_cis__cnj,axiom,
% 5.12/5.44 ! [T: real] :
% 5.12/5.44 ( ( cnj @ ( cis @ T ) )
% 5.12/5.44 = ( cis @ ( uminus_uminus_real @ T ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % cis_cnj
% 5.12/5.44 thf(fact_9048_cnj_Ocode,axiom,
% 5.12/5.44 ( cnj
% 5.12/5.44 = ( ^ [Z6: complex] : ( complex2 @ ( re @ Z6 ) @ ( uminus_uminus_real @ ( im @ Z6 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % cnj.code
% 5.12/5.44 thf(fact_9049_Re__complex__div__eq__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.12/5.44 = zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_complex_div_eq_0
% 5.12/5.44 thf(fact_9050_Im__complex__div__eq__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.12/5.44 = zero_zero_real )
% 5.12/5.44 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.12/5.44 = zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_complex_div_eq_0
% 5.12/5.44 thf(fact_9051_Re__complex__div__lt__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.12/5.44 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_complex_div_lt_0
% 5.12/5.44 thf(fact_9052_Re__complex__div__gt__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_complex_div_gt_0
% 5.12/5.44 thf(fact_9053_Re__complex__div__le__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.12/5.44 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_complex_div_le_0
% 5.12/5.44 thf(fact_9054_Re__complex__div__ge__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Re_complex_div_ge_0
% 5.12/5.44 thf(fact_9055_Im__complex__div__lt__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.12/5.44 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_complex_div_lt_0
% 5.12/5.44 thf(fact_9056_Im__complex__div__gt__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_complex_div_gt_0
% 5.12/5.44 thf(fact_9057_Im__complex__div__le__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.12/5.44 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_complex_div_le_0
% 5.12/5.44 thf(fact_9058_Im__complex__div__ge__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Im_complex_div_ge_0
% 5.12/5.44 thf(fact_9059_complex__div__gt__0,axiom,
% 5.12/5.44 ! [A: complex,B: complex] :
% 5.12/5.44 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.12/5.44 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.12/5.44 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_div_gt_0
% 5.12/5.44 thf(fact_9060_complex__div__cnj,axiom,
% 5.12/5.44 ( divide1717551699836669952omplex
% 5.12/5.44 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % complex_div_cnj
% 5.12/5.44 thf(fact_9061_or__int__rec,axiom,
% 5.12/5.44 ( bit_se1409905431419307370or_int
% 5.12/5.44 = ( ^ [K3: int,L2: int] :
% 5.12/5.44 ( plus_plus_int
% 5.12/5.44 @ ( zero_n2684676970156552555ol_int
% 5.12/5.44 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.12/5.44 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.12/5.44 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_int_rec
% 5.12/5.44 thf(fact_9062_bezw__0,axiom,
% 5.12/5.44 ! [X: nat] :
% 5.12/5.44 ( ( bezw @ X @ zero_zero_nat )
% 5.12/5.44 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % bezw_0
% 5.12/5.44 thf(fact_9063_prod__decode__aux_Oelims,axiom,
% 5.12/5.44 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.12/5.44 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % prod_decode_aux.elims
% 5.12/5.44 thf(fact_9064_or__nonnegative__int__iff,axiom,
% 5.12/5.44 ! [K: int,L: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.12/5.44 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.12/5.44 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nonnegative_int_iff
% 5.12/5.44 thf(fact_9065_or__negative__int__iff,axiom,
% 5.12/5.44 ! [K: int,L: int] :
% 5.12/5.44 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.12/5.44 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.12/5.44 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_negative_int_iff
% 5.12/5.44 thf(fact_9066_or__minus__numerals_I2_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(2)
% 5.12/5.44 thf(fact_9067_or__minus__numerals_I6_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(6)
% 5.12/5.44 thf(fact_9068_or__minus__minus__numerals,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_minus_numerals
% 5.12/5.44 thf(fact_9069_and__minus__minus__numerals,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % and_minus_minus_numerals
% 5.12/5.44 thf(fact_9070_or__greater__eq,axiom,
% 5.12/5.44 ! [L: int,K: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.12/5.44 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_greater_eq
% 5.12/5.44 thf(fact_9071_OR__lower,axiom,
% 5.12/5.44 ! [X: int,Y: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % OR_lower
% 5.12/5.44 thf(fact_9072_or__not__numerals_I1_J,axiom,
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(1)
% 5.12/5.44 thf(fact_9073_set__bit__int__def,axiom,
% 5.12/5.44 ( bit_se7879613467334960850it_int
% 5.12/5.44 = ( ^ [N4: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_bit_int_def
% 5.12/5.44 thf(fact_9074_or__not__numerals_I2_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(2)
% 5.12/5.44 thf(fact_9075_or__not__numerals_I4_J,axiom,
% 5.12/5.44 ! [M2: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(4)
% 5.12/5.44 thf(fact_9076_or__not__numerals_I3_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(3)
% 5.12/5.44 thf(fact_9077_or__not__numerals_I7_J,axiom,
% 5.12/5.44 ! [M2: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.12/5.44 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(7)
% 5.12/5.44 thf(fact_9078_OR__upper,axiom,
% 5.12/5.44 ! [X: int,N: nat,Y: int] :
% 5.12/5.44 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.44 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.44 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.12/5.44 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % OR_upper
% 5.12/5.44 thf(fact_9079_or__not__numerals_I5_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(5)
% 5.12/5.44 thf(fact_9080_or__not__numerals_I9_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(9)
% 5.12/5.44 thf(fact_9081_or__not__numerals_I8_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_not_numerals(8)
% 5.12/5.44 thf(fact_9082_prod__decode__aux_Osimps,axiom,
% 5.12/5.44 ( nat_prod_decode_aux
% 5.12/5.44 = ( ^ [K3: nat,M5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M5 @ K3 ) @ ( product_Pair_nat_nat @ M5 @ ( minus_minus_nat @ K3 @ M5 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M5 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % prod_decode_aux.simps
% 5.12/5.44 thf(fact_9083_bezw_Oelims,axiom,
% 5.12/5.44 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 5.12/5.44 ( ( ( bezw @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bezw.elims
% 5.12/5.44 thf(fact_9084_bezw_Osimps,axiom,
% 5.12/5.44 ( bezw
% 5.12/5.44 = ( ^ [X2: nat,Y6: nat] : ( if_Pro3027730157355071871nt_int @ ( Y6 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y6 ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bezw.simps
% 5.12/5.44 thf(fact_9085_or__minus__numerals_I5_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(5)
% 5.12/5.44 thf(fact_9086_or__nat__numerals_I2_J,axiom,
% 5.12/5.44 ! [Y: num] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.12/5.44 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_numerals(2)
% 5.12/5.44 thf(fact_9087_or__nat__numerals_I4_J,axiom,
% 5.12/5.44 ! [X: num] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.44 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_numerals(4)
% 5.12/5.44 thf(fact_9088_or__nat__numerals_I3_J,axiom,
% 5.12/5.44 ! [X: num] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.12/5.44 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_numerals(3)
% 5.12/5.44 thf(fact_9089_or__nat__numerals_I1_J,axiom,
% 5.12/5.44 ! [Y: num] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.12/5.44 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_numerals(1)
% 5.12/5.44 thf(fact_9090_or__minus__numerals_I8_J,axiom,
% 5.12/5.44 ! [N: num,M2: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ ( bit0 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(8)
% 5.12/5.44 thf(fact_9091_or__minus__numerals_I4_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ ( bit0 @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(4)
% 5.12/5.44 thf(fact_9092_or__minus__numerals_I7_J,axiom,
% 5.12/5.44 ! [N: num,M2: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ ( bitM @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(7)
% 5.12/5.44 thf(fact_9093_or__minus__numerals_I3_J,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ ( bitM @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(3)
% 5.12/5.44 thf(fact_9094_or__minus__numerals_I1_J,axiom,
% 5.12/5.44 ! [N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_minus_numerals(1)
% 5.12/5.44 thf(fact_9095_set__bit__nat__def,axiom,
% 5.12/5.44 ( bit_se7882103937844011126it_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % set_bit_nat_def
% 5.12/5.44 thf(fact_9096_or__nat__def,axiom,
% 5.12/5.44 ( bit_se1412395901928357646or_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_def
% 5.12/5.44 thf(fact_9097_numeral__or__not__num__eq,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ N ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % numeral_or_not_num_eq
% 5.12/5.44 thf(fact_9098_int__numeral__not__or__num__neg,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M2 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_numeral_not_or_num_neg
% 5.12/5.44 thf(fact_9099_int__numeral__or__not__num__neg,axiom,
% 5.12/5.44 ! [M2: num,N: num] :
% 5.12/5.44 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.44 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M2 @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % int_numeral_or_not_num_neg
% 5.12/5.44 thf(fact_9100_floor__real__def,axiom,
% 5.12/5.44 ( archim6058952711729229775r_real
% 5.12/5.44 = ( ^ [X2: real] :
% 5.12/5.44 ( the_int
% 5.12/5.44 @ ^ [Z6: int] :
% 5.12/5.44 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X2 )
% 5.12/5.44 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % floor_real_def
% 5.12/5.44 thf(fact_9101_Suc__0__or__eq,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.12/5.44 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Suc_0_or_eq
% 5.12/5.44 thf(fact_9102_or__Suc__0__eq,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.44 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_Suc_0_eq
% 5.12/5.44 thf(fact_9103_or__nat__rec,axiom,
% 5.12/5.44 ( bit_se1412395901928357646or_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.44 ( plus_plus_nat
% 5.12/5.44 @ ( zero_n2687167440665602831ol_nat
% 5.12/5.44 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.12/5.44 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.44 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_rec
% 5.12/5.44 thf(fact_9104_bezw__non__0,axiom,
% 5.12/5.44 ! [Y: nat,X: nat] :
% 5.12/5.44 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.12/5.44 => ( ( bezw @ X @ Y )
% 5.12/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bezw_non_0
% 5.12/5.44 thf(fact_9105_bezw_Opelims,axiom,
% 5.12/5.44 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 5.12/5.44 ( ( ( bezw @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.12/5.44 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.12/5.44 & ( ( Xa != zero_zero_nat )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % bezw.pelims
% 5.12/5.44 thf(fact_9106_or__int__unfold,axiom,
% 5.12/5.44 ( bit_se1409905431419307370or_int
% 5.12/5.44 = ( ^ [K3: int,L2: int] :
% 5.12/5.44 ( if_int
% 5.12/5.44 @ ( ( K3
% 5.12/5.44 = ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.44 | ( L2
% 5.12/5.44 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.12/5.44 @ ( uminus_uminus_int @ one_one_int )
% 5.12/5.44 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( 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 @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_int_unfold
% 5.12/5.44 thf(fact_9107_fst__divmod__nat,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( product_fst_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 5.12/5.44 = ( divide_divide_nat @ M2 @ N ) ) ).
% 5.12/5.44
% 5.12/5.44 % fst_divmod_nat
% 5.12/5.44 thf(fact_9108_fst__divmod__integer,axiom,
% 5.12/5.44 ! [K: code_integer,L: code_integer] :
% 5.12/5.44 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 5.12/5.44 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 5.12/5.44
% 5.12/5.44 % fst_divmod_integer
% 5.12/5.44 thf(fact_9109_fst__divmod__abs,axiom,
% 5.12/5.44 ! [K: code_integer,L: code_integer] :
% 5.12/5.44 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 5.12/5.44 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % fst_divmod_abs
% 5.12/5.44 thf(fact_9110_Suc__0__div__numeral,axiom,
% 5.12/5.44 ! [K: num] :
% 5.12/5.44 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.44 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Suc_0_div_numeral
% 5.12/5.44 thf(fact_9111_prod__decode__aux_Opelims,axiom,
% 5.12/5.44 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.12/5.44 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.12/5.44 = Y )
% 5.12/5.44 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.12/5.44 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.12/5.44 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.12/5.44 => ( Y
% 5.12/5.44 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 5.12/5.44 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % prod_decode_aux.pelims
% 5.12/5.44 thf(fact_9112_floor__rat__def,axiom,
% 5.12/5.44 ( archim3151403230148437115or_rat
% 5.12/5.44 = ( ^ [X2: rat] :
% 5.12/5.44 ( the_int
% 5.12/5.44 @ ^ [Z6: int] :
% 5.12/5.44 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z6 ) @ X2 )
% 5.12/5.44 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % floor_rat_def
% 5.12/5.44 thf(fact_9113_max__Suc__Suc,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.12/5.44 = ( suc @ ( ord_max_nat @ M2 @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_Suc_Suc
% 5.12/5.44 thf(fact_9114_max__nat_Oeq__neutr__iff,axiom,
% 5.12/5.44 ! [A: nat,B: nat] :
% 5.12/5.44 ( ( ( ord_max_nat @ A @ B )
% 5.12/5.44 = zero_zero_nat )
% 5.12/5.44 = ( ( A = zero_zero_nat )
% 5.12/5.44 & ( B = zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_nat.eq_neutr_iff
% 5.12/5.44 thf(fact_9115_max__nat_Oleft__neutral,axiom,
% 5.12/5.44 ! [A: nat] :
% 5.12/5.44 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.12/5.44 = A ) ).
% 5.12/5.44
% 5.12/5.44 % max_nat.left_neutral
% 5.12/5.44 thf(fact_9116_max__nat_Oneutr__eq__iff,axiom,
% 5.12/5.44 ! [A: nat,B: nat] :
% 5.12/5.44 ( ( zero_zero_nat
% 5.12/5.44 = ( ord_max_nat @ A @ B ) )
% 5.12/5.44 = ( ( A = zero_zero_nat )
% 5.12/5.44 & ( B = zero_zero_nat ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_nat.neutr_eq_iff
% 5.12/5.44 thf(fact_9117_max__nat_Oright__neutral,axiom,
% 5.12/5.44 ! [A: nat] :
% 5.12/5.44 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.12/5.44 = A ) ).
% 5.12/5.44
% 5.12/5.44 % max_nat.right_neutral
% 5.12/5.44 thf(fact_9118_max__0L,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.12/5.44 = N ) ).
% 5.12/5.44
% 5.12/5.44 % max_0L
% 5.12/5.44 thf(fact_9119_max__0R,axiom,
% 5.12/5.44 ! [N: nat] :
% 5.12/5.44 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.12/5.44 = N ) ).
% 5.12/5.44
% 5.12/5.44 % max_0R
% 5.12/5.44 thf(fact_9120_max__numeral__Suc,axiom,
% 5.12/5.44 ! [K: num,N: nat] :
% 5.12/5.44 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.12/5.44 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_numeral_Suc
% 5.12/5.44 thf(fact_9121_max__Suc__numeral,axiom,
% 5.12/5.44 ! [N: nat,K: num] :
% 5.12/5.44 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.44 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_Suc_numeral
% 5.12/5.44 thf(fact_9122_nat__mult__max__left,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.44 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N ) @ Q5 )
% 5.12/5.44 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q5 ) @ ( times_times_nat @ N @ Q5 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % nat_mult_max_left
% 5.12/5.44 thf(fact_9123_nat__mult__max__right,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.44 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N @ Q5 ) )
% 5.12/5.44 = ( ord_max_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q5 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % nat_mult_max_right
% 5.12/5.44 thf(fact_9124_nat__add__max__right,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.44 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N @ Q5 ) )
% 5.12/5.44 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N ) @ ( plus_plus_nat @ M2 @ Q5 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % nat_add_max_right
% 5.12/5.44 thf(fact_9125_nat__add__max__left,axiom,
% 5.12/5.44 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.44 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N ) @ Q5 )
% 5.12/5.44 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q5 ) @ ( plus_plus_nat @ N @ Q5 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % nat_add_max_left
% 5.12/5.44 thf(fact_9126_obtain__pos__sum,axiom,
% 5.12/5.44 ! [R4: rat] :
% 5.12/5.44 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 5.12/5.44 => ~ ! [S2: rat] :
% 5.12/5.44 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 5.12/5.44 => ! [T3: rat] :
% 5.12/5.44 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.12/5.44 => ( R4
% 5.12/5.44 != ( plus_plus_rat @ S2 @ T3 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % obtain_pos_sum
% 5.12/5.44 thf(fact_9127_sgn__rat__def,axiom,
% 5.12/5.44 ( sgn_sgn_rat
% 5.12/5.44 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % sgn_rat_def
% 5.12/5.44 thf(fact_9128_abs__rat__def,axiom,
% 5.12/5.44 ( abs_abs_rat
% 5.12/5.44 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % abs_rat_def
% 5.12/5.44 thf(fact_9129_nat__minus__add__max,axiom,
% 5.12/5.44 ! [N: nat,M2: nat] :
% 5.12/5.44 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M2 ) @ M2 )
% 5.12/5.44 = ( ord_max_nat @ N @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % nat_minus_add_max
% 5.12/5.44 thf(fact_9130_max__Suc1,axiom,
% 5.12/5.44 ! [N: nat,M2: nat] :
% 5.12/5.44 ( ( ord_max_nat @ ( suc @ N ) @ M2 )
% 5.12/5.44 = ( case_nat_nat @ ( suc @ N )
% 5.12/5.44 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ N @ M4 ) )
% 5.12/5.44 @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_Suc1
% 5.12/5.44 thf(fact_9131_max__Suc2,axiom,
% 5.12/5.44 ! [M2: nat,N: nat] :
% 5.12/5.44 ( ( ord_max_nat @ M2 @ ( suc @ N ) )
% 5.12/5.44 = ( case_nat_nat @ ( suc @ N )
% 5.12/5.44 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ M4 @ N ) )
% 5.12/5.44 @ M2 ) ) ).
% 5.12/5.44
% 5.12/5.44 % max_Suc2
% 5.12/5.44 thf(fact_9132_or__nat__unfold,axiom,
% 5.12/5.44 ( bit_se1412395901928357646or_nat
% 5.12/5.44 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % or_nat_unfold
% 5.12/5.44 thf(fact_9133_rat__inverse__code,axiom,
% 5.12/5.44 ! [P4: rat] :
% 5.12/5.44 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 5.12/5.44 = ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 5.12/5.44 @ ( quotient_of @ P4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_inverse_code
% 5.12/5.44 thf(fact_9134_quotient__of__number_I3_J,axiom,
% 5.12/5.44 ! [K: num] :
% 5.12/5.44 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.12/5.44 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_number(3)
% 5.12/5.44 thf(fact_9135_rat__one__code,axiom,
% 5.12/5.44 ( ( quotient_of @ one_one_rat )
% 5.12/5.44 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_one_code
% 5.12/5.44 thf(fact_9136_rat__zero__code,axiom,
% 5.12/5.44 ( ( quotient_of @ zero_zero_rat )
% 5.12/5.44 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_zero_code
% 5.12/5.44 thf(fact_9137_quotient__of__number_I5_J,axiom,
% 5.12/5.44 ! [K: num] :
% 5.12/5.44 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.12/5.44 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_number(5)
% 5.12/5.44 thf(fact_9138_quotient__of__number_I4_J,axiom,
% 5.12/5.44 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.12/5.44 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_number(4)
% 5.12/5.44 thf(fact_9139_diff__rat__def,axiom,
% 5.12/5.44 ( minus_minus_rat
% 5.12/5.44 = ( ^ [Q4: rat,R: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % diff_rat_def
% 5.12/5.44 thf(fact_9140_divide__rat__def,axiom,
% 5.12/5.44 ( divide_divide_rat
% 5.12/5.44 = ( ^ [Q4: rat,R: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % divide_rat_def
% 5.12/5.44 thf(fact_9141_quotient__of__div,axiom,
% 5.12/5.44 ! [R4: rat,N: int,D: int] :
% 5.12/5.44 ( ( ( quotient_of @ R4 )
% 5.12/5.44 = ( product_Pair_int_int @ N @ D ) )
% 5.12/5.44 => ( R4
% 5.12/5.44 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_div
% 5.12/5.44 thf(fact_9142_quotient__of__denom__pos,axiom,
% 5.12/5.44 ! [R4: rat,P4: int,Q5: int] :
% 5.12/5.44 ( ( ( quotient_of @ R4 )
% 5.12/5.44 = ( product_Pair_int_int @ P4 @ Q5 ) )
% 5.12/5.44 => ( ord_less_int @ zero_zero_int @ Q5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_denom_pos
% 5.12/5.44 thf(fact_9143_quotient__of__denom__pos_H,axiom,
% 5.12/5.44 ! [R4: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_denom_pos'
% 5.12/5.44 thf(fact_9144_rat__uminus__code,axiom,
% 5.12/5.44 ! [P4: rat] :
% 5.12/5.44 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 5.12/5.44 = ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 5.12/5.44 @ ( quotient_of @ P4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_uminus_code
% 5.12/5.44 thf(fact_9145_rat__sgn__code,axiom,
% 5.12/5.44 ! [P4: rat] :
% 5.12/5.44 ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 5.12/5.44 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_sgn_code
% 5.12/5.44 thf(fact_9146_rat__less__code,axiom,
% 5.12/5.44 ( ord_less_rat
% 5.12/5.44 = ( ^ [P6: rat,Q4: rat] :
% 5.12/5.44 ( produc4947309494688390418_int_o
% 5.12/5.44 @ ^ [A3: int,C3: int] :
% 5.12/5.44 ( produc4947309494688390418_int_o
% 5.12/5.44 @ ^ [B2: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C3 @ B2 ) )
% 5.12/5.44 @ ( quotient_of @ Q4 ) )
% 5.12/5.44 @ ( quotient_of @ P6 ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_less_code
% 5.12/5.44 thf(fact_9147_quotient__of__int,axiom,
% 5.12/5.44 ! [A: int] :
% 5.12/5.44 ( ( quotient_of @ ( of_int @ A ) )
% 5.12/5.44 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % quotient_of_int
% 5.12/5.44 thf(fact_9148_rat__minus__code,axiom,
% 5.12/5.44 ! [P4: rat,Q5: rat] :
% 5.12/5.44 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q5 ) )
% 5.12/5.44 = ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [A3: int,C3: int] :
% 5.12/5.44 ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D4 ) ) )
% 5.12/5.44 @ ( quotient_of @ Q5 ) )
% 5.12/5.44 @ ( quotient_of @ P4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_minus_code
% 5.12/5.44 thf(fact_9149_normalize__negative,axiom,
% 5.12/5.44 ! [Q5: int,P4: int] :
% 5.12/5.44 ( ( ord_less_int @ Q5 @ zero_zero_int )
% 5.12/5.44 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q5 ) )
% 5.12/5.44 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q5 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % normalize_negative
% 5.12/5.44 thf(fact_9150_normalize__denom__zero,axiom,
% 5.12/5.44 ! [P4: int] :
% 5.12/5.44 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 5.12/5.44 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.12/5.44
% 5.12/5.44 % normalize_denom_zero
% 5.12/5.44 thf(fact_9151_normalize__denom__pos,axiom,
% 5.12/5.44 ! [R4: product_prod_int_int,P4: int,Q5: int] :
% 5.12/5.44 ( ( ( normalize @ R4 )
% 5.12/5.44 = ( product_Pair_int_int @ P4 @ Q5 ) )
% 5.12/5.44 => ( ord_less_int @ zero_zero_int @ Q5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % normalize_denom_pos
% 5.12/5.44 thf(fact_9152_normalize__crossproduct,axiom,
% 5.12/5.44 ! [Q5: int,S: int,P4: int,R4: int] :
% 5.12/5.44 ( ( Q5 != zero_zero_int )
% 5.12/5.44 => ( ( S != zero_zero_int )
% 5.12/5.44 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q5 ) )
% 5.12/5.44 = ( normalize @ ( product_Pair_int_int @ R4 @ S ) ) )
% 5.12/5.44 => ( ( times_times_int @ P4 @ S )
% 5.12/5.44 = ( times_times_int @ R4 @ Q5 ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % normalize_crossproduct
% 5.12/5.44 thf(fact_9153_rat__divide__code,axiom,
% 5.12/5.44 ! [P4: rat,Q5: rat] :
% 5.12/5.44 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q5 ) )
% 5.12/5.44 = ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [A3: int,C3: int] :
% 5.12/5.44 ( produc4245557441103728435nt_int
% 5.12/5.44 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C3 @ B2 ) ) )
% 5.12/5.44 @ ( quotient_of @ Q5 ) )
% 5.12/5.44 @ ( quotient_of @ P4 ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % rat_divide_code
% 5.12/5.44 thf(fact_9154_Frct__code__post_I5_J,axiom,
% 5.12/5.44 ! [K: num] :
% 5.12/5.44 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.12/5.44 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Frct_code_post(5)
% 5.12/5.44 thf(fact_9155_normalize__def,axiom,
% 5.12/5.44 ( normalize
% 5.12/5.44 = ( ^ [P6: product_prod_int_int] :
% 5.12/5.44 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 5.12/5.44 @ ( if_Pro3027730157355071871nt_int
% 5.12/5.44 @ ( ( product_snd_int_int @ P6 )
% 5.12/5.44 = zero_zero_int )
% 5.12/5.44 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.44 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % normalize_def
% 5.12/5.44 thf(fact_9156_Frct__code__post_I6_J,axiom,
% 5.12/5.44 ! [K: num,L: num] :
% 5.12/5.44 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.12/5.44 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % Frct_code_post(6)
% 5.12/5.44 thf(fact_9157_gcd__1__int,axiom,
% 5.12/5.44 ! [M2: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ M2 @ one_one_int )
% 5.12/5.44 = one_one_int ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_1_int
% 5.12/5.44 thf(fact_9158_gcd__neg2__int,axiom,
% 5.12/5.44 ! [X: int,Y: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.12/5.44 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_neg2_int
% 5.12/5.44 thf(fact_9159_gcd__neg1__int,axiom,
% 5.12/5.44 ! [X: int,Y: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.12/5.44 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_neg1_int
% 5.12/5.44 thf(fact_9160_gcd__pos__int,axiom,
% 5.12/5.44 ! [M2: int,N: int] :
% 5.12/5.44 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M2 @ N ) )
% 5.12/5.44 = ( ( M2 != zero_zero_int )
% 5.12/5.44 | ( N != zero_zero_int ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_pos_int
% 5.12/5.44 thf(fact_9161_gcd__neg__numeral__2__int,axiom,
% 5.12/5.44 ! [X: int,N: num] :
% 5.12/5.44 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.44 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_neg_numeral_2_int
% 5.12/5.44 thf(fact_9162_gcd__neg__numeral__1__int,axiom,
% 5.12/5.44 ! [N: num,X: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 5.12/5.44 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_neg_numeral_1_int
% 5.12/5.44 thf(fact_9163_gcd__0__int,axiom,
% 5.12/5.44 ! [X: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ X @ zero_zero_int )
% 5.12/5.44 = ( abs_abs_int @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_0_int
% 5.12/5.44 thf(fact_9164_gcd__0__left__int,axiom,
% 5.12/5.44 ! [X: int] :
% 5.12/5.44 ( ( gcd_gcd_int @ zero_zero_int @ X )
% 5.12/5.44 = ( abs_abs_int @ X ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_0_left_int
% 5.12/5.44 thf(fact_9165_gcd__ge__0__int,axiom,
% 5.12/5.44 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_ge_0_int
% 5.12/5.44 thf(fact_9166_Frct__code__post_I9_J,axiom,
% 5.12/5.44 ! [Q5: product_prod_int_int] :
% 5.12/5.44 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ ( frct @ Q5 ) ) )
% 5.12/5.44 = ( frct @ Q5 ) ) ).
% 5.12/5.44
% 5.12/5.44 % Frct_code_post(9)
% 5.12/5.44 thf(fact_9167_gcd__le1__int,axiom,
% 5.12/5.44 ! [A: int,B: int] :
% 5.12/5.44 ( ( ord_less_int @ zero_zero_int @ A )
% 5.12/5.44 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.12/5.44
% 5.12/5.44 % gcd_le1_int
% 5.12/5.44 thf(fact_9168_gcd__le2__int,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_le2_int
% 5.12/5.45 thf(fact_9169_gcd__cases__int,axiom,
% 5.12/5.45 ! [X: int,Y: int,P: int > $o] :
% 5.12/5.45 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.45 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 5.12/5.45 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.45 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.12/5.45 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.12/5.45 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.12/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.45 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 5.12/5.45 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.12/5.45 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.12/5.45 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.12/5.45 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_cases_int
% 5.12/5.45 thf(fact_9170_gcd__unique__int,axiom,
% 5.12/5.45 ! [D: int,A: int,B: int] :
% 5.12/5.45 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.12/5.45 & ( dvd_dvd_int @ D @ A )
% 5.12/5.45 & ( dvd_dvd_int @ D @ B )
% 5.12/5.45 & ! [E3: int] :
% 5.12/5.45 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.12/5.45 & ( dvd_dvd_int @ E3 @ B ) )
% 5.12/5.45 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.12/5.45 = ( D
% 5.12/5.45 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_unique_int
% 5.12/5.45 thf(fact_9171_gcd__non__0__int,axiom,
% 5.12/5.45 ! [Y: int,X: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.12/5.45 => ( ( gcd_gcd_int @ X @ Y )
% 5.12/5.45 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_non_0_int
% 5.12/5.45 thf(fact_9172_gcd__code__int,axiom,
% 5.12/5.45 ( gcd_gcd_int
% 5.12/5.45 = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_code_int
% 5.12/5.45 thf(fact_9173_Frct__code__post_I1_J,axiom,
% 5.12/5.45 ! [A: int] :
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.12/5.45 = zero_zero_rat ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(1)
% 5.12/5.45 thf(fact_9174_Frct__code__post_I2_J,axiom,
% 5.12/5.45 ! [A: int] :
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.12/5.45 = zero_zero_rat ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(2)
% 5.12/5.45 thf(fact_9175_Frct__code__post_I8_J,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.12/5.45 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(8)
% 5.12/5.45 thf(fact_9176_Frct__code__post_I7_J,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.12/5.45 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(7)
% 5.12/5.45 thf(fact_9177_Frct__code__post_I3_J,axiom,
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.12/5.45 = one_one_rat ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(3)
% 5.12/5.45 thf(fact_9178_Frct__code__post_I4_J,axiom,
% 5.12/5.45 ! [K: num] :
% 5.12/5.45 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.12/5.45 = ( numeral_numeral_rat @ K ) ) ).
% 5.12/5.45
% 5.12/5.45 % Frct_code_post(4)
% 5.12/5.45 thf(fact_9179_drop__bit__numeral__minus__bit1,axiom,
% 5.12/5.45 ! [L: num,K: num] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.45 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_numeral_minus_bit1
% 5.12/5.45 thf(fact_9180_divmod__integer__eq__cases,axiom,
% 5.12/5.45 ( code_divmod_integer
% 5.12/5.45 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.12/5.45 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.12/5.45 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.12/5.45 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.12/5.45 @ ( if_Pro6119634080678213985nteger
% 5.12/5.45 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.12/5.45 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.12/5.45 @ ( code_divmod_abs @ K3 @ L2 )
% 5.12/5.45 @ ( produc6916734918728496179nteger
% 5.12/5.45 @ ^ [R: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S4 ) ) )
% 5.12/5.45 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % divmod_integer_eq_cases
% 5.12/5.45 thf(fact_9181_gcd__0__left__nat,axiom,
% 5.12/5.45 ! [X: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 5.12/5.45 = X ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_0_left_nat
% 5.12/5.45 thf(fact_9182_gcd__0__nat,axiom,
% 5.12/5.45 ! [X: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 5.12/5.45 = X ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_0_nat
% 5.12/5.45 thf(fact_9183_gcd__nat_Oright__neutral,axiom,
% 5.12/5.45 ! [A: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.12/5.45 = A ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.right_neutral
% 5.12/5.45 thf(fact_9184_gcd__nat_Oneutr__eq__iff,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( zero_zero_nat
% 5.12/5.45 = ( gcd_gcd_nat @ A @ B ) )
% 5.12/5.45 = ( ( A = zero_zero_nat )
% 5.12/5.45 & ( B = zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.neutr_eq_iff
% 5.12/5.45 thf(fact_9185_gcd__nat_Oleft__neutral,axiom,
% 5.12/5.45 ! [A: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.12/5.45 = A ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.left_neutral
% 5.12/5.45 thf(fact_9186_gcd__nat_Oeq__neutr__iff,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( ( gcd_gcd_nat @ A @ B )
% 5.12/5.45 = zero_zero_nat )
% 5.12/5.45 = ( ( A = zero_zero_nat )
% 5.12/5.45 & ( B = zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.eq_neutr_iff
% 5.12/5.45 thf(fact_9187_gcd__1__nat,axiom,
% 5.12/5.45 ! [M2: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ M2 @ one_one_nat )
% 5.12/5.45 = one_one_nat ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_1_nat
% 5.12/5.45 thf(fact_9188_gcd__Suc__0,axiom,
% 5.12/5.45 ! [M2: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 5.12/5.45 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_Suc_0
% 5.12/5.45 thf(fact_9189_gcd__pos__nat,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 5.12/5.45 = ( ( M2 != zero_zero_nat )
% 5.12/5.45 | ( N != zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_pos_nat
% 5.12/5.45 thf(fact_9190_gcd__int__int__eq,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.45 = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_int_int_eq
% 5.12/5.45 thf(fact_9191_drop__bit__of__Suc__0,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.12/5.45 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_of_Suc_0
% 5.12/5.45 thf(fact_9192_drop__bit__nonnegative__int__iff,axiom,
% 5.12/5.45 ! [N: nat,K: int] :
% 5.12/5.45 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.12/5.45 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_nonnegative_int_iff
% 5.12/5.45 thf(fact_9193_drop__bit__negative__int__iff,axiom,
% 5.12/5.45 ! [N: nat,K: int] :
% 5.12/5.45 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.12/5.45 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_negative_int_iff
% 5.12/5.45 thf(fact_9194_drop__bit__minus__one,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.12/5.45 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_minus_one
% 5.12/5.45 thf(fact_9195_gcd__nat__abs__right__eq,axiom,
% 5.12/5.45 ! [N: nat,K: int] :
% 5.12/5.45 ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.12/5.45 = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat_abs_right_eq
% 5.12/5.45 thf(fact_9196_gcd__nat__abs__left__eq,axiom,
% 5.12/5.45 ! [K: int,N: nat] :
% 5.12/5.45 ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.12/5.45 = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat_abs_left_eq
% 5.12/5.45 thf(fact_9197_drop__bit__Suc__minus__bit0,axiom,
% 5.12/5.45 ! [N: nat,K: num] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.45 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_Suc_minus_bit0
% 5.12/5.45 thf(fact_9198_drop__bit__numeral__minus__bit0,axiom,
% 5.12/5.45 ! [L: num,K: num] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.12/5.45 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_numeral_minus_bit0
% 5.12/5.45 thf(fact_9199_drop__bit__Suc__minus__bit1,axiom,
% 5.12/5.45 ! [N: nat,K: num] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.12/5.45 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_Suc_minus_bit1
% 5.12/5.45 thf(fact_9200_gcd__le1__nat,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( A != zero_zero_nat )
% 5.12/5.45 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_le1_nat
% 5.12/5.45 thf(fact_9201_gcd__le2__nat,axiom,
% 5.12/5.45 ! [B: nat,A: nat] :
% 5.12/5.45 ( ( B != zero_zero_nat )
% 5.12/5.45 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_le2_nat
% 5.12/5.45 thf(fact_9202_gcd__diff1__nat,axiom,
% 5.12/5.45 ! [N: nat,M2: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ N @ M2 )
% 5.12/5.45 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M2 @ N ) @ N )
% 5.12/5.45 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_diff1_nat
% 5.12/5.45 thf(fact_9203_gcd__diff2__nat,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ M2 @ N )
% 5.12/5.45 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M2 ) @ N )
% 5.12/5.45 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_diff2_nat
% 5.12/5.45 thf(fact_9204_gcd__non__0__nat,axiom,
% 5.12/5.45 ! [Y: nat,X: nat] :
% 5.12/5.45 ( ( Y != zero_zero_nat )
% 5.12/5.45 => ( ( gcd_gcd_nat @ X @ Y )
% 5.12/5.45 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_non_0_nat
% 5.12/5.45 thf(fact_9205_gcd__nat_Osimps,axiom,
% 5.12/5.45 ( gcd_gcd_nat
% 5.12/5.45 = ( ^ [X2: nat,Y6: nat] : ( if_nat @ ( Y6 = zero_zero_nat ) @ X2 @ ( gcd_gcd_nat @ Y6 @ ( modulo_modulo_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.simps
% 5.12/5.45 thf(fact_9206_gcd__nat_Oelims,axiom,
% 5.12/5.45 ! [X: nat,Xa: nat,Y: nat] :
% 5.12/5.45 ( ( ( gcd_gcd_nat @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( ( Xa = zero_zero_nat )
% 5.12/5.45 => ( Y = X ) )
% 5.12/5.45 & ( ( Xa != zero_zero_nat )
% 5.12/5.45 => ( Y
% 5.12/5.45 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.elims
% 5.12/5.45 thf(fact_9207_drop__bit__push__bit__int,axiom,
% 5.12/5.45 ! [M2: nat,N: nat,K: int] :
% 5.12/5.45 ( ( bit_se8568078237143864401it_int @ M2 @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.12/5.45 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M2 @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M2 ) @ K ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_push_bit_int
% 5.12/5.45 thf(fact_9208_bezout__nat,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( A != zero_zero_nat )
% 5.12/5.45 => ? [X3: nat,Y3: nat] :
% 5.12/5.45 ( ( times_times_nat @ A @ X3 )
% 5.12/5.45 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % bezout_nat
% 5.12/5.45 thf(fact_9209_bezout__gcd__nat_H,axiom,
% 5.12/5.45 ! [B: nat,A: nat] :
% 5.12/5.45 ? [X3: nat,Y3: nat] :
% 5.12/5.45 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.12/5.45 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.12/5.45 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.12/5.45 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.12/5.45 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.12/5.45 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % bezout_gcd_nat'
% 5.12/5.45 thf(fact_9210_gcd__int__def,axiom,
% 5.12/5.45 ( gcd_gcd_int
% 5.12/5.45 = ( ^ [X2: int,Y6: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X2 ) ) @ ( nat2 @ ( abs_abs_int @ Y6 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_int_def
% 5.12/5.45 thf(fact_9211_drop__bit__int__def,axiom,
% 5.12/5.45 ( bit_se8568078237143864401it_int
% 5.12/5.45 = ( ^ [N4: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_int_def
% 5.12/5.45 thf(fact_9212_drop__bit__nat__def,axiom,
% 5.12/5.45 ( bit_se8570568707652914677it_nat
% 5.12/5.45 = ( ^ [N4: nat,M5: nat] : ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % drop_bit_nat_def
% 5.12/5.45 thf(fact_9213_bezw__aux,axiom,
% 5.12/5.45 ! [X: nat,Y: nat] :
% 5.12/5.45 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 5.12/5.45 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % bezw_aux
% 5.12/5.45 thf(fact_9214_gcd__nat_Opelims,axiom,
% 5.12/5.45 ! [X: nat,Xa: nat,Y: nat] :
% 5.12/5.45 ( ( ( gcd_gcd_nat @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.12/5.45 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.12/5.45 => ( Y = X ) )
% 5.12/5.45 & ( ( Xa != zero_zero_nat )
% 5.12/5.45 => ( Y
% 5.12/5.45 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 5.12/5.45 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.pelims
% 5.12/5.45 thf(fact_9215_xor__minus__numerals_I2_J,axiom,
% 5.12/5.45 ! [K: int,N: num] :
% 5.12/5.45 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.45 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % xor_minus_numerals(2)
% 5.12/5.45 thf(fact_9216_xor__minus__numerals_I1_J,axiom,
% 5.12/5.45 ! [N: num,K: int] :
% 5.12/5.45 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.12/5.45 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % xor_minus_numerals(1)
% 5.12/5.45 thf(fact_9217_card_Ocomp__fun__commute__on,axiom,
% 5.12/5.45 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.12/5.45 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.12/5.45
% 5.12/5.45 % card.comp_fun_commute_on
% 5.12/5.45 thf(fact_9218_sub__BitM__One__eq,axiom,
% 5.12/5.45 ! [N: num] :
% 5.12/5.45 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.12/5.45 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sub_BitM_One_eq
% 5.12/5.45 thf(fact_9219_Code__Numeral_Onegative__def,axiom,
% 5.12/5.45 ( code_negative
% 5.12/5.45 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 5.12/5.45
% 5.12/5.45 % Code_Numeral.negative_def
% 5.12/5.45 thf(fact_9220_Code__Target__Int_Onegative__def,axiom,
% 5.12/5.45 ( code_Target_negative
% 5.12/5.45 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % Code_Target_Int.negative_def
% 5.12/5.45 thf(fact_9221_nat__of__integer__non__positive,axiom,
% 5.12/5.45 ! [K: code_integer] :
% 5.12/5.45 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.12/5.45 => ( ( code_nat_of_integer @ K )
% 5.12/5.45 = zero_zero_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat_of_integer_non_positive
% 5.12/5.45 thf(fact_9222_card__Collect__less__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [I2: nat] : ( ord_less_nat @ I2 @ N ) ) )
% 5.12/5.45 = N ) ).
% 5.12/5.45
% 5.12/5.45 % card_Collect_less_nat
% 5.12/5.45 thf(fact_9223_Suc__funpow,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( compow_nat_nat @ N @ suc )
% 5.12/5.45 = ( plus_plus_nat @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % Suc_funpow
% 5.12/5.45 thf(fact_9224_card__atMost,axiom,
% 5.12/5.45 ! [U: nat] :
% 5.12/5.45 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.12/5.45 = ( suc @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atMost
% 5.12/5.45 thf(fact_9225_card__atLeastLessThan,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.12/5.45 = ( minus_minus_nat @ U @ L ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atLeastLessThan
% 5.12/5.45 thf(fact_9226_card__Collect__le__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 5.12/5.45 = ( suc @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_Collect_le_nat
% 5.12/5.45 thf(fact_9227_card__atLeastAtMost,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.12/5.45 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atLeastAtMost
% 5.12/5.45 thf(fact_9228_card__atLeastLessThan__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.12/5.45 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atLeastLessThan_int
% 5.12/5.45 thf(fact_9229_card__atLeastAtMost__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.12/5.45 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atLeastAtMost_int
% 5.12/5.45 thf(fact_9230_card__less__Suc2,axiom,
% 5.12/5.45 ! [M10: set_nat,I: nat] :
% 5.12/5.45 ( ~ ( member_nat @ zero_zero_nat @ M10 )
% 5.12/5.45 => ( ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [K3: nat] :
% 5.12/5.45 ( ( member_nat @ ( suc @ K3 ) @ M10 )
% 5.12/5.45 & ( ord_less_nat @ K3 @ I ) ) ) )
% 5.12/5.45 = ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [K3: nat] :
% 5.12/5.45 ( ( member_nat @ K3 @ M10 )
% 5.12/5.45 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_less_Suc2
% 5.12/5.45 thf(fact_9231_card__less__Suc,axiom,
% 5.12/5.45 ! [M10: set_nat,I: nat] :
% 5.12/5.45 ( ( member_nat @ zero_zero_nat @ M10 )
% 5.12/5.45 => ( ( suc
% 5.12/5.45 @ ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [K3: nat] :
% 5.12/5.45 ( ( member_nat @ ( suc @ K3 ) @ M10 )
% 5.12/5.45 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 5.12/5.45 = ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [K3: nat] :
% 5.12/5.45 ( ( member_nat @ K3 @ M10 )
% 5.12/5.45 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_less_Suc
% 5.12/5.45 thf(fact_9232_card__less,axiom,
% 5.12/5.45 ! [M10: set_nat,I: nat] :
% 5.12/5.45 ( ( member_nat @ zero_zero_nat @ M10 )
% 5.12/5.45 => ( ( finite_card_nat
% 5.12/5.45 @ ( collect_nat
% 5.12/5.45 @ ^ [K3: nat] :
% 5.12/5.45 ( ( member_nat @ K3 @ M10 )
% 5.12/5.45 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 5.12/5.45 != zero_zero_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_less
% 5.12/5.45 thf(fact_9233_card__atLeastZeroLessThan__int,axiom,
% 5.12/5.45 ! [U: int] :
% 5.12/5.45 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.12/5.45 = ( nat2 @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_atLeastZeroLessThan_int
% 5.12/5.45 thf(fact_9234_nat__of__integer__code__post_I1_J,axiom,
% 5.12/5.45 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.12/5.45 = zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % nat_of_integer_code_post(1)
% 5.12/5.45 thf(fact_9235_nat__of__integer__code__post_I2_J,axiom,
% 5.12/5.45 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.12/5.45 = one_one_nat ) ).
% 5.12/5.45
% 5.12/5.45 % nat_of_integer_code_post(2)
% 5.12/5.45 thf(fact_9236_subset__eq__atLeast0__lessThan__card,axiom,
% 5.12/5.45 ! [N5: set_nat,N: nat] :
% 5.12/5.45 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.12/5.45 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % subset_eq_atLeast0_lessThan_card
% 5.12/5.45 thf(fact_9237_card__sum__le__nat__sum,axiom,
% 5.12/5.45 ! [S3: set_nat] :
% 5.12/5.45 ( ord_less_eq_nat
% 5.12/5.45 @ ( groups3542108847815614940at_nat
% 5.12/5.45 @ ^ [X2: nat] : X2
% 5.12/5.45 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.12/5.45 @ ( groups3542108847815614940at_nat
% 5.12/5.45 @ ^ [X2: nat] : X2
% 5.12/5.45 @ S3 ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_sum_le_nat_sum
% 5.12/5.45 thf(fact_9238_card__nth__roots,axiom,
% 5.12/5.45 ! [C: complex,N: nat] :
% 5.12/5.45 ( ( C != zero_zero_complex )
% 5.12/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( finite_card_complex
% 5.12/5.45 @ ( collect_complex
% 5.12/5.45 @ ^ [Z6: complex] :
% 5.12/5.45 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.45 = C ) ) )
% 5.12/5.45 = N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_nth_roots
% 5.12/5.45 thf(fact_9239_card__roots__unity__eq,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( finite_card_complex
% 5.12/5.45 @ ( collect_complex
% 5.12/5.45 @ ^ [Z6: complex] :
% 5.12/5.45 ( ( power_power_complex @ Z6 @ N )
% 5.12/5.45 = one_one_complex ) ) )
% 5.12/5.45 = N ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_roots_unity_eq
% 5.12/5.45 thf(fact_9240_nat__of__integer__code,axiom,
% 5.12/5.45 ( code_nat_of_integer
% 5.12/5.45 = ( ^ [K3: code_integer] :
% 5.12/5.45 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.12/5.45 @ ( produc1555791787009142072er_nat
% 5.12/5.45 @ ^ [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 ) )
% 5.12/5.45 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat_of_integer_code
% 5.12/5.45 thf(fact_9241_finite__enumerate,axiom,
% 5.12/5.45 ! [S3: set_nat] :
% 5.12/5.45 ( ( finite_finite_nat @ S3 )
% 5.12/5.45 => ? [R3: nat > nat] :
% 5.12/5.45 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.12/5.45 & ! [N6: nat] :
% 5.12/5.45 ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S3 ) )
% 5.12/5.45 => ( member_nat @ ( R3 @ N6 ) @ S3 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % finite_enumerate
% 5.12/5.45 thf(fact_9242_card__greaterThanLessThan__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.12/5.45 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_greaterThanLessThan_int
% 5.12/5.45 thf(fact_9243_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.12/5.45 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X2 )
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % max_nat.semilattice_neutr_order_axioms
% 5.12/5.45 thf(fact_9244_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.12/5.45 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.12/5.45 thf(fact_9245_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.12/5.45 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.12/5.45 @ ^ [M5: nat,N4: nat] :
% 5.12/5.45 ( ( dvd_dvd_nat @ M5 @ N4 )
% 5.12/5.45 & ( M5 != N4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % gcd_nat.semilattice_neutr_order_axioms
% 5.12/5.45 thf(fact_9246_int__of__integer__code,axiom,
% 5.12/5.45 ( code_int_of_integer
% 5.12/5.45 = ( ^ [K3: code_integer] :
% 5.12/5.45 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.12/5.45 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.12/5.45 @ ( produc1553301316500091796er_int
% 5.12/5.45 @ ^ [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 ) )
% 5.12/5.45 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_of_integer_code
% 5.12/5.45 thf(fact_9247_int__of__integer__of__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.12/5.45 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_of_integer_of_nat
% 5.12/5.45 thf(fact_9248_zero__integer_Orep__eq,axiom,
% 5.12/5.45 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 5.12/5.45 = zero_zero_int ) ).
% 5.12/5.45
% 5.12/5.45 % zero_integer.rep_eq
% 5.12/5.45 thf(fact_9249_card__greaterThanLessThan,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.12/5.45 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_greaterThanLessThan
% 5.12/5.45 thf(fact_9250_uminus__integer_Orep__eq,axiom,
% 5.12/5.45 ! [X: code_integer] :
% 5.12/5.45 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 5.12/5.45 = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_integer.rep_eq
% 5.12/5.45 thf(fact_9251_one__integer_Orep__eq,axiom,
% 5.12/5.45 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.12/5.45 = one_one_int ) ).
% 5.12/5.45
% 5.12/5.45 % one_integer.rep_eq
% 5.12/5.45 thf(fact_9252_minus__integer_Orep__eq,axiom,
% 5.12/5.45 ! [X: code_integer,Xa: code_integer] :
% 5.12/5.45 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa ) )
% 5.12/5.45 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_integer.rep_eq
% 5.12/5.45 thf(fact_9253_divide__integer_Orep__eq,axiom,
% 5.12/5.45 ! [X: code_integer,Xa: code_integer] :
% 5.12/5.45 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa ) )
% 5.12/5.45 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % divide_integer.rep_eq
% 5.12/5.45 thf(fact_9254_less__integer_Orep__eq,axiom,
% 5.12/5.45 ( ord_le6747313008572928689nteger
% 5.12/5.45 = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_integer.rep_eq
% 5.12/5.45 thf(fact_9255_integer__less__iff,axiom,
% 5.12/5.45 ( ord_le6747313008572928689nteger
% 5.12/5.45 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % integer_less_iff
% 5.12/5.45 thf(fact_9256_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.12/5.45 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeastSucLessThan_greaterThanLessThan
% 5.12/5.45 thf(fact_9257_tanh__real__bounds,axiom,
% 5.12/5.45 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % tanh_real_bounds
% 5.12/5.45 thf(fact_9258_times__int_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.12/5.45 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( abs_Integ
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) )
% 5.12/5.45 @ Xa
% 5.12/5.45 @ X ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % times_int.abs_eq
% 5.12/5.45 thf(fact_9259_Gcd__remove0__nat,axiom,
% 5.12/5.45 ! [M10: set_nat] :
% 5.12/5.45 ( ( finite_finite_nat @ M10 )
% 5.12/5.45 => ( ( gcd_Gcd_nat @ M10 )
% 5.12/5.45 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M10 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Gcd_remove0_nat
% 5.12/5.45 thf(fact_9260_int_Oabs__induct,axiom,
% 5.12/5.45 ! [P: int > $o,X: int] :
% 5.12/5.45 ( ! [Y3: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y3 ) )
% 5.12/5.45 => ( P @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % int.abs_induct
% 5.12/5.45 thf(fact_9261_Gcd__nat__eq__one,axiom,
% 5.12/5.45 ! [N5: set_nat] :
% 5.12/5.45 ( ( member_nat @ one_one_nat @ N5 )
% 5.12/5.45 => ( ( gcd_Gcd_nat @ N5 )
% 5.12/5.45 = one_one_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % Gcd_nat_eq_one
% 5.12/5.45 thf(fact_9262_eq__Abs__Integ,axiom,
% 5.12/5.45 ! [Z2: int] :
% 5.12/5.45 ~ ! [X3: nat,Y3: nat] :
% 5.12/5.45 ( Z2
% 5.12/5.45 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % eq_Abs_Integ
% 5.12/5.45 thf(fact_9263_nat_Oabs__eq,axiom,
% 5.12/5.45 ! [X: product_prod_nat_nat] :
% 5.12/5.45 ( ( nat2 @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat.abs_eq
% 5.12/5.45 thf(fact_9264_zero__int__def,axiom,
% 5.12/5.45 ( zero_zero_int
% 5.12/5.45 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_int_def
% 5.12/5.45 thf(fact_9265_int__def,axiom,
% 5.12/5.45 ( semiri1314217659103216013at_int
% 5.12/5.45 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_def
% 5.12/5.45 thf(fact_9266_uminus__int_Oabs__eq,axiom,
% 5.12/5.45 ! [X: product_prod_nat_nat] :
% 5.12/5.45 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( abs_Integ
% 5.12/5.45 @ ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X2 )
% 5.12/5.45 @ X ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_int.abs_eq
% 5.12/5.45 thf(fact_9267_one__int__def,axiom,
% 5.12/5.45 ( one_one_int
% 5.12/5.45 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % one_int_def
% 5.12/5.45 thf(fact_9268_less__int_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.12/5.45 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.12/5.45 @ Xa
% 5.12/5.45 @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_int.abs_eq
% 5.12/5.45 thf(fact_9269_less__eq__int_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.12/5.45 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.12/5.45 @ Xa
% 5.12/5.45 @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_eq_int.abs_eq
% 5.12/5.45 thf(fact_9270_plus__int_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.12/5.45 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( abs_Integ
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) )
% 5.12/5.45 @ Xa
% 5.12/5.45 @ X ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % plus_int.abs_eq
% 5.12/5.45 thf(fact_9271_minus__int_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.12/5.45 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.12/5.45 = ( abs_Integ
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) )
% 5.12/5.45 @ Xa
% 5.12/5.45 @ X ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_int.abs_eq
% 5.12/5.45 thf(fact_9272_num__of__nat_Osimps_I2_J,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( num_of_nat @ ( suc @ N ) )
% 5.12/5.45 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.12/5.45 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( num_of_nat @ ( suc @ N ) )
% 5.12/5.45 = one ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat.simps(2)
% 5.12/5.45 thf(fact_9273_num__of__nat__numeral__eq,axiom,
% 5.12/5.45 ! [Q5: num] :
% 5.12/5.45 ( ( num_of_nat @ ( numeral_numeral_nat @ Q5 ) )
% 5.12/5.45 = Q5 ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat_numeral_eq
% 5.12/5.45 thf(fact_9274_Gcd__int__greater__eq__0,axiom,
% 5.12/5.45 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % Gcd_int_greater_eq_0
% 5.12/5.45 thf(fact_9275_num__of__nat_Osimps_I1_J,axiom,
% 5.12/5.45 ( ( num_of_nat @ zero_zero_nat )
% 5.12/5.45 = one ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat.simps(1)
% 5.12/5.45 thf(fact_9276_numeral__num__of__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.12/5.45 = N ) ) ).
% 5.12/5.45
% 5.12/5.45 % numeral_num_of_nat
% 5.12/5.45 thf(fact_9277_num__of__nat__One,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.12/5.45 => ( ( num_of_nat @ N )
% 5.12/5.45 = one ) ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat_One
% 5.12/5.45 thf(fact_9278_num__of__nat__double,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.12/5.45 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat_double
% 5.12/5.45 thf(fact_9279_num__of__nat__plus__distrib,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 5.12/5.45 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_nat_plus_distrib
% 5.12/5.45 thf(fact_9280_less__eq__int_Orep__eq,axiom,
% 5.12/5.45 ( ord_less_eq_int
% 5.12/5.45 = ( ^ [X2: int,Xa4: int] :
% 5.12/5.45 ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [Y6: nat,Z6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.12/5.45 @ ( rep_Integ @ X2 )
% 5.12/5.45 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_eq_int.rep_eq
% 5.12/5.45 thf(fact_9281_less__int_Orep__eq,axiom,
% 5.12/5.45 ( ord_less_int
% 5.12/5.45 = ( ^ [X2: int,Xa4: int] :
% 5.12/5.45 ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [Y6: nat,Z6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.12/5.45 @ ( rep_Integ @ X2 )
% 5.12/5.45 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_int.rep_eq
% 5.12/5.45 thf(fact_9282_prod__encode__def,axiom,
% 5.12/5.45 ( nat_prod_encode
% 5.12/5.45 = ( produc6842872674320459806at_nat
% 5.12/5.45 @ ^ [M5: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M5 @ N4 ) ) @ M5 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % prod_encode_def
% 5.12/5.45 thf(fact_9283_prod__encode__eq,axiom,
% 5.12/5.45 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.12/5.45 ( ( ( nat_prod_encode @ X )
% 5.12/5.45 = ( nat_prod_encode @ Y ) )
% 5.12/5.45 = ( X = Y ) ) ).
% 5.12/5.45
% 5.12/5.45 % prod_encode_eq
% 5.12/5.45 thf(fact_9284_le__prod__encode__1,axiom,
% 5.12/5.45 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % le_prod_encode_1
% 5.12/5.45 thf(fact_9285_le__prod__encode__2,axiom,
% 5.12/5.45 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % le_prod_encode_2
% 5.12/5.45 thf(fact_9286_nat_Orep__eq,axiom,
% 5.12/5.45 ( nat2
% 5.12/5.45 = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat.rep_eq
% 5.12/5.45 thf(fact_9287_prod__encode__prod__decode__aux,axiom,
% 5.12/5.45 ! [K: nat,M2: nat] :
% 5.12/5.45 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M2 ) )
% 5.12/5.45 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % prod_encode_prod_decode_aux
% 5.12/5.45 thf(fact_9288_uminus__int__def,axiom,
% 5.12/5.45 ( uminus_uminus_int
% 5.12/5.45 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.12/5.45 @ ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_int_def
% 5.12/5.45 thf(fact_9289_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.12/5.45 ! [N: nat,J2: nat,I: nat] :
% 5.12/5.45 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ ( suc @ I ) ) )
% 5.12/5.45 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J2 ) ) @ N )
% 5.12/5.45 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nth_sorted_list_of_set_greaterThanLessThan
% 5.12/5.45 thf(fact_9290_times__int__def,axiom,
% 5.12/5.45 ( times_times_int
% 5.12/5.45 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % times_int_def
% 5.12/5.45 thf(fact_9291_minus__int__def,axiom,
% 5.12/5.45 ( minus_minus_int
% 5.12/5.45 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_int_def
% 5.12/5.45 thf(fact_9292_plus__int__def,axiom,
% 5.12/5.45 ( plus_plus_int
% 5.12/5.45 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % plus_int_def
% 5.12/5.45 thf(fact_9293_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.12/5.45 ! [N: nat,J2: nat,I: nat] :
% 5.12/5.45 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ I ) )
% 5.12/5.45 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J2 ) ) @ N )
% 5.12/5.45 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nth_sorted_list_of_set_greaterThanAtMost
% 5.12/5.45 thf(fact_9294_card__greaterThanAtMost,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.12/5.45 = ( minus_minus_nat @ U @ L ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_greaterThanAtMost
% 5.12/5.45 thf(fact_9295_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.12/5.45 ! [L: nat,U: nat] :
% 5.12/5.45 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.12/5.45 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeastSucAtMost_greaterThanAtMost
% 5.12/5.45 thf(fact_9296_image__minus__const__atLeastLessThan__nat,axiom,
% 5.12/5.45 ! [C: nat,Y: nat,X: nat] :
% 5.12/5.45 ( ( ( ord_less_nat @ C @ Y )
% 5.12/5.45 => ( ( image_nat_nat
% 5.12/5.45 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.12/5.45 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.12/5.45 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.12/5.45 & ( ~ ( ord_less_nat @ C @ Y )
% 5.12/5.45 => ( ( ( ord_less_nat @ X @ Y )
% 5.12/5.45 => ( ( image_nat_nat
% 5.12/5.45 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.12/5.45 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.12/5.45 & ( ~ ( ord_less_nat @ X @ Y )
% 5.12/5.45 => ( ( image_nat_nat
% 5.12/5.45 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.12/5.45 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.12/5.45 = bot_bot_set_nat ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_minus_const_atLeastLessThan_nat
% 5.12/5.45 thf(fact_9297_rat__floor__lemma,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.12/5.45 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_floor_lemma
% 5.12/5.45 thf(fact_9298_minus__rat__cancel,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( fract @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.12/5.45 = ( fract @ A @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_rat_cancel
% 5.12/5.45 thf(fact_9299_bij__betw__Suc,axiom,
% 5.12/5.45 ! [M10: set_nat,N5: set_nat] :
% 5.12/5.45 ( ( bij_betw_nat_nat @ suc @ M10 @ N5 )
% 5.12/5.45 = ( ( image_nat_nat @ suc @ M10 )
% 5.12/5.45 = N5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % bij_betw_Suc
% 5.12/5.45 thf(fact_9300_image__Suc__atLeastAtMost,axiom,
% 5.12/5.45 ! [I: nat,J2: nat] :
% 5.12/5.45 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J2 ) )
% 5.12/5.45 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_Suc_atLeastAtMost
% 5.12/5.45 thf(fact_9301_image__Suc__atLeastLessThan,axiom,
% 5.12/5.45 ! [I: nat,J2: nat] :
% 5.12/5.45 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J2 ) )
% 5.12/5.45 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_Suc_atLeastLessThan
% 5.12/5.45 thf(fact_9302_minus__rat,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( uminus_uminus_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( fract @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_rat
% 5.12/5.45 thf(fact_9303_divide__rat,axiom,
% 5.12/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.12/5.45 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.12/5.45 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % divide_rat
% 5.12/5.45 thf(fact_9304_card__greaterThanAtMost__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.12/5.45 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_greaterThanAtMost_int
% 5.12/5.45 thf(fact_9305_floor__Fract,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( divide_divide_int @ A @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % floor_Fract
% 5.12/5.45 thf(fact_9306_less__rat,axiom,
% 5.12/5.45 ! [B: int,D: int,A: int,C: int] :
% 5.12/5.45 ( ( B != zero_zero_int )
% 5.12/5.45 => ( ( D != zero_zero_int )
% 5.12/5.45 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.12/5.45 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_rat
% 5.12/5.45 thf(fact_9307_add__rat,axiom,
% 5.12/5.45 ! [B: int,D: int,A: int,C: int] :
% 5.12/5.45 ( ( B != zero_zero_int )
% 5.12/5.45 => ( ( D != zero_zero_int )
% 5.12/5.45 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.12/5.45 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % add_rat
% 5.12/5.45 thf(fact_9308_le__rat,axiom,
% 5.12/5.45 ! [B: int,D: int,A: int,C: int] :
% 5.12/5.45 ( ( B != zero_zero_int )
% 5.12/5.45 => ( ( D != zero_zero_int )
% 5.12/5.45 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.12/5.45 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % le_rat
% 5.12/5.45 thf(fact_9309_diff__rat,axiom,
% 5.12/5.45 ! [B: int,D: int,A: int,C: int] :
% 5.12/5.45 ( ( B != zero_zero_int )
% 5.12/5.45 => ( ( D != zero_zero_int )
% 5.12/5.45 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.12/5.45 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % diff_rat
% 5.12/5.45 thf(fact_9310_eq__rat_I3_J,axiom,
% 5.12/5.45 ! [A: int,C: int] :
% 5.12/5.45 ( ( fract @ zero_zero_int @ A )
% 5.12/5.45 = ( fract @ zero_zero_int @ C ) ) ).
% 5.12/5.45
% 5.12/5.45 % eq_rat(3)
% 5.12/5.45 thf(fact_9311_zero__notin__Suc__image,axiom,
% 5.12/5.45 ! [A2: set_nat] :
% 5.12/5.45 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_notin_Suc_image
% 5.12/5.45 thf(fact_9312_eq__rat_I2_J,axiom,
% 5.12/5.45 ! [A: int] :
% 5.12/5.45 ( ( fract @ A @ zero_zero_int )
% 5.12/5.45 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % eq_rat(2)
% 5.12/5.45 thf(fact_9313_Rat__induct__pos,axiom,
% 5.12/5.45 ! [P: rat > $o,Q5: rat] :
% 5.12/5.45 ( ! [A4: int,B3: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.12/5.45 => ( P @ ( fract @ A4 @ B3 ) ) )
% 5.12/5.45 => ( P @ Q5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat_induct_pos
% 5.12/5.45 thf(fact_9314_mult__rat__cancel,axiom,
% 5.12/5.45 ! [C: int,A: int,B: int] :
% 5.12/5.45 ( ( C != zero_zero_int )
% 5.12/5.45 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.12/5.45 = ( fract @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % mult_rat_cancel
% 5.12/5.45 thf(fact_9315_eq__rat_I1_J,axiom,
% 5.12/5.45 ! [B: int,D: int,A: int,C: int] :
% 5.12/5.45 ( ( B != zero_zero_int )
% 5.12/5.45 => ( ( D != zero_zero_int )
% 5.12/5.45 => ( ( ( fract @ A @ B )
% 5.12/5.45 = ( fract @ C @ D ) )
% 5.12/5.45 = ( ( times_times_int @ A @ D )
% 5.12/5.45 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % eq_rat(1)
% 5.12/5.45 thf(fact_9316_Fract__of__nat__eq,axiom,
% 5.12/5.45 ! [K: nat] :
% 5.12/5.45 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.12/5.45 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_of_nat_eq
% 5.12/5.45 thf(fact_9317_rat__number__collapse_I6_J,axiom,
% 5.12/5.45 ! [K: int] :
% 5.12/5.45 ( ( fract @ K @ zero_zero_int )
% 5.12/5.45 = zero_zero_rat ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_collapse(6)
% 5.12/5.45 thf(fact_9318_rat__number__collapse_I1_J,axiom,
% 5.12/5.45 ! [K: int] :
% 5.12/5.45 ( ( fract @ zero_zero_int @ K )
% 5.12/5.45 = zero_zero_rat ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_collapse(1)
% 5.12/5.45 thf(fact_9319_Fract__coprime,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.12/5.45 = ( fract @ A @ B ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_coprime
% 5.12/5.45 thf(fact_9320_One__rat__def,axiom,
% 5.12/5.45 ( one_one_rat
% 5.12/5.45 = ( fract @ one_one_int @ one_one_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % One_rat_def
% 5.12/5.45 thf(fact_9321_Fract__of__int__eq,axiom,
% 5.12/5.45 ! [K: int] :
% 5.12/5.45 ( ( fract @ K @ one_one_int )
% 5.12/5.45 = ( ring_1_of_int_rat @ K ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_of_int_eq
% 5.12/5.45 thf(fact_9322_Fract__of__int__quotient,axiom,
% 5.12/5.45 ( fract
% 5.12/5.45 = ( ^ [K3: int,L2: int] : ( divide_divide_rat @ ( ring_1_of_int_rat @ K3 ) @ ( ring_1_of_int_rat @ L2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_of_int_quotient
% 5.12/5.45 thf(fact_9323_Zero__rat__def,axiom,
% 5.12/5.45 ( zero_zero_rat
% 5.12/5.45 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % Zero_rat_def
% 5.12/5.45 thf(fact_9324_rat__number__collapse_I3_J,axiom,
% 5.12/5.45 ! [W: num] :
% 5.12/5.45 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.12/5.45 = ( numeral_numeral_rat @ W ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_collapse(3)
% 5.12/5.45 thf(fact_9325_rat__number__expand_I3_J,axiom,
% 5.12/5.45 ( numeral_numeral_rat
% 5.12/5.45 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_expand(3)
% 5.12/5.45 thf(fact_9326_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.12/5.45 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.12/5.45 thf(fact_9327_image__Suc__lessThan,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_Suc_lessThan
% 5.12/5.45 thf(fact_9328_image__Suc__atMost,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.12/5.45 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_Suc_atMost
% 5.12/5.45 thf(fact_9329_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeast0_atMost_Suc_eq_insert_0
% 5.12/5.45 thf(fact_9330_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % atLeast0_lessThan_Suc_eq_insert_0
% 5.12/5.45 thf(fact_9331_lessThan__Suc__eq__insert__0,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lessThan_Suc_eq_insert_0
% 5.12/5.45 thf(fact_9332_atMost__Suc__eq__insert__0,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % atMost_Suc_eq_insert_0
% 5.12/5.45 thf(fact_9333_Fract__less__zero__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.12/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_less_zero_iff
% 5.12/5.45 thf(fact_9334_zero__less__Fract__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_less_Fract_iff
% 5.12/5.45 thf(fact_9335_Fract__less__one__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.12/5.45 = ( ord_less_int @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_less_one_iff
% 5.12/5.45 thf(fact_9336_one__less__Fract__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( ord_less_int @ B @ A ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % one_less_Fract_iff
% 5.12/5.45 thf(fact_9337_rat__number__collapse_I5_J,axiom,
% 5.12/5.45 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.12/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_collapse(5)
% 5.12/5.45 thf(fact_9338_Fract__add__one,axiom,
% 5.12/5.45 ! [N: int,M2: int] :
% 5.12/5.45 ( ( N != zero_zero_int )
% 5.12/5.45 => ( ( fract @ ( plus_plus_int @ M2 @ N ) @ N )
% 5.12/5.45 = ( plus_plus_rat @ ( fract @ M2 @ N ) @ one_one_rat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_add_one
% 5.12/5.45 thf(fact_9339_zero__le__Fract__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_le_Fract_iff
% 5.12/5.45 thf(fact_9340_Fract__le__zero__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.12/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_le_zero_iff
% 5.12/5.45 thf(fact_9341_Fract__le__one__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.12/5.45 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract_le_one_iff
% 5.12/5.45 thf(fact_9342_one__le__Fract__iff,axiom,
% 5.12/5.45 ! [B: int,A: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.12/5.45 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.12/5.45 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % one_le_Fract_iff
% 5.12/5.45 thf(fact_9343_rat__number__expand_I5_J,axiom,
% 5.12/5.45 ! [K: num] :
% 5.12/5.45 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.12/5.45 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_expand(5)
% 5.12/5.45 thf(fact_9344_rat__number__collapse_I4_J,axiom,
% 5.12/5.45 ! [W: num] :
% 5.12/5.45 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.12/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rat_number_collapse(4)
% 5.12/5.45 thf(fact_9345_take__bit__numeral__minus__numeral__int,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int
% 5.12/5.45 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M2 ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.12/5.45 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M2 ) @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_numeral_minus_numeral_int
% 5.12/5.45 thf(fact_9346_of__nat__eq__id,axiom,
% 5.12/5.45 semiri1316708129612266289at_nat = id_nat ).
% 5.12/5.45
% 5.12/5.45 % of_nat_eq_id
% 5.12/5.45 thf(fact_9347_take__bit__num__simps_I1_J,axiom,
% 5.12/5.45 ! [M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_simps(1)
% 5.12/5.45 thf(fact_9348_take__bit__num__simps_I2_J,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.12/5.45 = ( some_num @ one ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_simps(2)
% 5.12/5.45 thf(fact_9349_Gcd__int__eq,axiom,
% 5.12/5.45 ! [N5: set_nat] :
% 5.12/5.45 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 5.12/5.45 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N5 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Gcd_int_eq
% 5.12/5.45 thf(fact_9350_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( bit_take_bit_num @ N @ one )
% 5.12/5.45 = ( case_nat_option_num @ none_num
% 5.12/5.45 @ ^ [N4: nat] : ( some_num @ one )
% 5.12/5.45 @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.12/5.45 thf(fact_9351_less__int__def,axiom,
% 5.12/5.45 ( ord_less_int
% 5.12/5.45 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_int_def
% 5.12/5.45 thf(fact_9352_less__eq__int__def,axiom,
% 5.12/5.45 ( ord_less_eq_int
% 5.12/5.45 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_eq_int_def
% 5.12/5.45 thf(fact_9353_nat__def,axiom,
% 5.12/5.45 ( nat2
% 5.12/5.45 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat_def
% 5.12/5.45 thf(fact_9354_image__int__atLeastAtMost,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.12/5.45 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_int_atLeastAtMost
% 5.12/5.45 thf(fact_9355_image__int__atLeastLessThan,axiom,
% 5.12/5.45 ! [A: nat,B: nat] :
% 5.12/5.45 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.12/5.45 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_int_atLeastLessThan
% 5.12/5.45 thf(fact_9356_image__add__int__atLeastLessThan,axiom,
% 5.12/5.45 ! [L: int,U: int] :
% 5.12/5.45 ( ( image_int_int
% 5.12/5.45 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L )
% 5.12/5.45 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.12/5.45 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_add_int_atLeastLessThan
% 5.12/5.45 thf(fact_9357_take__bit__num__def,axiom,
% 5.12/5.45 ( bit_take_bit_num
% 5.12/5.45 = ( ^ [N4: nat,M5: num] :
% 5.12/5.45 ( if_option_num
% 5.12/5.45 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M5 ) )
% 5.12/5.45 = zero_zero_nat )
% 5.12/5.45 @ none_num
% 5.12/5.45 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M5 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_def
% 5.12/5.45 thf(fact_9358_Gcd__int__def,axiom,
% 5.12/5.45 ( gcd_Gcd_int
% 5.12/5.45 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Gcd_int_def
% 5.12/5.45 thf(fact_9359_image__atLeastZeroLessThan__int,axiom,
% 5.12/5.45 ! [U: int] :
% 5.12/5.45 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.12/5.45 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.12/5.45 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % image_atLeastZeroLessThan_int
% 5.12/5.45 thf(fact_9360_and__minus__numerals_I3_J,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_minus_numerals(3)
% 5.12/5.45 thf(fact_9361_and__minus__numerals_I7_J,axiom,
% 5.12/5.45 ! [N: num,M2: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bitM @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_minus_numerals(7)
% 5.12/5.45 thf(fact_9362_and__minus__numerals_I8_J,axiom,
% 5.12/5.45 ! [N: num,M2: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M2 ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_minus_numerals(8)
% 5.12/5.45 thf(fact_9363_take__bit__num__simps_I4_J,axiom,
% 5.12/5.45 ! [N: nat,M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M2 ) )
% 5.12/5.45 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_simps(4)
% 5.12/5.45 thf(fact_9364_take__bit__num__simps_I3_J,axiom,
% 5.12/5.45 ! [N: nat,M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M2 ) )
% 5.12/5.45 = ( case_o6005452278849405969um_num @ none_num
% 5.12/5.45 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.12/5.45 @ ( bit_take_bit_num @ N @ M2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_simps(3)
% 5.12/5.45 thf(fact_9365_take__bit__num__simps_I6_J,axiom,
% 5.12/5.45 ! [R4: num,M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R4 ) @ ( bit0 @ M2 ) )
% 5.12/5.45 = ( case_o6005452278849405969um_num @ none_num
% 5.12/5.45 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.12/5.45 @ ( bit_take_bit_num @ ( pred_numeral @ R4 ) @ M2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_num_simps(6)
% 5.12/5.45 thf(fact_9366_and__minus__numerals_I4_J,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ ( bit0 @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_minus_numerals(4)
% 5.12/5.45 thf(fact_9367_and__not__num_Osimps_I1_J,axiom,
% 5.12/5.45 ( ( bit_and_not_num @ one @ one )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % and_not_num.simps(1)
% 5.12/5.45 thf(fact_9368_and__not__num_Osimps_I3_J,axiom,
% 5.12/5.45 ! [N: num] :
% 5.12/5.45 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % and_not_num.simps(3)
% 5.12/5.45 thf(fact_9369_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.12/5.45 ! [N: nat,M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ N @ ( bit0 @ M2 ) )
% 5.12/5.45 = ( case_nat_option_num @ none_num
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( case_o6005452278849405969um_num @ none_num
% 5.12/5.45 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.12/5.45 @ ( bit_take_bit_num @ N4 @ M2 ) )
% 5.12/5.45 @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.12/5.45 thf(fact_9370_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.12/5.45 ! [N: nat,M2: num] :
% 5.12/5.45 ( ( bit_take_bit_num @ N @ ( bit1 @ M2 ) )
% 5.12/5.45 = ( case_nat_option_num @ none_num
% 5.12/5.45 @ ^ [N4: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N4 @ M2 ) ) )
% 5.12/5.45 @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.12/5.45 thf(fact_9371_and__not__num__eq__None__iff,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( ( bit_and_not_num @ M2 @ N )
% 5.12/5.45 = none_num )
% 5.12/5.45 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.45 = zero_zero_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_not_num_eq_None_iff
% 5.12/5.45 thf(fact_9372_int__numeral__and__not__num,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M2 @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_numeral_and_not_num
% 5.12/5.45 thf(fact_9373_int__numeral__not__and__num,axiom,
% 5.12/5.45 ! [M2: num,N: num] :
% 5.12/5.45 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.45 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_numeral_not_and_num
% 5.12/5.45 thf(fact_9374_measure__function__int,axiom,
% 5.12/5.45 fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 5.12/5.45
% 5.12/5.45 % measure_function_int
% 5.12/5.45 thf(fact_9375_positive__rat,axiom,
% 5.12/5.45 ! [A: int,B: int] :
% 5.12/5.45 ( ( positive @ ( fract @ A @ B ) )
% 5.12/5.45 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % positive_rat
% 5.12/5.45 thf(fact_9376_Rat_Opositive__minus,axiom,
% 5.12/5.45 ! [X: rat] :
% 5.12/5.45 ( ~ ( positive @ X )
% 5.12/5.45 => ( ( X != zero_zero_rat )
% 5.12/5.45 => ( positive @ ( uminus_uminus_rat @ X ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive_minus
% 5.12/5.45 thf(fact_9377_less__rat__def,axiom,
% 5.12/5.45 ( ord_less_rat
% 5.12/5.45 = ( ^ [X2: rat,Y6: rat] : ( positive @ ( minus_minus_rat @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_rat_def
% 5.12/5.45 thf(fact_9378_Rat_Opositive_Orep__eq,axiom,
% 5.12/5.45 ( positive
% 5.12/5.45 = ( ^ [X2: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X2 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X2 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive.rep_eq
% 5.12/5.45 thf(fact_9379_and__not__num_Oelims,axiom,
% 5.12/5.45 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.45 ( ( ( bit_and_not_num @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y != none_num ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ? [N2: num] :
% 5.12/5.45 ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ one ) ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ? [N2: num] :
% 5.12/5.45 ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y != none_num ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.12/5.45 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 5.12/5.45 @ ( bit_and_not_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ~ ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_not_num.elims
% 5.12/5.45 thf(fact_9380_Bit__Operations_Otake__bit__num__code,axiom,
% 5.12/5.45 ( bit_take_bit_num
% 5.12/5.45 = ( ^ [N4: nat,M5: num] :
% 5.12/5.45 ( produc478579273971653890on_num
% 5.12/5.45 @ ^ [A3: nat,X2: num] :
% 5.12/5.45 ( case_nat_option_num @ none_num
% 5.12/5.45 @ ^ [O: nat] :
% 5.12/5.45 ( case_num_option_num @ ( some_num @ one )
% 5.12/5.45 @ ^ [P6: num] :
% 5.12/5.45 ( case_o6005452278849405969um_num @ none_num
% 5.12/5.45 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.12/5.45 @ ( bit_take_bit_num @ O @ P6 ) )
% 5.12/5.45 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 5.12/5.45 @ X2 )
% 5.12/5.45 @ A3 )
% 5.12/5.45 @ ( product_Pair_nat_num @ N4 @ M5 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Bit_Operations.take_bit_num_code
% 5.12/5.45 thf(fact_9381_Rat_Opositive__def,axiom,
% 5.12/5.45 ( positive
% 5.12/5.45 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive_def
% 5.12/5.45 thf(fact_9382_and__num_Oelims,axiom,
% 5.12/5.45 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.45 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ one ) ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ? [N2: num] :
% 5.12/5.45 ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y != none_num ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ? [N2: num] :
% 5.12/5.45 ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ one ) ) ) )
% 5.12/5.45 => ( ( ? [M3: num] :
% 5.12/5.45 ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y != none_num ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ( ? [M3: num] :
% 5.12/5.45 ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ one ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ~ ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.12/5.45 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 5.12/5.45 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % and_num.elims
% 5.12/5.45 thf(fact_9383_and__num_Osimps_I4_J,axiom,
% 5.12/5.45 ! [M2: num] :
% 5.12/5.45 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M2 ) @ one )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % and_num.simps(4)
% 5.12/5.45 thf(fact_9384_and__num_Osimps_I2_J,axiom,
% 5.12/5.45 ! [N: num] :
% 5.12/5.45 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % and_num.simps(2)
% 5.12/5.45 thf(fact_9385_xor__num_Oelims,axiom,
% 5.12/5.45 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.45 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y != none_num ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit1 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ( ( X = one )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit0 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit1 @ M3 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit0 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ( ( Xa = one )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.12/5.45 => ( ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit0 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) ) ) )
% 5.12/5.45 => ~ ! [M3: num] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( bit1 @ M3 ) )
% 5.12/5.45 => ! [N2: num] :
% 5.12/5.45 ( ( Xa
% 5.12/5.45 = ( bit1 @ N2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % xor_num.elims
% 5.12/5.45 thf(fact_9386_of__rat__dense,axiom,
% 5.12/5.45 ! [X: real,Y: real] :
% 5.12/5.45 ( ( ord_less_real @ X @ Y )
% 5.12/5.45 => ? [Q3: rat] :
% 5.12/5.45 ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q3 ) )
% 5.12/5.45 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % of_rat_dense
% 5.12/5.45 thf(fact_9387_xor__num_Osimps_I1_J,axiom,
% 5.12/5.45 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.12/5.45 = none_num ) ).
% 5.12/5.45
% 5.12/5.45 % xor_num.simps(1)
% 5.12/5.45 thf(fact_9388_inverse__rat__def,axiom,
% 5.12/5.45 ( inverse_inverse_rat
% 5.12/5.45 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.12/5.45 @ ^ [X2: product_prod_int_int] :
% 5.12/5.45 ( if_Pro3027730157355071871nt_int
% 5.12/5.45 @ ( ( product_fst_int_int @ X2 )
% 5.12/5.45 = zero_zero_int )
% 5.12/5.45 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.45 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_rat_def
% 5.12/5.45 thf(fact_9389_uminus__rat__def,axiom,
% 5.12/5.45 ( uminus_uminus_rat
% 5.12/5.45 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_rat_def
% 5.12/5.45 thf(fact_9390_one__rat__def,axiom,
% 5.12/5.45 ( one_one_rat
% 5.12/5.45 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % one_rat_def
% 5.12/5.45 thf(fact_9391_Fract_Oabs__eq,axiom,
% 5.12/5.45 ( fract
% 5.12/5.45 = ( ^ [Xa4: int,X2: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract.abs_eq
% 5.12/5.45 thf(fact_9392_zero__rat__def,axiom,
% 5.12/5.45 ( zero_zero_rat
% 5.12/5.45 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_rat_def
% 5.12/5.45 thf(fact_9393_inverse__rat_Oabs__eq,axiom,
% 5.12/5.45 ! [X: product_prod_int_int] :
% 5.12/5.45 ( ( ratrel @ X @ X )
% 5.12/5.45 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 5.12/5.45 = ( abs_Rat
% 5.12/5.45 @ ( if_Pro3027730157355071871nt_int
% 5.12/5.45 @ ( ( product_fst_int_int @ X )
% 5.12/5.45 = zero_zero_int )
% 5.12/5.45 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.45 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_rat.abs_eq
% 5.12/5.45 thf(fact_9394_Rat_Opositive_Oabs__eq,axiom,
% 5.12/5.45 ! [X: product_prod_int_int] :
% 5.12/5.45 ( ( ratrel @ X @ X )
% 5.12/5.45 => ( ( positive @ ( abs_Rat @ X ) )
% 5.12/5.45 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive.abs_eq
% 5.12/5.45 thf(fact_9395_uminus__rat_Oabs__eq,axiom,
% 5.12/5.45 ! [X: product_prod_int_int] :
% 5.12/5.45 ( ( ratrel @ X @ X )
% 5.12/5.45 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 5.12/5.45 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_rat.abs_eq
% 5.12/5.45 thf(fact_9396_ratrel__iff,axiom,
% 5.12/5.45 ( ratrel
% 5.12/5.45 = ( ^ [X2: product_prod_int_int,Y6: product_prod_int_int] :
% 5.12/5.45 ( ( ( product_snd_int_int @ X2 )
% 5.12/5.45 != zero_zero_int )
% 5.12/5.45 & ( ( product_snd_int_int @ Y6 )
% 5.12/5.45 != zero_zero_int )
% 5.12/5.45 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y6 ) )
% 5.12/5.45 = ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % ratrel_iff
% 5.12/5.45 thf(fact_9397_one__rat_Orsp,axiom,
% 5.12/5.45 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 5.12/5.45
% 5.12/5.45 % one_rat.rsp
% 5.12/5.45 thf(fact_9398_zero__rat_Orsp,axiom,
% 5.12/5.45 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 5.12/5.45
% 5.12/5.45 % zero_rat.rsp
% 5.12/5.45 thf(fact_9399_ratrel__def,axiom,
% 5.12/5.45 ( ratrel
% 5.12/5.45 = ( ^ [X2: product_prod_int_int,Y6: product_prod_int_int] :
% 5.12/5.45 ( ( ( product_snd_int_int @ X2 )
% 5.12/5.45 != zero_zero_int )
% 5.12/5.45 & ( ( product_snd_int_int @ Y6 )
% 5.12/5.45 != zero_zero_int )
% 5.12/5.45 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y6 ) )
% 5.12/5.45 = ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % ratrel_def
% 5.12/5.45 thf(fact_9400_num__of__integer__code,axiom,
% 5.12/5.45 ( code_num_of_integer
% 5.12/5.45 = ( ^ [K3: code_integer] :
% 5.12/5.45 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.12/5.45 @ ( produc7336495610019696514er_num
% 5.12/5.45 @ ^ [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 ) )
% 5.12/5.45 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % num_of_integer_code
% 5.12/5.45 thf(fact_9401_min__Suc__Suc,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 5.12/5.45 = ( suc @ ( ord_min_nat @ M2 @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_Suc_Suc
% 5.12/5.45 thf(fact_9402_min__0L,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.12/5.45 = zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % min_0L
% 5.12/5.45 thf(fact_9403_min__0R,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.12/5.45 = zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % min_0R
% 5.12/5.45 thf(fact_9404_min__numeral__Suc,axiom,
% 5.12/5.45 ! [K: num,N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.12/5.45 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_numeral_Suc
% 5.12/5.45 thf(fact_9405_min__Suc__numeral,axiom,
% 5.12/5.45 ! [N: nat,K: num] :
% 5.12/5.45 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.12/5.45 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_Suc_numeral
% 5.12/5.45 thf(fact_9406_min__diff,axiom,
% 5.12/5.45 ! [M2: nat,I: nat,N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.12/5.45 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N ) @ I ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_diff
% 5.12/5.45 thf(fact_9407_nat__mult__min__left,axiom,
% 5.12/5.45 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.45 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N ) @ Q5 )
% 5.12/5.45 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q5 ) @ ( times_times_nat @ N @ Q5 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat_mult_min_left
% 5.12/5.45 thf(fact_9408_nat__mult__min__right,axiom,
% 5.12/5.45 ! [M2: nat,N: nat,Q5: nat] :
% 5.12/5.45 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N @ Q5 ) )
% 5.12/5.45 = ( ord_min_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q5 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat_mult_min_right
% 5.12/5.45 thf(fact_9409_inf__nat__def,axiom,
% 5.12/5.45 inf_inf_nat = ord_min_nat ).
% 5.12/5.45
% 5.12/5.45 % inf_nat_def
% 5.12/5.45 thf(fact_9410_concat__bit__assoc__sym,axiom,
% 5.12/5.45 ! [M2: nat,N: nat,K: int,L: int,R4: int] :
% 5.12/5.45 ( ( bit_concat_bit @ M2 @ ( bit_concat_bit @ N @ K @ L ) @ R4 )
% 5.12/5.45 = ( bit_concat_bit @ ( ord_min_nat @ M2 @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M2 @ N ) @ L @ R4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % concat_bit_assoc_sym
% 5.12/5.45 thf(fact_9411_take__bit__concat__bit__eq,axiom,
% 5.12/5.45 ! [M2: nat,N: nat,K: int,L: int] :
% 5.12/5.45 ( ( bit_se2923211474154528505it_int @ M2 @ ( bit_concat_bit @ N @ K @ L ) )
% 5.12/5.45 = ( bit_concat_bit @ ( ord_min_nat @ M2 @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M2 @ N ) @ L ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % take_bit_concat_bit_eq
% 5.12/5.45 thf(fact_9412_min__Suc1,axiom,
% 5.12/5.45 ! [N: nat,M2: nat] :
% 5.12/5.45 ( ( ord_min_nat @ ( suc @ N ) @ M2 )
% 5.12/5.45 = ( case_nat_nat @ zero_zero_nat
% 5.12/5.45 @ ^ [M4: nat] : ( suc @ ( ord_min_nat @ N @ M4 ) )
% 5.12/5.45 @ M2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_Suc1
% 5.12/5.45 thf(fact_9413_min__Suc2,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( ord_min_nat @ M2 @ ( suc @ N ) )
% 5.12/5.45 = ( case_nat_nat @ zero_zero_nat
% 5.12/5.45 @ ^ [M4: nat] : ( suc @ ( ord_min_nat @ M4 @ N ) )
% 5.12/5.45 @ M2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % min_Suc2
% 5.12/5.45 thf(fact_9414_inf__int__def,axiom,
% 5.12/5.45 inf_inf_int = ord_min_int ).
% 5.12/5.45
% 5.12/5.45 % inf_int_def
% 5.12/5.45 thf(fact_9415_rcis__cnj,axiom,
% 5.12/5.45 ( cnj
% 5.12/5.45 = ( ^ [A3: complex] : ( rcis @ ( real_V1022390504157884413omplex @ A3 ) @ ( uminus_uminus_real @ ( arg @ A3 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rcis_cnj
% 5.12/5.45 thf(fact_9416_cis__rcis__eq,axiom,
% 5.12/5.45 ( cis
% 5.12/5.45 = ( rcis @ one_one_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % cis_rcis_eq
% 5.12/5.45 thf(fact_9417_rcis__divide,axiom,
% 5.12/5.45 ! [R1: real,A: real,R22: real,B: real] :
% 5.12/5.45 ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.12/5.45 = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rcis_divide
% 5.12/5.45 thf(fact_9418_rcis__inverse,axiom,
% 5.12/5.45 ! [R4: real,A: real] :
% 5.12/5.45 ( ( invers8013647133539491842omplex @ ( rcis @ R4 @ A ) )
% 5.12/5.45 = ( rcis @ ( divide_divide_real @ one_one_real @ R4 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % rcis_inverse
% 5.12/5.45 thf(fact_9419_quotient__of__def,axiom,
% 5.12/5.45 ( quotient_of
% 5.12/5.45 = ( ^ [X2: rat] :
% 5.12/5.45 ( the_Pr4378521158711661632nt_int
% 5.12/5.45 @ ^ [Pair: product_prod_int_int] :
% 5.12/5.45 ( ( X2
% 5.12/5.45 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.12/5.45 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.12/5.45 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % quotient_of_def
% 5.12/5.45 thf(fact_9420_normalize__stable,axiom,
% 5.12/5.45 ! [Q5: int,P4: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ Q5 )
% 5.12/5.45 => ( ( algebr932160517623751201me_int @ P4 @ Q5 )
% 5.12/5.45 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q5 ) )
% 5.12/5.45 = ( product_Pair_int_int @ P4 @ Q5 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % normalize_stable
% 5.12/5.45 thf(fact_9421_Rat__cases,axiom,
% 5.12/5.45 ! [Q5: rat] :
% 5.12/5.45 ~ ! [A4: int,B3: int] :
% 5.12/5.45 ( ( Q5
% 5.12/5.45 = ( fract @ A4 @ B3 ) )
% 5.12/5.45 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.12/5.45 => ~ ( algebr932160517623751201me_int @ A4 @ B3 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat_cases
% 5.12/5.45 thf(fact_9422_Rat__induct,axiom,
% 5.12/5.45 ! [P: rat > $o,Q5: rat] :
% 5.12/5.45 ( ! [A4: int,B3: int] :
% 5.12/5.45 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.12/5.45 => ( ( algebr932160517623751201me_int @ A4 @ B3 )
% 5.12/5.45 => ( P @ ( fract @ A4 @ B3 ) ) ) )
% 5.12/5.45 => ( P @ Q5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat_induct
% 5.12/5.45 thf(fact_9423_coprime__common__divisor__int,axiom,
% 5.12/5.45 ! [A: int,B: int,X: int] :
% 5.12/5.45 ( ( algebr932160517623751201me_int @ A @ B )
% 5.12/5.45 => ( ( dvd_dvd_int @ X @ A )
% 5.12/5.45 => ( ( dvd_dvd_int @ X @ B )
% 5.12/5.45 => ( ( abs_abs_int @ X )
% 5.12/5.45 = one_one_int ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_common_divisor_int
% 5.12/5.45 thf(fact_9424_Rat__cases__nonzero,axiom,
% 5.12/5.45 ! [Q5: rat] :
% 5.12/5.45 ( ! [A4: int,B3: int] :
% 5.12/5.45 ( ( Q5
% 5.12/5.45 = ( fract @ A4 @ B3 ) )
% 5.12/5.45 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.12/5.45 => ( ( A4 != zero_zero_int )
% 5.12/5.45 => ~ ( algebr932160517623751201me_int @ A4 @ B3 ) ) ) )
% 5.12/5.45 => ( Q5 = zero_zero_rat ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat_cases_nonzero
% 5.12/5.45 thf(fact_9425_quotient__of__unique,axiom,
% 5.12/5.45 ! [R4: rat] :
% 5.12/5.45 ? [X3: product_prod_int_int] :
% 5.12/5.45 ( ( R4
% 5.12/5.45 = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.12/5.45 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 5.12/5.45 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 5.12/5.45 & ! [Y5: product_prod_int_int] :
% 5.12/5.45 ( ( ( R4
% 5.12/5.45 = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.12/5.45 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 5.12/5.45 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.12/5.45 => ( Y5 = X3 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % quotient_of_unique
% 5.12/5.45 thf(fact_9426_Rats__abs__iff,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 5.12/5.45 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_abs_iff
% 5.12/5.45 thf(fact_9427_coprime__int__iff,axiom,
% 5.12/5.45 ! [M2: nat,N: nat] :
% 5.12/5.45 ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.45 = ( algebr934650988132801477me_nat @ M2 @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_int_iff
% 5.12/5.45 thf(fact_9428_coprime__nat__abs__left__iff,axiom,
% 5.12/5.45 ! [K: int,N: nat] :
% 5.12/5.45 ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.12/5.45 = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_nat_abs_left_iff
% 5.12/5.45 thf(fact_9429_coprime__nat__abs__right__iff,axiom,
% 5.12/5.45 ! [N: nat,K: int] :
% 5.12/5.45 ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.12/5.45 = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_nat_abs_right_iff
% 5.12/5.45 thf(fact_9430_coprime__common__divisor__nat,axiom,
% 5.12/5.45 ! [A: nat,B: nat,X: nat] :
% 5.12/5.45 ( ( algebr934650988132801477me_nat @ A @ B )
% 5.12/5.45 => ( ( dvd_dvd_nat @ X @ A )
% 5.12/5.45 => ( ( dvd_dvd_nat @ X @ B )
% 5.12/5.45 => ( X = one_one_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_common_divisor_nat
% 5.12/5.45 thf(fact_9431_coprime__Suc__0__right,axiom,
% 5.12/5.45 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_Suc_0_right
% 5.12/5.45 thf(fact_9432_coprime__Suc__0__left,axiom,
% 5.12/5.45 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_Suc_0_left
% 5.12/5.45 thf(fact_9433_coprime__Suc__right__nat,axiom,
% 5.12/5.45 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_Suc_right_nat
% 5.12/5.45 thf(fact_9434_coprime__Suc__left__nat,axiom,
% 5.12/5.45 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_Suc_left_nat
% 5.12/5.45 thf(fact_9435_Rats__no__top__le,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ? [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.12/5.45 & ( ord_less_eq_real @ X @ X3 ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_no_top_le
% 5.12/5.45 thf(fact_9436_Rats__no__bot__less,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ? [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.12/5.45 & ( ord_less_real @ X3 @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_no_bot_less
% 5.12/5.45 thf(fact_9437_Rats__dense__in__real,axiom,
% 5.12/5.45 ! [X: real,Y: real] :
% 5.12/5.45 ( ( ord_less_real @ X @ Y )
% 5.12/5.45 => ? [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.12/5.45 & ( ord_less_real @ X @ X3 )
% 5.12/5.45 & ( ord_less_real @ X3 @ Y ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_dense_in_real
% 5.12/5.45 thf(fact_9438_Rats__abs__nat__div__natE,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( member_real @ X @ field_5140801741446780682s_real )
% 5.12/5.45 => ~ ! [M3: nat,N2: nat] :
% 5.12/5.45 ( ( N2 != zero_zero_nat )
% 5.12/5.45 => ( ( ( abs_abs_real @ X )
% 5.12/5.45 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.12/5.45 => ~ ( algebr934650988132801477me_nat @ M3 @ N2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_abs_nat_div_natE
% 5.12/5.45 thf(fact_9439_coprime__diff__one__right__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_diff_one_right_nat
% 5.12/5.45 thf(fact_9440_coprime__diff__one__left__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.12/5.45
% 5.12/5.45 % coprime_diff_one_left_nat
% 5.12/5.45 thf(fact_9441_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.45 ( ~ ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( Xa = one_one_nat ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X3: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.elims(3)
% 5.12/5.45 thf(fact_9442_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.45 ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( Xa != one_one_nat ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ~ ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X4: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.elims(2)
% 5.12/5.45 thf(fact_9443_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.45 ( ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 = ( Xa != one_one_nat ) ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ( Y
% 5.12/5.45 = ( ~ ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.elims(1)
% 5.12/5.45 thf(fact_9444_Rats__eq__int__div__int,axiom,
% 5.12/5.45 ( field_5140801741446780682s_real
% 5.12/5.45 = ( collect_real
% 5.12/5.45 @ ^ [Uu3: real] :
% 5.12/5.45 ? [I2: int,J3: int] :
% 5.12/5.45 ( ( Uu3
% 5.12/5.45 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.12/5.45 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_eq_int_div_int
% 5.12/5.45 thf(fact_9445_Rats__eq__int__div__nat,axiom,
% 5.12/5.45 ( field_5140801741446780682s_real
% 5.12/5.45 = ( collect_real
% 5.12/5.45 @ ^ [Uu3: real] :
% 5.12/5.45 ? [I2: int,N4: nat] :
% 5.12/5.45 ( ( Uu3
% 5.12/5.45 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.12/5.45 & ( N4 != zero_zero_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rats_eq_int_div_nat
% 5.12/5.45 thf(fact_9446_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.12/5.45 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.12/5.45 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.12/5.45 = ( ( Deg = Deg4 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.simps(2)
% 5.12/5.45 thf(fact_9447_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.45 ( ~ ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.45 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.12/5.45 => ( Xa = one_one_nat ) ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.12/5.45 => ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X3: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.pelims(3)
% 5.12/5.45 thf(fact_9448_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat] :
% 5.12/5.45 ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.45 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.12/5.45 => ( Xa != one_one_nat ) ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.12/5.45 => ~ ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X4: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.pelims(2)
% 5.12/5.45 thf(fact_9449_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.12/5.45 ! [X: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.12/5.45 ( ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.12/5.45 = Y )
% 5.12/5.45 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.12/5.45 => ( ! [Uu2: $o,Uv2: $o] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.12/5.45 => ( ( Y
% 5.12/5.45 = ( Xa = one_one_nat ) )
% 5.12/5.45 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.12/5.45 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.45 ( ( X
% 5.12/5.45 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.45 => ( ( Y
% 5.12/5.45 = ( ( Deg2 = Xa )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.12/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 & ( case_o184042715313410164at_nat
% 5.12/5.45 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 5.12/5.45 & ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 @ ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [Mi3: nat,Ma3: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.12/5.45 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 & ! [I2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 5.12/5.45 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.12/5.45 & ( ( Mi3 = Ma3 )
% 5.12/5.45 => ! [X2: vEBT_VEBT] :
% 5.12/5.45 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.12/5.45 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 5.12/5.45 & ( ( Mi3 != Ma3 )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.12/5.45 & ! [X2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.12/5.45 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 5.12/5.45 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.12/5.45 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.12/5.45 @ Mima ) ) )
% 5.12/5.45 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % VEBT_internal.valid'.pelims(1)
% 5.12/5.45 thf(fact_9450_Rat_Opositive_Orsp,axiom,
% 5.12/5.45 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive.rsp
% 5.12/5.45 thf(fact_9451_card__length__sum__list__rec,axiom,
% 5.12/5.45 ! [M2: nat,N5: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 5.12/5.45 => ( ( finite_card_list_nat
% 5.12/5.45 @ ( collect_list_nat
% 5.12/5.45 @ ^ [L2: list_nat] :
% 5.12/5.45 ( ( ( size_size_list_nat @ L2 )
% 5.12/5.45 = M2 )
% 5.12/5.45 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.12/5.45 = N5 ) ) ) )
% 5.12/5.45 = ( plus_plus_nat
% 5.12/5.45 @ ( finite_card_list_nat
% 5.12/5.45 @ ( collect_list_nat
% 5.12/5.45 @ ^ [L2: list_nat] :
% 5.12/5.45 ( ( ( size_size_list_nat @ L2 )
% 5.12/5.45 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 5.12/5.45 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.12/5.45 = N5 ) ) ) )
% 5.12/5.45 @ ( finite_card_list_nat
% 5.12/5.45 @ ( collect_list_nat
% 5.12/5.45 @ ^ [L2: list_nat] :
% 5.12/5.45 ( ( ( size_size_list_nat @ L2 )
% 5.12/5.45 = M2 )
% 5.12/5.45 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.12/5.45 = N5 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_length_sum_list_rec
% 5.12/5.45 thf(fact_9452_card__length__sum__list,axiom,
% 5.12/5.45 ! [M2: nat,N5: nat] :
% 5.12/5.45 ( ( finite_card_list_nat
% 5.12/5.45 @ ( collect_list_nat
% 5.12/5.45 @ ^ [L2: list_nat] :
% 5.12/5.45 ( ( ( size_size_list_nat @ L2 )
% 5.12/5.45 = M2 )
% 5.12/5.45 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.12/5.45 = N5 ) ) ) )
% 5.12/5.45 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M2 ) @ one_one_nat ) @ N5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % card_length_sum_list
% 5.12/5.45 thf(fact_9453_vanishes__mult__bounded,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ? [A7: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 5.12/5.45 & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N2 ) ) @ A7 ) )
% 5.12/5.45 => ( ( vanishes @ Y7 )
% 5.12/5.45 => ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_mult_bounded
% 5.12/5.45 thf(fact_9454_range__mod,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( image_nat_nat
% 5.12/5.45 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N )
% 5.12/5.45 @ top_top_set_nat )
% 5.12/5.45 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % range_mod
% 5.12/5.45 thf(fact_9455_vanishes__const,axiom,
% 5.12/5.45 ! [C: rat] :
% 5.12/5.45 ( ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : C )
% 5.12/5.45 = ( C = zero_zero_rat ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_const
% 5.12/5.45 thf(fact_9456_uminus__integer_Orsp,axiom,
% 5.12/5.45 ( bNF_re4712519889275205905nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ uminus_uminus_int
% 5.12/5.45 @ uminus_uminus_int ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_integer.rsp
% 5.12/5.45 thf(fact_9457_Suc_Orsp,axiom,
% 5.12/5.45 ( bNF_re5653821019739307937at_nat
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ suc
% 5.12/5.45 @ suc ) ).
% 5.12/5.45
% 5.12/5.45 % Suc.rsp
% 5.12/5.45 thf(fact_9458_less__natural_Orsp,axiom,
% 5.12/5.45 ( bNF_re578469030762574527_nat_o
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re4705727531993890431at_o_o
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ord_less_nat
% 5.12/5.45 @ ord_less_nat ) ).
% 5.12/5.45
% 5.12/5.45 % less_natural.rsp
% 5.12/5.45 thf(fact_9459_less__integer_Orsp,axiom,
% 5.12/5.45 ( bNF_re3403563459893282935_int_o
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re5089333283451836215nt_o_o
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ord_less_int
% 5.12/5.45 @ ord_less_int ) ).
% 5.12/5.45
% 5.12/5.45 % less_integer.rsp
% 5.12/5.45 thf(fact_9460_sub_Orsp,axiom,
% 5.12/5.45 ( bNF_re8402795839162346335um_int
% 5.12/5.45 @ ^ [Y4: num,Z: num] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re1822329894187522285nt_int
% 5.12/5.45 @ ^ [Y4: num,Z: num] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 5.12/5.45 @ ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) )
% 5.12/5.45 @ ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sub.rsp
% 5.12/5.45 thf(fact_9461_minus__natural_Orsp,axiom,
% 5.12/5.45 ( bNF_re1345281282404953727at_nat
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re5653821019739307937at_nat
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 5.12/5.45 @ minus_minus_nat
% 5.12/5.45 @ minus_minus_nat ) ).
% 5.12/5.45
% 5.12/5.45 % minus_natural.rsp
% 5.12/5.45 thf(fact_9462_minus__integer_Orsp,axiom,
% 5.12/5.45 ( bNF_re711492959462206631nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re4712519889275205905nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 5.12/5.45 @ minus_minus_int
% 5.12/5.45 @ minus_minus_int ) ).
% 5.12/5.45
% 5.12/5.45 % minus_integer.rsp
% 5.12/5.45 thf(fact_9463_divide__integer_Orsp,axiom,
% 5.12/5.45 ( bNF_re711492959462206631nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re4712519889275205905nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z ) )
% 5.12/5.45 @ divide_divide_int
% 5.12/5.45 @ divide_divide_int ) ).
% 5.12/5.45
% 5.12/5.45 % divide_integer.rsp
% 5.12/5.45 thf(fact_9464_divide__natural_Orsp,axiom,
% 5.12/5.45 ( bNF_re1345281282404953727at_nat
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re5653821019739307937at_nat
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 5.12/5.45 @ divide_divide_nat
% 5.12/5.45 @ divide_divide_nat ) ).
% 5.12/5.45
% 5.12/5.45 % divide_natural.rsp
% 5.12/5.45 thf(fact_9465_integer__of__natural_Orsp,axiom,
% 5.12/5.45 ( bNF_re6650684261131312217nt_int
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ semiri1314217659103216013at_int
% 5.12/5.45 @ semiri1314217659103216013at_int ) ).
% 5.12/5.45
% 5.12/5.45 % integer_of_natural.rsp
% 5.12/5.45 thf(fact_9466_Fract_Orsp,axiom,
% 5.12/5.45 ( bNF_re157797125943740599nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re6250860962936578807nt_int
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ratrel )
% 5.12/5.45 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.12/5.45 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Fract.rsp
% 5.12/5.45 thf(fact_9467_vanishes__minus,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( vanishes @ X8 )
% 5.12/5.45 => ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_minus
% 5.12/5.45 thf(fact_9468_vanishes__add,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( vanishes @ X8 )
% 5.12/5.45 => ( ( vanishes @ Y7 )
% 5.12/5.45 => ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_add
% 5.12/5.45 thf(fact_9469_vanishes__diff,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( vanishes @ X8 )
% 5.12/5.45 => ( ( vanishes @ Y7 )
% 5.12/5.45 => ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_diff
% 5.12/5.45 thf(fact_9470_uminus__rat_Orsp,axiom,
% 5.12/5.45 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_rat.rsp
% 5.12/5.45 thf(fact_9471_vanishes__def,axiom,
% 5.12/5.45 ( vanishes
% 5.12/5.45 = ( ^ [X7: nat > rat] :
% 5.12/5.45 ! [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 => ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N4 ) ) @ R ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_def
% 5.12/5.45 thf(fact_9472_vanishesI,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ! [R3: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.12/5.45 => ? [K4: nat] :
% 5.12/5.45 ! [N2: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.12/5.45 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N2 ) ) @ R3 ) ) )
% 5.12/5.45 => ( vanishes @ X8 ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishesI
% 5.12/5.45 thf(fact_9473_vanishesD,axiom,
% 5.12/5.45 ! [X8: nat > rat,R4: rat] :
% 5.12/5.45 ( ( vanishes @ X8 )
% 5.12/5.45 => ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 5.12/5.45 => ? [K2: nat] :
% 5.12/5.45 ! [N6: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.12/5.45 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ R4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishesD
% 5.12/5.45 thf(fact_9474_inverse__rat_Orsp,axiom,
% 5.12/5.45 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.12/5.45 @ ^ [X2: product_prod_int_int] :
% 5.12/5.45 ( if_Pro3027730157355071871nt_int
% 5.12/5.45 @ ( ( product_fst_int_int @ X2 )
% 5.12/5.45 = zero_zero_int )
% 5.12/5.45 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.45 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.12/5.45 @ ^ [X2: product_prod_int_int] :
% 5.12/5.45 ( if_Pro3027730157355071871nt_int
% 5.12/5.45 @ ( ( product_fst_int_int @ X2 )
% 5.12/5.45 = zero_zero_int )
% 5.12/5.45 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.45 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_rat.rsp
% 5.12/5.45 thf(fact_9475_UNIV__nat__eq,axiom,
% 5.12/5.45 ( top_top_set_nat
% 5.12/5.45 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % UNIV_nat_eq
% 5.12/5.45 thf(fact_9476_inverse__rat_Otransfer,axiom,
% 5.12/5.45 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.12/5.45 @ ^ [X2: product_prod_int_int] :
% 5.12/5.45 ( if_Pro3027730157355071871nt_int
% 5.12/5.45 @ ( ( product_fst_int_int @ X2 )
% 5.12/5.45 = zero_zero_int )
% 5.12/5.45 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.12/5.45 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 5.12/5.45 @ inverse_inverse_rat ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_rat.transfer
% 5.12/5.45 thf(fact_9477_Rat_Opositive_Otransfer,axiom,
% 5.12/5.45 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 5.12/5.45 @ positive ) ).
% 5.12/5.45
% 5.12/5.45 % Rat.positive.transfer
% 5.12/5.45 thf(fact_9478_card__UNIV__unit,axiom,
% 5.12/5.45 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.12/5.45 = one_one_nat ) ).
% 5.12/5.45
% 5.12/5.45 % card_UNIV_unit
% 5.12/5.45 thf(fact_9479_range__abs__Nats,axiom,
% 5.12/5.45 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 5.12/5.45 = semiring_1_Nats_int ) ).
% 5.12/5.45
% 5.12/5.45 % range_abs_Nats
% 5.12/5.45 thf(fact_9480_infinite__UNIV__int,axiom,
% 5.12/5.45 ~ ( finite_finite_int @ top_top_set_int ) ).
% 5.12/5.45
% 5.12/5.45 % infinite_UNIV_int
% 5.12/5.45 thf(fact_9481_surj__prod__encode,axiom,
% 5.12/5.45 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 5.12/5.45 = top_top_set_nat ) ).
% 5.12/5.45
% 5.12/5.45 % surj_prod_encode
% 5.12/5.45 thf(fact_9482_bij__prod__encode,axiom,
% 5.12/5.45 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 5.12/5.45
% 5.12/5.45 % bij_prod_encode
% 5.12/5.45 thf(fact_9483_int__in__range__abs,axiom,
% 5.12/5.45 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_in_range_abs
% 5.12/5.45 thf(fact_9484_one__rat_Otransfer,axiom,
% 5.12/5.45 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 5.12/5.45
% 5.12/5.45 % one_rat.transfer
% 5.12/5.45 thf(fact_9485_zero__rat_Otransfer,axiom,
% 5.12/5.45 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 5.12/5.45
% 5.12/5.45 % zero_rat.transfer
% 5.12/5.45 thf(fact_9486_Fract_Otransfer,axiom,
% 5.12/5.45 ( bNF_re3461391660133120880nt_rat
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ ( bNF_re2214769303045360666nt_rat
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.45 @ pcr_rat )
% 5.12/5.45 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.12/5.45 @ fract ) ).
% 5.12/5.45
% 5.12/5.45 % Fract.transfer
% 5.12/5.45 thf(fact_9487_uminus__rat_Otransfer,axiom,
% 5.12/5.45 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.12/5.45 @ ^ [X2: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X2 ) ) @ ( product_snd_int_int @ X2 ) )
% 5.12/5.45 @ uminus_uminus_rat ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_rat.transfer
% 5.12/5.45 thf(fact_9488_root__def,axiom,
% 5.12/5.45 ( root
% 5.12/5.45 = ( ^ [N4: nat,X2: real] :
% 5.12/5.45 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 5.12/5.45 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.12/5.45 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N4 ) )
% 5.12/5.45 @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % root_def
% 5.12/5.45 thf(fact_9489_times__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) ) )
% 5.12/5.45 @ times_times_int ) ).
% 5.12/5.45
% 5.12/5.45 % times_int.transfer
% 5.12/5.45 thf(fact_9490_zero__int_Otransfer,axiom,
% 5.12/5.45 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.12/5.45
% 5.12/5.45 % zero_int.transfer
% 5.12/5.45 thf(fact_9491_int__transfer,axiom,
% 5.12/5.45 ( bNF_re6830278522597306478at_int
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ pcr_int
% 5.12/5.45 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 5.12/5.45 @ semiri1314217659103216013at_int ) ).
% 5.12/5.45
% 5.12/5.45 % int_transfer
% 5.12/5.45 thf(fact_9492_uminus__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.12/5.45 @ ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X2 ) )
% 5.12/5.45 @ uminus_uminus_int ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_int.transfer
% 5.12/5.45 thf(fact_9493_nat_Otransfer,axiom,
% 5.12/5.45 ( bNF_re4555766996558763186at_nat @ pcr_int
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.12/5.45 @ nat2 ) ).
% 5.12/5.45
% 5.12/5.45 % nat.transfer
% 5.12/5.45 thf(fact_9494_one__int_Otransfer,axiom,
% 5.12/5.45 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.12/5.45
% 5.12/5.45 % one_int.transfer
% 5.12/5.45 thf(fact_9495_less__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.12/5.45 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) )
% 5.12/5.45 @ ord_less_int ) ).
% 5.12/5.45
% 5.12/5.45 % less_int.transfer
% 5.12/5.45 thf(fact_9496_less__eq__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.12/5.45 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) )
% 5.12/5.45 @ ord_less_eq_int ) ).
% 5.12/5.45
% 5.12/5.45 % less_eq_int.transfer
% 5.12/5.45 thf(fact_9497_plus__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) )
% 5.12/5.45 @ plus_plus_int ) ).
% 5.12/5.45
% 5.12/5.45 % plus_int.transfer
% 5.12/5.45 thf(fact_9498_minus__int_Otransfer,axiom,
% 5.12/5.45 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) ) )
% 5.12/5.45 @ minus_minus_int ) ).
% 5.12/5.45
% 5.12/5.45 % minus_int.transfer
% 5.12/5.45 thf(fact_9499_DERIV__even__real__root,axiom,
% 5.12/5.45 ! [N: nat,X: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_even_real_root
% 5.12/5.45 thf(fact_9500_DERIV__real__root__generic,axiom,
% 5.12/5.45 ! [N: nat,X: real,D6: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( X != zero_zero_real )
% 5.12/5.45 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( D6
% 5.12/5.45 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.12/5.45 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.45 => ( D6
% 5.12/5.45 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.12/5.45 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( D6
% 5.12/5.45 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D6 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_real_root_generic
% 5.12/5.45 thf(fact_9501_DERIV__arctan__series,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X9: real] :
% 5.12/5.45 ( suminf_real
% 5.12/5.45 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_arctan_series
% 5.12/5.45 thf(fact_9502_DERIV__pos__inc__left,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.12/5.45 => ? [D5: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.45 & ! [H3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.12/5.45 => ( ( ord_less_real @ H3 @ D5 )
% 5.12/5.45 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H3 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_pos_inc_left
% 5.12/5.45 thf(fact_9503_DERIV__neg__dec__left,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.12/5.45 => ? [D5: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.45 & ! [H3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.12/5.45 => ( ( ord_less_real @ H3 @ D5 )
% 5.12/5.45 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H3 ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_neg_dec_left
% 5.12/5.45 thf(fact_9504_DERIV__const__ratio__const2,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,K: real] :
% 5.12/5.45 ( ( A != B )
% 5.12/5.45 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.12/5.45 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.12/5.45 = K ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_const_ratio_const2
% 5.12/5.45 thf(fact_9505_DERIV__const__ratio__const,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,K: real] :
% 5.12/5.45 ( ( A != B )
% 5.12/5.45 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.12/5.45 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.12/5.45 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_const_ratio_const
% 5.12/5.45 thf(fact_9506_DERIV__mirror,axiom,
% 5.12/5.45 ! [F: real > real,Y: real,X: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X ) @ top_top_set_real ) )
% 5.12/5.45 = ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( F @ ( uminus_uminus_real @ X2 ) )
% 5.12/5.45 @ ( uminus_uminus_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_mirror
% 5.12/5.45 thf(fact_9507_has__real__derivative__pos__inc__left,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.12/5.45 => ? [D5: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.45 & ! [H3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.12/5.45 => ( ( member_real @ ( minus_minus_real @ X @ H3 ) @ S3 )
% 5.12/5.45 => ( ( ord_less_real @ H3 @ D5 )
% 5.12/5.45 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H3 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % has_real_derivative_pos_inc_left
% 5.12/5.45 thf(fact_9508_has__real__derivative__neg__dec__left,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real,S3: set_real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.12/5.45 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.12/5.45 => ? [D5: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.12/5.45 & ! [H3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.12/5.45 => ( ( member_real @ ( minus_minus_real @ X @ H3 ) @ S3 )
% 5.12/5.45 => ( ( ord_less_real @ H3 @ D5 )
% 5.12/5.45 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H3 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % has_real_derivative_neg_dec_left
% 5.12/5.45 thf(fact_9509_MVT2,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,F3: real > real] :
% 5.12/5.45 ( ( ord_less_real @ A @ B )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ A @ X3 )
% 5.12/5.45 => ( ( ord_less_eq_real @ X3 @ B )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.12/5.45 => ? [Z4: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ Z4 )
% 5.12/5.45 & ( ord_less_real @ Z4 @ B )
% 5.12/5.45 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.12/5.45 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F3 @ Z4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % MVT2
% 5.12/5.45 thf(fact_9510_DERIV__local__const,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real,D: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.12/5.45 => ( ! [Y3: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.12/5.45 => ( ( F @ X )
% 5.12/5.45 = ( F @ Y3 ) ) )
% 5.12/5.45 => ( L = zero_zero_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_local_const
% 5.12/5.45 thf(fact_9511_DERIV__ln,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_ln
% 5.12/5.45 thf(fact_9512_DERIV__const__average,axiom,
% 5.12/5.45 ! [A: real,B: real,V: real > real,K: real] :
% 5.12/5.45 ( ( A != B )
% 5.12/5.45 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.12/5.45 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.12/5.45 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_const_average
% 5.12/5.45 thf(fact_9513_DERIV__local__max,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real,D: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.12/5.45 => ( ! [Y3: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.12/5.45 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 5.12/5.45 => ( L = zero_zero_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_local_max
% 5.12/5.45 thf(fact_9514_DERIV__local__min,axiom,
% 5.12/5.45 ! [F: real > real,L: real,X: real,D: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.12/5.45 => ( ! [Y3: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 5.12/5.45 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 5.12/5.45 => ( L = zero_zero_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_local_min
% 5.12/5.45 thf(fact_9515_DERIV__ln__divide,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_ln_divide
% 5.12/5.45 thf(fact_9516_DERIV__pow,axiom,
% 5.12/5.45 ! [N: nat,X: real,S: set_real] :
% 5.12/5.45 ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 5.12/5.45 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_pow
% 5.12/5.45 thf(fact_9517_DERIV__fun__pow,axiom,
% 5.12/5.45 ! [G: real > real,M2: real,X: real,N: nat] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ G @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 5.12/5.45 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M2 )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_fun_pow
% 5.12/5.45 thf(fact_9518_has__real__derivative__powr,axiom,
% 5.12/5.45 ! [Z2: real,R4: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [Z6: real] : ( powr_real @ Z6 @ R4 )
% 5.12/5.45 @ ( times_times_real @ R4 @ ( powr_real @ Z2 @ ( minus_minus_real @ R4 @ one_one_real ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % has_real_derivative_powr
% 5.12/5.45 thf(fact_9519_DERIV__log,axiom,
% 5.12/5.45 ! [X: real,B: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( log2 @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_log
% 5.12/5.45 thf(fact_9520_DERIV__fun__powr,axiom,
% 5.12/5.45 ! [G: real > real,M2: real,X: real,R4: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ G @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R4 )
% 5.12/5.45 @ ( times_times_real @ ( times_times_real @ R4 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R4 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M2 )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_fun_powr
% 5.12/5.45 thf(fact_9521_DERIV__powr,axiom,
% 5.12/5.45 ! [G: real > real,M2: real,X: real,F: real > real,R4: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ G @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.12/5.45 => ( ( has_fi5821293074295781190e_real @ F @ R4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.12/5.45 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R4 @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M2 @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_powr
% 5.12/5.45 thf(fact_9522_DERIV__real__sqrt,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_real_sqrt
% 5.12/5.45 thf(fact_9523_DERIV__series_H,axiom,
% 5.12/5.45 ! [F: real > nat > real,F3: real > nat > real,X0: real,A: real,B: real,L4: nat > real] :
% 5.12/5.45 ( ! [N2: nat] :
% 5.12/5.45 ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( F @ X2 @ N2 )
% 5.12/5.45 @ ( F3 @ X0 @ N2 )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.12/5.45 => ( summable_real @ ( F @ X3 ) ) )
% 5.12/5.45 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.12/5.45 => ( ( summable_real @ ( F3 @ X0 ) )
% 5.12/5.45 => ( ( summable_real @ L4 )
% 5.12/5.45 => ( ! [N2: nat,X3: real,Y3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.12/5.45 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.12/5.45 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N2 ) @ ( F @ Y3 @ N2 ) ) ) @ ( times_times_real @ ( L4 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.12/5.45 @ ( suminf_real @ ( F3 @ X0 ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_series'
% 5.12/5.45 thf(fact_9524_DERIV__arctan,axiom,
% 5.12/5.45 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_arctan
% 5.12/5.45 thf(fact_9525_arsinh__real__has__field__derivative,axiom,
% 5.12/5.45 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.12/5.45
% 5.12/5.45 % arsinh_real_has_field_derivative
% 5.12/5.45 thf(fact_9526_DERIV__real__sqrt__generic,axiom,
% 5.12/5.45 ! [X: real,D6: real] :
% 5.12/5.45 ( ( X != zero_zero_real )
% 5.12/5.45 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( D6
% 5.12/5.45 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.12/5.45 => ( D6
% 5.12/5.45 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ sqrt @ D6 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_real_sqrt_generic
% 5.12/5.45 thf(fact_9527_arcosh__real__has__field__derivative,axiom,
% 5.12/5.45 ! [X: real,A2: set_real] :
% 5.12/5.45 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % arcosh_real_has_field_derivative
% 5.12/5.45 thf(fact_9528_artanh__real__has__field__derivative,axiom,
% 5.12/5.45 ! [X: real,A2: set_real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % artanh_real_has_field_derivative
% 5.12/5.45 thf(fact_9529_DERIV__power__series_H,axiom,
% 5.12/5.45 ! [R2: real,F: nat > real,X0: real] :
% 5.12/5.45 ( ! [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.12/5.45 => ( summable_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X3 @ N4 ) ) ) )
% 5.12/5.45 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( suminf_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X2 @ ( suc @ N4 ) ) ) )
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_power_series'
% 5.12/5.45 thf(fact_9530_DERIV__real__root,axiom,
% 5.12/5.45 ! [N: nat,X: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_real_root
% 5.12/5.45 thf(fact_9531_DERIV__arccos,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_arccos
% 5.12/5.45 thf(fact_9532_DERIV__arcsin,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_arcsin
% 5.12/5.45 thf(fact_9533_Maclaurin__all__le__objl,axiom,
% 5.12/5.45 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.12/5.45 ( ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 & ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.45 & ( ( F @ X )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_all_le_objl
% 5.12/5.45 thf(fact_9534_Maclaurin__all__le,axiom,
% 5.12/5.45 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.12/5.45 ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.45 & ( ( F @ X )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_all_le
% 5.12/5.45 thf(fact_9535_DERIV__odd__real__root,axiom,
% 5.12/5.45 ! [N: nat,X: real] :
% 5.12/5.45 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( ( X != zero_zero_real )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % DERIV_odd_real_root
% 5.12/5.45 thf(fact_9536_Maclaurin__minus,axiom,
% 5.12/5.45 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.12/5.45 ( ( ord_less_real @ H @ zero_zero_real )
% 5.12/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ H @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ H @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.12/5.45 & ( ( F @ H )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_minus
% 5.12/5.45 thf(fact_9537_Maclaurin2,axiom,
% 5.12/5.45 ! [H: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ H ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ H )
% 5.12/5.45 & ( ( F @ H )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin2
% 5.12/5.45 thf(fact_9538_Maclaurin,axiom,
% 5.12/5.45 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ H )
% 5.12/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ H ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ H )
% 5.12/5.45 & ( ( F @ H )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin
% 5.12/5.45 thf(fact_9539_Maclaurin__all__lt,axiom,
% 5.12/5.45 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.12/5.45 ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( X != zero_zero_real )
% 5.12/5.45 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.12/5.45 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.45 & ( ( F @ X )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_all_lt
% 5.12/5.45 thf(fact_9540_Maclaurin__bi__le,axiom,
% 5.12/5.45 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.12/5.45 ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.12/5.45 & ( ( F @ X )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_bi_le
% 5.12/5.45 thf(fact_9541_Taylor,axiom,
% 5.12/5.45 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ A @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ B ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ( ( ord_less_eq_real @ A @ C )
% 5.12/5.45 => ( ( ord_less_eq_real @ C @ B )
% 5.12/5.45 => ( ( ord_less_eq_real @ A @ X )
% 5.12/5.45 => ( ( ord_less_eq_real @ X @ B )
% 5.12/5.45 => ( ( X != C )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ( ord_less_real @ X @ C )
% 5.12/5.45 => ( ( ord_less_real @ X @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ C ) ) )
% 5.12/5.45 & ( ~ ( ord_less_real @ X @ C )
% 5.12/5.45 => ( ( ord_less_real @ C @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ X ) ) )
% 5.12/5.45 & ( ( F @ X )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Taylor
% 5.12/5.45 thf(fact_9542_Taylor__up,axiom,
% 5.12/5.45 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ A @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ B ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ( ( ord_less_eq_real @ A @ C )
% 5.12/5.45 => ( ( ord_less_real @ C @ B )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ C @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ B )
% 5.12/5.45 & ( ( F @ B )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Taylor_up
% 5.12/5.45 thf(fact_9543_Taylor__down,axiom,
% 5.12/5.45 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( ( Diff @ zero_zero_nat )
% 5.12/5.45 = F )
% 5.12/5.45 => ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ A @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ B ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ( ( ord_less_real @ A @ C )
% 5.12/5.45 => ( ( ord_less_eq_real @ C @ B )
% 5.12/5.45 => ? [T3: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ T3 )
% 5.12/5.45 & ( ord_less_real @ T3 @ C )
% 5.12/5.45 & ( ( F @ A )
% 5.12/5.45 = ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M5 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ N ) )
% 5.12/5.45 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Taylor_down
% 5.12/5.45 thf(fact_9544_Maclaurin__lemma2,axiom,
% 5.12/5.45 ! [N: nat,H: real,Diff: nat > real > real,K: nat,B5: real] :
% 5.12/5.45 ( ! [M3: nat,T3: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M3 @ N )
% 5.12/5.45 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.12/5.45 & ( ord_less_eq_real @ T3 @ H ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.12/5.45 => ( ( N
% 5.12/5.45 = ( suc @ K ) )
% 5.12/5.45 => ! [M: nat,T4: real] :
% 5.12/5.45 ( ( ( ord_less_nat @ M @ N )
% 5.12/5.45 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.12/5.45 & ( ord_less_eq_real @ T4 @ H ) )
% 5.12/5.45 => ( has_fi5821293074295781190e_real
% 5.12/5.45 @ ^ [U2: real] :
% 5.12/5.45 ( minus_minus_real @ ( Diff @ M @ U2 )
% 5.12/5.45 @ ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U2 @ P6 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M ) ) )
% 5.12/5.45 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M ) ) ) ) ) )
% 5.12/5.45 @ ( minus_minus_real @ ( Diff @ ( suc @ M ) @ T4 )
% 5.12/5.45 @ ( plus_plus_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T4 @ P6 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) )
% 5.12/5.45 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) ) ) ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Maclaurin_lemma2
% 5.12/5.45 thf(fact_9545_surj__int__encode,axiom,
% 5.12/5.45 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 5.12/5.45 = top_top_set_nat ) ).
% 5.12/5.45
% 5.12/5.45 % surj_int_encode
% 5.12/5.45 thf(fact_9546_int__encode__eq,axiom,
% 5.12/5.45 ! [X: int,Y: int] :
% 5.12/5.45 ( ( ( nat_int_encode @ X )
% 5.12/5.45 = ( nat_int_encode @ Y ) )
% 5.12/5.45 = ( X = Y ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_encode_eq
% 5.12/5.45 thf(fact_9547_LIM__fun__gt__zero,axiom,
% 5.12/5.45 ! [F: real > real,L: real,C: real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.12/5.45 => ? [R3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.12/5.45 & ! [X4: real] :
% 5.12/5.45 ( ( ( X4 != C )
% 5.12/5.45 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.12/5.45 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIM_fun_gt_zero
% 5.12/5.45 thf(fact_9548_LIM__fun__not__zero,axiom,
% 5.12/5.45 ! [F: real > real,L: real,C: real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.12/5.45 => ( ( L != zero_zero_real )
% 5.12/5.45 => ? [R3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.12/5.45 & ! [X4: real] :
% 5.12/5.45 ( ( ( X4 != C )
% 5.12/5.45 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.12/5.45 => ( ( F @ X4 )
% 5.12/5.45 != zero_zero_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIM_fun_not_zero
% 5.12/5.45 thf(fact_9549_LIM__fun__less__zero,axiom,
% 5.12/5.45 ! [F: real > real,L: real,C: real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.12/5.45 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.12/5.45 => ? [R3: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.12/5.45 & ! [X4: real] :
% 5.12/5.45 ( ( ( X4 != C )
% 5.12/5.45 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R3 ) )
% 5.12/5.45 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIM_fun_less_zero
% 5.12/5.45 thf(fact_9550_isCont__arctan,axiom,
% 5.12/5.45 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arctan ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_arctan
% 5.12/5.45 thf(fact_9551_isCont__arsinh,axiom,
% 5.12/5.45 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arsinh_real ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_arsinh
% 5.12/5.45 thf(fact_9552_isCont__ln,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( X != zero_zero_real )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_ln
% 5.12/5.45 thf(fact_9553_bij__int__encode,axiom,
% 5.12/5.45 bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 5.12/5.45
% 5.12/5.45 % bij_int_encode
% 5.12/5.45 thf(fact_9554_isCont__arcosh,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_arcosh
% 5.12/5.45 thf(fact_9555_LIM__cos__div__sin,axiom,
% 5.12/5.45 ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIM_cos_div_sin
% 5.12/5.45 thf(fact_9556_isCont__arccos,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_arccos
% 5.12/5.45 thf(fact_9557_isCont__arcsin,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_arcsin
% 5.12/5.45 thf(fact_9558_isCont__artanh,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_artanh
% 5.12/5.45 thf(fact_9559_isCont__inverse__function,axiom,
% 5.12/5.45 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ D )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.12/5.45 => ( ( G @ ( F @ Z4 ) )
% 5.12/5.45 = Z4 ) )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % isCont_inverse_function
% 5.12/5.45 thf(fact_9560_GMVT_H,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F3: real > real] :
% 5.12/5.45 ( ( ord_less_real @ A @ B )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ A @ Z4 )
% 5.12/5.45 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ A @ Z4 )
% 5.12/5.45 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ G ) ) )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ Z4 )
% 5.12/5.45 => ( ( ord_less_real @ Z4 @ B )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.12/5.45 => ( ! [Z4: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ Z4 )
% 5.12/5.45 => ( ( ord_less_real @ Z4 @ B )
% 5.12/5.45 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.12/5.45 => ? [C2: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ C2 )
% 5.12/5.45 & ( ord_less_real @ C2 @ B )
% 5.12/5.45 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.12/5.45 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F3 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % GMVT'
% 5.12/5.45 thf(fact_9561_summable__Leibniz_I2_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ( topolo6980174941875973593q_real @ A )
% 5.12/5.45 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.12/5.45 => ! [N6: nat] :
% 5.12/5.45 ( member_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.12/5.45 @ ( set_or1222579329274155063t_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz(2)
% 5.12/5.45 thf(fact_9562_summable__Leibniz_I3_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ( topolo6980174941875973593q_real @ A )
% 5.12/5.45 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.12/5.45 => ! [N6: nat] :
% 5.12/5.45 ( member_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.12/5.45 @ ( set_or1222579329274155063t_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz(3)
% 5.12/5.45 thf(fact_9563_summable__Leibniz_H_I4_J,axiom,
% 5.12/5.45 ! [A: nat > real,N: nat] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( ord_less_eq_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz'(4)
% 5.12/5.45 thf(fact_9564_mult__nat__right__at__top,axiom,
% 5.12/5.45 ! [C: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.45 => ( filterlim_nat_nat
% 5.12/5.45 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.12/5.45 @ at_top_nat
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % mult_nat_right_at_top
% 5.12/5.45 thf(fact_9565_mult__nat__left__at__top,axiom,
% 5.12/5.45 ! [C: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.12/5.45 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % mult_nat_left_at_top
% 5.12/5.45 thf(fact_9566_LIMSEQ__root,axiom,
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( root @ N4 @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_root
% 5.12/5.45 thf(fact_9567_nested__sequence__unique,axiom,
% 5.12/5.45 ! [F: nat > real,G: nat > real] :
% 5.12/5.45 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.12/5.45 => ( ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat )
% 5.12/5.45 => ? [L3: real] :
% 5.12/5.45 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L3 )
% 5.12/5.45 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat )
% 5.12/5.45 & ! [N6: nat] : ( ord_less_eq_real @ L3 @ ( G @ N6 ) )
% 5.12/5.45 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % nested_sequence_unique
% 5.12/5.45 thf(fact_9568_lim__inverse__n_H,axiom,
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % lim_inverse_n'
% 5.12/5.45 thf(fact_9569_LIMSEQ__root__const,axiom,
% 5.12/5.45 ! [C: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ C )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( root @ N4 @ C )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_root_const
% 5.12/5.45 thf(fact_9570_LIMSEQ__inverse__real__of__nat,axiom,
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_inverse_real_of_nat
% 5.12/5.45 thf(fact_9571_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.12/5.45 ! [R4: real] :
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_real @ R4 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ R4 )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_inverse_real_of_nat_add
% 5.12/5.45 thf(fact_9572_increasing__LIMSEQ,axiom,
% 5.12/5.45 ! [F: nat > real,L: real] :
% 5.12/5.45 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 5.12/5.45 => ( ! [E: real] :
% 5.12/5.45 ( ( ord_less_real @ zero_zero_real @ E )
% 5.12/5.45 => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 5.12/5.45 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % increasing_LIMSEQ
% 5.12/5.45 thf(fact_9573_LIMSEQ__realpow__zero,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.12/5.45 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_realpow_zero
% 5.12/5.45 thf(fact_9574_LIMSEQ__divide__realpow__zero,axiom,
% 5.12/5.45 ! [X: real,A: real] :
% 5.12/5.45 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N4 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_divide_realpow_zero
% 5.12/5.45 thf(fact_9575_LIMSEQ__abs__realpow__zero,axiom,
% 5.12/5.45 ! [C: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.12/5.45 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_abs_realpow_zero
% 5.12/5.45 thf(fact_9576_LIMSEQ__abs__realpow__zero2,axiom,
% 5.12/5.45 ! [C: real] :
% 5.12/5.45 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.12/5.45 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_abs_realpow_zero2
% 5.12/5.45 thf(fact_9577_LIMSEQ__inverse__realpow__zero,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_real @ one_one_real @ X )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N4 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_inverse_realpow_zero
% 5.12/5.45 thf(fact_9578_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.12/5.45 ! [R4: real] :
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_real @ R4 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ R4 )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.12/5.45 thf(fact_9579_tendsto__exp__limit__sequentially,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N4 ) ) ) @ N4 )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % tendsto_exp_limit_sequentially
% 5.12/5.45 thf(fact_9580_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.12/5.45 ! [R4: real] :
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ R4 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ R4 )
% 5.12/5.45 @ at_top_nat ) ).
% 5.12/5.45
% 5.12/5.45 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.12/5.45 thf(fact_9581_summable__Leibniz_I1_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ( topolo6980174941875973593q_real @ A )
% 5.12/5.45 => ( summable_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz(1)
% 5.12/5.45 thf(fact_9582_summable,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( summable_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable
% 5.12/5.45 thf(fact_9583_cos__diff__limit__1,axiom,
% 5.12/5.45 ! [Theta: nat > real,Theta2: real] :
% 5.12/5.45 ( ( filterlim_nat_real
% 5.12/5.45 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.12/5.45 @ at_top_nat )
% 5.12/5.45 => ~ ! [K2: nat > int] :
% 5.12/5.45 ~ ( filterlim_nat_real
% 5.12/5.45 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % cos_diff_limit_1
% 5.12/5.45 thf(fact_9584_cos__limit__1,axiom,
% 5.12/5.45 ! [Theta: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real
% 5.12/5.45 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.12/5.45 @ at_top_nat )
% 5.12/5.45 => ? [K2: nat > int] :
% 5.12/5.45 ( filterlim_nat_real
% 5.12/5.45 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % cos_limit_1
% 5.12/5.45 thf(fact_9585_summable__Leibniz_I4_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ( topolo6980174941875973593q_real @ A )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.12/5.45 @ at_top_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz(4)
% 5.12/5.45 thf(fact_9586_zeroseq__arctan__series,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % zeroseq_arctan_series
% 5.12/5.45 thf(fact_9587_summable__Leibniz_H_I3_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.12/5.45 @ at_top_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz'(3)
% 5.12/5.45 thf(fact_9588_summable__Leibniz_H_I2_J,axiom,
% 5.12/5.45 ! [A: nat > real,N: nat] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( ord_less_eq_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz'(2)
% 5.12/5.45 thf(fact_9589_sums__alternating__upper__lower,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ? [L3: real] :
% 5.12/5.45 ( ! [N6: nat] :
% 5.12/5.45 ( ord_less_eq_real
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.12/5.45 @ L3 )
% 5.12/5.45 & ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ L3 )
% 5.12/5.45 @ at_top_nat )
% 5.12/5.45 & ! [N6: nat] :
% 5.12/5.45 ( ord_less_eq_real @ L3
% 5.12/5.45 @ ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 5.12/5.45 & ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ L3 )
% 5.12/5.45 @ at_top_nat ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sums_alternating_upper_lower
% 5.12/5.45 thf(fact_9590_summable__Leibniz_I5_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ( topolo6980174941875973593q_real @ A )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.12/5.45 @ at_top_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz(5)
% 5.12/5.45 thf(fact_9591_summable__Leibniz_H_I5_J,axiom,
% 5.12/5.45 ! [A: nat > real] :
% 5.12/5.45 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.12/5.45 => ( filterlim_nat_real
% 5.12/5.45 @ ^ [N4: nat] :
% 5.12/5.45 ( groups6591440286371151544t_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.12/5.45 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real
% 5.12/5.45 @ ( suminf_real
% 5.12/5.45 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.12/5.45 @ at_top_nat ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % summable_Leibniz'(5)
% 5.12/5.45 thf(fact_9592_eventually__sequentially__Suc,axiom,
% 5.12/5.45 ! [P: nat > $o] :
% 5.12/5.45 ( ( eventually_nat
% 5.12/5.45 @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 5.12/5.45 @ at_top_nat )
% 5.12/5.45 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % eventually_sequentially_Suc
% 5.12/5.45 thf(fact_9593_filterlim__Suc,axiom,
% 5.12/5.45 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.12/5.45
% 5.12/5.45 % filterlim_Suc
% 5.12/5.45 thf(fact_9594_cosh__real__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ cosh_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % cosh_real_at_top
% 5.12/5.45 thf(fact_9595_sinh__real__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ sinh_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % sinh_real_at_top
% 5.12/5.45 thf(fact_9596_arcosh__real__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ arcosh_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % arcosh_real_at_top
% 5.12/5.45 thf(fact_9597_arsinh__real__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ arsinh_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % arsinh_real_at_top
% 5.12/5.45 thf(fact_9598_lhopital__at__top__at__top,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_at_top_at_top
% 5.12/5.45 thf(fact_9599_lhopital__left__at__top__at__top,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_left_at_top_at_top
% 5.12/5.45 thf(fact_9600_ln__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ ln_ln_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % ln_at_top
% 5.12/5.45 thf(fact_9601_exp__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ exp_real @ at_top_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % exp_at_top
% 5.12/5.45 thf(fact_9602_filterlim__int__sequentially,axiom,
% 5.12/5.45 filterlim_nat_int @ semiri1314217659103216013at_int @ at_top_int @ at_top_nat ).
% 5.12/5.45
% 5.12/5.45 % filterlim_int_sequentially
% 5.12/5.45 thf(fact_9603_lhospital__at__top__at__top,axiom,
% 5.12/5.45 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X: real] :
% 5.12/5.45 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ at_top_real )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ at_top_real )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ at_top_real )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ X )
% 5.12/5.45 @ at_top_real )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ X )
% 5.12/5.45 @ at_top_real ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhospital_at_top_at_top
% 5.12/5.45 thf(fact_9604_lhopital__at__top,axiom,
% 5.12/5.45 ! [G: real > real,X: real,G2: real > real,F: real > real,F3: real > real,Y: real] :
% 5.12/5.45 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_at_top
% 5.12/5.45 thf(fact_9605_lhopital__left__at__top,axiom,
% 5.12/5.45 ! [G: real > real,X: real,G2: real > real,F: real > real,F3: real > real,Y: real] :
% 5.12/5.45 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_left_at_top
% 5.12/5.45 thf(fact_9606_tanh__real__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % tanh_real_at_top
% 5.12/5.45 thf(fact_9607_artanh__real__at__left__1,axiom,
% 5.12/5.45 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % artanh_real_at_left_1
% 5.12/5.45 thf(fact_9608_ln__x__over__x__tendsto__0,axiom,
% 5.12/5.45 ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_real ) ).
% 5.12/5.45
% 5.12/5.45 % ln_x_over_x_tendsto_0
% 5.12/5.45 thf(fact_9609_tendsto__power__div__exp__0,axiom,
% 5.12/5.45 ! [K: nat] :
% 5.12/5.45 ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.12/5.45 @ at_top_real ) ).
% 5.12/5.45
% 5.12/5.45 % tendsto_power_div_exp_0
% 5.12/5.45 thf(fact_9610_lhopital,axiom,
% 5.12/5.45 ! [F: real > real,X: real,G: real > real,G2: real > real,F3: real > real,F4: filter_real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital
% 5.12/5.45 thf(fact_9611_lhopital__left,axiom,
% 5.12/5.45 ! [F: real > real,X: real,G: real > real,G2: real > real,F3: real > real,F4: filter_real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_left
% 5.12/5.45 thf(fact_9612_tendsto__exp__limit__at__top,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( filterlim_real_real
% 5.12/5.45 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y6 ) ) @ Y6 )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.12/5.45 @ at_top_real ) ).
% 5.12/5.45
% 5.12/5.45 % tendsto_exp_limit_at_top
% 5.12/5.45 thf(fact_9613_filterlim__tan__at__left,axiom,
% 5.12/5.45 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 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % filterlim_tan_at_left
% 5.12/5.45 thf(fact_9614_tendsto__arctan__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % tendsto_arctan_at_top
% 5.12/5.45 thf(fact_9615_dist__real__def,axiom,
% 5.12/5.45 ( real_V975177566351809787t_real
% 5.12/5.45 = ( ^ [X2: real,Y6: real] : ( abs_abs_real @ ( minus_minus_real @ X2 @ Y6 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % dist_real_def
% 5.12/5.45 thf(fact_9616_dist__complex__def,axiom,
% 5.12/5.45 ( real_V3694042436643373181omplex
% 5.12/5.45 = ( ^ [X2: complex,Y6: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y6 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % dist_complex_def
% 5.12/5.45 thf(fact_9617_filterlim__pow__at__bot__even,axiom,
% 5.12/5.45 ! [N: nat,F: real > real,F4: filter_real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 5.12/5.45 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ F4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % filterlim_pow_at_bot_even
% 5.12/5.45 thf(fact_9618_tendsto__exp__limit__at__right,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( filterlim_real_real
% 5.12/5.45 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y6 ) ) @ ( divide_divide_real @ one_one_real @ Y6 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % tendsto_exp_limit_at_right
% 5.12/5.45 thf(fact_9619_ln__at__0,axiom,
% 5.12/5.45 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % ln_at_0
% 5.12/5.45 thf(fact_9620_artanh__real__at__right__1,axiom,
% 5.12/5.45 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % artanh_real_at_right_1
% 5.12/5.45 thf(fact_9621_sinh__real__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ sinh_real @ at_bot_real @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % sinh_real_at_bot
% 5.12/5.45 thf(fact_9622_arsinh__real__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ arsinh_real @ at_bot_real @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % arsinh_real_at_bot
% 5.12/5.45 thf(fact_9623_cosh__real__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ cosh_real @ at_top_real @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % cosh_real_at_bot
% 5.12/5.45 thf(fact_9624_lhopital__right__at__top__at__bot,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right_at_top_at_bot
% 5.12/5.45 thf(fact_9625_filterlim__uminus__at__top__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % filterlim_uminus_at_top_at_bot
% 5.12/5.45 thf(fact_9626_filterlim__uminus__at__bot__at__top,axiom,
% 5.12/5.45 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 5.12/5.45
% 5.12/5.45 % filterlim_uminus_at_bot_at_top
% 5.12/5.45 thf(fact_9627_eventually__at__left__to__right,axiom,
% 5.12/5.45 ! [P: real > $o,A: real] :
% 5.12/5.45 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 = ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( P @ ( uminus_uminus_real @ X2 ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % eventually_at_left_to_right
% 5.12/5.45 thf(fact_9628_filterlim__tan__at__right,axiom,
% 5.12/5.45 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 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % filterlim_tan_at_right
% 5.12/5.45 thf(fact_9629_exp__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % exp_at_bot
% 5.12/5.45 thf(fact_9630_tanh__real__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % tanh_real_at_bot
% 5.12/5.45 thf(fact_9631_tendsto__arcosh__at__left__1,axiom,
% 5.12/5.45 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % tendsto_arcosh_at_left_1
% 5.12/5.45 thf(fact_9632_lhopital__right__at__top__at__top,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_top_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right_at_top_at_top
% 5.12/5.45 thf(fact_9633_lhopital__right__0,axiom,
% 5.12/5.45 ! [F0: real > real,G0: real > real,G2: real > real,F3: real > real,F4: filter_real] :
% 5.12/5.45 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G0 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right_0
% 5.12/5.45 thf(fact_9634_lhopital__right,axiom,
% 5.12/5.45 ! [F: real > real,X: real,G: real > real,G2: real > real,F3: real > real,F4: filter_real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ F4
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right
% 5.12/5.45 thf(fact_9635_lhopital__at__top__at__bot,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_at_top_at_bot
% 5.12/5.45 thf(fact_9636_filterlim__pow__at__bot__odd,axiom,
% 5.12/5.45 ! [N: nat,F: real > real,F4: filter_real] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 5.12/5.45 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ F4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % filterlim_pow_at_bot_odd
% 5.12/5.45 thf(fact_9637_lhopital__right__at__top,axiom,
% 5.12/5.45 ! [G: real > real,X: real,G2: real > real,F: real > real,F3: real > real,Y: real] :
% 5.12/5.45 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ Y )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right_at_top
% 5.12/5.45 thf(fact_9638_lhopital__right__0__at__top,axiom,
% 5.12/5.45 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X: real] :
% 5.12/5.45 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] :
% 5.12/5.45 ( ( G2 @ X2 )
% 5.12/5.45 != zero_zero_real )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ X )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ ( topolo2815343760600316023s_real @ X )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_right_0_at_top
% 5.12/5.45 thf(fact_9639_lhopital__left__at__top__at__bot,axiom,
% 5.12/5.45 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.12/5.45 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( eventually_real
% 5.12/5.45 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F3 @ X2 ) @ ( G2 @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.12/5.45 => ( filterlim_real_real
% 5.12/5.45 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.12/5.45 @ at_bot_real
% 5.12/5.45 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % lhopital_left_at_top_at_bot
% 5.12/5.45 thf(fact_9640_tendsto__arctan__at__bot,axiom,
% 5.12/5.45 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.12/5.45
% 5.12/5.45 % tendsto_arctan_at_bot
% 5.12/5.45 thf(fact_9641_GMVT,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.12/5.45 ( ( ord_less_real @ A @ B )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.12/5.45 & ( ord_less_eq_real @ X3 @ B ) )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ( ord_less_real @ A @ X3 )
% 5.12/5.45 & ( ord_less_real @ X3 @ B ) )
% 5.12/5.45 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.12/5.45 & ( ord_less_eq_real @ X3 @ B ) )
% 5.12/5.45 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ( ord_less_real @ A @ X3 )
% 5.12/5.45 & ( ord_less_real @ X3 @ B ) )
% 5.12/5.45 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.12/5.45 => ? [G_c: real,F_c: real,C2: real] :
% 5.12/5.45 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.12/5.45 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.12/5.45 & ( ord_less_real @ A @ C2 )
% 5.12/5.45 & ( ord_less_real @ C2 @ B )
% 5.12/5.45 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.12/5.45 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % GMVT
% 5.12/5.45 thf(fact_9642_greaterThan__0,axiom,
% 5.12/5.45 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.12/5.45 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % greaterThan_0
% 5.12/5.45 thf(fact_9643_greaterThan__Suc,axiom,
% 5.12/5.45 ! [K: nat] :
% 5.12/5.45 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.12/5.45 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % greaterThan_Suc
% 5.12/5.45 thf(fact_9644_MVT,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real] :
% 5.12/5.45 ( ( ord_less_real @ A @ B )
% 5.12/5.45 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ X3 )
% 5.12/5.45 => ( ( ord_less_real @ X3 @ B )
% 5.12/5.45 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.12/5.45 => ? [L3: real,Z4: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ Z4 )
% 5.12/5.45 & ( ord_less_real @ Z4 @ B )
% 5.12/5.45 & ( has_fi5821293074295781190e_real @ F @ L3 @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) )
% 5.12/5.45 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.12/5.45 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L3 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % MVT
% 5.12/5.45 thf(fact_9645_continuous__on__arsinh_H,axiom,
% 5.12/5.45 ! [A2: set_real,F: real > real] :
% 5.12/5.45 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.12/5.45 => ( topolo5044208981011980120l_real @ A2
% 5.12/5.45 @ ^ [X2: real] : ( arsinh_real @ ( F @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_arsinh'
% 5.12/5.45 thf(fact_9646_continuous__on__arsinh,axiom,
% 5.12/5.45 ! [A2: set_real] : ( topolo5044208981011980120l_real @ A2 @ arsinh_real ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_arsinh
% 5.12/5.45 thf(fact_9647_continuous__on__sin__real,axiom,
% 5.12/5.45 ! [A: real,B: real] : ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ sin_real ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_sin_real
% 5.12/5.45 thf(fact_9648_continuous__on__cos__real,axiom,
% 5.12/5.45 ! [A: real,B: real] : ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ cos_real ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_cos_real
% 5.12/5.45 thf(fact_9649_continuous__on__arcosh_H,axiom,
% 5.12/5.45 ! [A2: set_real,F: real > real] :
% 5.12/5.45 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ A2 )
% 5.12/5.45 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.12/5.45 => ( topolo5044208981011980120l_real @ A2
% 5.12/5.45 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_arcosh'
% 5.12/5.45 thf(fact_9650_continuous__on__arccos_H,axiom,
% 5.12/5.45 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_arccos'
% 5.12/5.45 thf(fact_9651_continuous__on__arcsin_H,axiom,
% 5.12/5.45 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_arcsin'
% 5.12/5.45 thf(fact_9652_continuous__on__artanh,axiom,
% 5.12/5.45 ! [A2: set_real] :
% 5.12/5.45 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.12/5.45 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_artanh
% 5.12/5.45 thf(fact_9653_continuous__on__artanh_H,axiom,
% 5.12/5.45 ! [A2: set_real,F: real > real] :
% 5.12/5.45 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( member_real @ X3 @ A2 )
% 5.12/5.45 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.12/5.45 => ( topolo5044208981011980120l_real @ A2
% 5.12/5.45 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % continuous_on_artanh'
% 5.12/5.45 thf(fact_9654_mvt,axiom,
% 5.12/5.45 ! [A: real,B: real,F: real > real,F3: real > real > real] :
% 5.12/5.45 ( ( ord_less_real @ A @ B )
% 5.12/5.45 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.12/5.45 => ( ! [X3: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ X3 )
% 5.12/5.45 => ( ( ord_less_real @ X3 @ B )
% 5.12/5.45 => ( has_de1759254742604945161l_real @ F @ ( F3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.12/5.45 => ~ ! [Xi: real] :
% 5.12/5.45 ( ( ord_less_real @ A @ Xi )
% 5.12/5.45 => ( ( ord_less_real @ Xi @ B )
% 5.12/5.45 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.12/5.45 != ( F3 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % mvt
% 5.12/5.45 thf(fact_9655_Bseq__realpow,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.45 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.45 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Bseq_realpow
% 5.12/5.45 thf(fact_9656_mono__Suc,axiom,
% 5.12/5.45 order_mono_nat_nat @ suc ).
% 5.12/5.45
% 5.12/5.45 % mono_Suc
% 5.12/5.45 thf(fact_9657_mono__times__nat,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % mono_times_nat
% 5.12/5.45 thf(fact_9658_mono__ge2__power__minus__self,axiom,
% 5.12/5.45 ! [K: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.12/5.45 => ( order_mono_nat_nat
% 5.12/5.45 @ ^ [M5: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M5 ) @ M5 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % mono_ge2_power_minus_self
% 5.12/5.45 thf(fact_9659_Sup__nat__empty,axiom,
% 5.12/5.45 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.12/5.45 = zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % Sup_nat_empty
% 5.12/5.45 thf(fact_9660_inj__sgn__power,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.45 => ( inj_on_real_real
% 5.12/5.45 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.12/5.45 @ top_top_set_real ) ) ).
% 5.12/5.45
% 5.12/5.45 % inj_sgn_power
% 5.12/5.45 thf(fact_9661_Inf__real__def,axiom,
% 5.12/5.45 ( comple4887499456419720421f_real
% 5.12/5.45 = ( ^ [X7: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X7 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Inf_real_def
% 5.12/5.45 thf(fact_9662_Inf__int__def,axiom,
% 5.12/5.45 ( complete_Inf_Inf_int
% 5.12/5.45 = ( ^ [X7: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X7 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Inf_int_def
% 5.12/5.45 thf(fact_9663_log__inj,axiom,
% 5.12/5.45 ! [B: real] :
% 5.12/5.45 ( ( ord_less_real @ one_one_real @ B )
% 5.12/5.45 => ( inj_on_real_real @ ( log2 @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % log_inj
% 5.12/5.45 thf(fact_9664_surj__int__decode,axiom,
% 5.12/5.45 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 5.12/5.45 = top_top_set_int ) ).
% 5.12/5.45
% 5.12/5.45 % surj_int_decode
% 5.12/5.45 thf(fact_9665_int__encode__inverse,axiom,
% 5.12/5.45 ! [X: int] :
% 5.12/5.45 ( ( nat_int_decode @ ( nat_int_encode @ X ) )
% 5.12/5.45 = X ) ).
% 5.12/5.45
% 5.12/5.45 % int_encode_inverse
% 5.12/5.45 thf(fact_9666_int__decode__inverse,axiom,
% 5.12/5.45 ! [N: nat] :
% 5.12/5.45 ( ( nat_int_encode @ ( nat_int_decode @ N ) )
% 5.12/5.45 = N ) ).
% 5.12/5.45
% 5.12/5.45 % int_decode_inverse
% 5.12/5.45 thf(fact_9667_inj__prod__encode,axiom,
% 5.12/5.45 ! [A2: set_Pr1261947904930325089at_nat] : ( inj_on2178005380612969504at_nat @ nat_prod_encode @ A2 ) ).
% 5.12/5.45
% 5.12/5.45 % inj_prod_encode
% 5.12/5.45 thf(fact_9668_inj__Suc,axiom,
% 5.12/5.45 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.12/5.45
% 5.12/5.45 % inj_Suc
% 5.12/5.45 thf(fact_9669_inj__int__decode,axiom,
% 5.12/5.45 ! [A2: set_nat] : ( inj_on_nat_int @ nat_int_decode @ A2 ) ).
% 5.12/5.45
% 5.12/5.45 % inj_int_decode
% 5.12/5.45 thf(fact_9670_inj__int__encode,axiom,
% 5.12/5.45 ! [A2: set_int] : ( inj_on_int_nat @ nat_int_encode @ A2 ) ).
% 5.12/5.45
% 5.12/5.45 % inj_int_encode
% 5.12/5.45 thf(fact_9671_inj__on__diff__nat,axiom,
% 5.12/5.45 ! [N5: set_nat,K: nat] :
% 5.12/5.45 ( ! [N2: nat] :
% 5.12/5.45 ( ( member_nat @ N2 @ N5 )
% 5.12/5.45 => ( ord_less_eq_nat @ K @ N2 ) )
% 5.12/5.45 => ( inj_on_nat_nat
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K )
% 5.12/5.45 @ N5 ) ) ).
% 5.12/5.45
% 5.12/5.45 % inj_on_diff_nat
% 5.12/5.45 thf(fact_9672_inj__on__set__encode,axiom,
% 5.12/5.45 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 5.12/5.45
% 5.12/5.45 % inj_on_set_encode
% 5.12/5.45 thf(fact_9673_int__decode__eq,axiom,
% 5.12/5.45 ! [X: nat,Y: nat] :
% 5.12/5.45 ( ( ( nat_int_decode @ X )
% 5.12/5.45 = ( nat_int_decode @ Y ) )
% 5.12/5.45 = ( X = Y ) ) ).
% 5.12/5.45
% 5.12/5.45 % int_decode_eq
% 5.12/5.45 thf(fact_9674_bij__int__decode,axiom,
% 5.12/5.45 bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 5.12/5.45
% 5.12/5.45 % bij_int_decode
% 5.12/5.45 thf(fact_9675_powr__real__of__int_H,axiom,
% 5.12/5.45 ! [X: real,N: int] :
% 5.12/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.45 => ( ( ( X != zero_zero_real )
% 5.12/5.45 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.12/5.45 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.12/5.45 = ( power_int_real @ X @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % powr_real_of_int'
% 5.12/5.45 thf(fact_9676_inverse__real_Otransfer,axiom,
% 5.12/5.45 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ( if_nat_rat @ ( vanishes @ X7 )
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X7 @ N4 ) ) )
% 5.12/5.45 @ inverse_inverse_real ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_real.transfer
% 5.12/5.45 thf(fact_9677_pow_Osimps_I1_J,axiom,
% 5.12/5.45 ! [X: num] :
% 5.12/5.45 ( ( pow @ X @ one )
% 5.12/5.45 = X ) ).
% 5.12/5.45
% 5.12/5.45 % pow.simps(1)
% 5.12/5.45 thf(fact_9678_zero__real_Otransfer,axiom,
% 5.12/5.45 ( pcr_real
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ zero_zero_real ) ).
% 5.12/5.45
% 5.12/5.45 % zero_real.transfer
% 5.12/5.45 thf(fact_9679_one__real_Otransfer,axiom,
% 5.12/5.45 ( pcr_real
% 5.12/5.45 @ ^ [N4: nat] : one_one_rat
% 5.12/5.45 @ one_one_real ) ).
% 5.12/5.45
% 5.12/5.45 % one_real.transfer
% 5.12/5.45 thf(fact_9680_uminus__real_Otransfer,axiom,
% 5.12/5.45 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.12/5.45 @ ^ [X7: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X7 @ N4 ) )
% 5.12/5.45 @ uminus_uminus_real ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_real.transfer
% 5.12/5.45 thf(fact_9681_plus__real_Otransfer,axiom,
% 5.12/5.45 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) )
% 5.12/5.45 @ plus_plus_real ) ).
% 5.12/5.45
% 5.12/5.45 % plus_real.transfer
% 5.12/5.45 thf(fact_9682_times__real_Otransfer,axiom,
% 5.12/5.45 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) )
% 5.12/5.45 @ times_times_real ) ).
% 5.12/5.45
% 5.12/5.45 % times_real.transfer
% 5.12/5.45 thf(fact_9683_Real_Opositive_Otransfer,axiom,
% 5.12/5.45 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 5.12/5.45 @ positive2 ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive.transfer
% 5.12/5.45 thf(fact_9684_pow_Osimps_I3_J,axiom,
% 5.12/5.45 ! [X: num,Y: num] :
% 5.12/5.45 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.12/5.45 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % pow.simps(3)
% 5.12/5.45 thf(fact_9685_sqr__conv__mult,axiom,
% 5.12/5.45 ( sqr
% 5.12/5.45 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sqr_conv_mult
% 5.12/5.45 thf(fact_9686_Real_Opositive__mult,axiom,
% 5.12/5.45 ! [X: real,Y: real] :
% 5.12/5.45 ( ( positive2 @ X )
% 5.12/5.45 => ( ( positive2 @ Y )
% 5.12/5.45 => ( positive2 @ ( times_times_real @ X @ Y ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive_mult
% 5.12/5.45 thf(fact_9687_Real_Opositive__zero,axiom,
% 5.12/5.45 ~ ( positive2 @ zero_zero_real ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive_zero
% 5.12/5.45 thf(fact_9688_Real_Opositive__add,axiom,
% 5.12/5.45 ! [X: real,Y: real] :
% 5.12/5.45 ( ( positive2 @ X )
% 5.12/5.45 => ( ( positive2 @ Y )
% 5.12/5.45 => ( positive2 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive_add
% 5.12/5.45 thf(fact_9689_sqr_Osimps_I1_J,axiom,
% 5.12/5.45 ( ( sqr @ one )
% 5.12/5.45 = one ) ).
% 5.12/5.45
% 5.12/5.45 % sqr.simps(1)
% 5.12/5.45 thf(fact_9690_sqr_Osimps_I2_J,axiom,
% 5.12/5.45 ! [N: num] :
% 5.12/5.45 ( ( sqr @ ( bit0 @ N ) )
% 5.12/5.45 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sqr.simps(2)
% 5.12/5.45 thf(fact_9691_Real_Opositive__minus,axiom,
% 5.12/5.45 ! [X: real] :
% 5.12/5.45 ( ~ ( positive2 @ X )
% 5.12/5.45 => ( ( X != zero_zero_real )
% 5.12/5.45 => ( positive2 @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive_minus
% 5.12/5.45 thf(fact_9692_less__real__def,axiom,
% 5.12/5.45 ( ord_less_real
% 5.12/5.45 = ( ^ [X2: real,Y6: real] : ( positive2 @ ( minus_minus_real @ Y6 @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_real_def
% 5.12/5.45 thf(fact_9693_pow_Osimps_I2_J,axiom,
% 5.12/5.45 ! [X: num,Y: num] :
% 5.12/5.45 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.12/5.45 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % pow.simps(2)
% 5.12/5.45 thf(fact_9694_sqr_Osimps_I3_J,axiom,
% 5.12/5.45 ! [N: num] :
% 5.12/5.45 ( ( sqr @ ( bit1 @ N ) )
% 5.12/5.45 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sqr.simps(3)
% 5.12/5.45 thf(fact_9695_Real_Opositive_Orep__eq,axiom,
% 5.12/5.45 ( positive2
% 5.12/5.45 = ( ^ [X2: real] :
% 5.12/5.45 ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( rep_real @ X2 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive.rep_eq
% 5.12/5.45 thf(fact_9696_Real_Opositive_Orsp,axiom,
% 5.12/5.45 ( bNF_re728719798268516973at_o_o @ realrel
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z )
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive.rsp
% 5.12/5.45 thf(fact_9697_times__real_Orsp,axiom,
% 5.12/5.45 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % times_real.rsp
% 5.12/5.45 thf(fact_9698_uminus__real_Orsp,axiom,
% 5.12/5.45 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.12/5.45 @ ^ [X7: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X7 @ N4 ) )
% 5.12/5.45 @ ^ [X7: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X7 @ N4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_real.rsp
% 5.12/5.45 thf(fact_9699_plus__real_Orsp,axiom,
% 5.12/5.45 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) )
% 5.12/5.45 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % plus_real.rsp
% 5.12/5.45 thf(fact_9700_one__real_Orsp,axiom,
% 5.12/5.45 ( realrel
% 5.12/5.45 @ ^ [N4: nat] : one_one_rat
% 5.12/5.45 @ ^ [N4: nat] : one_one_rat ) ).
% 5.12/5.45
% 5.12/5.45 % one_real.rsp
% 5.12/5.45 thf(fact_9701_zero__real_Orsp,axiom,
% 5.12/5.45 ( realrel
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat ) ).
% 5.12/5.45
% 5.12/5.45 % zero_real.rsp
% 5.12/5.45 thf(fact_9702_real_Orel__eq__transfer,axiom,
% 5.12/5.45 ( bNF_re4521903465945308077real_o @ pcr_real
% 5.12/5.45 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ realrel
% 5.12/5.45 @ ^ [Y4: real,Z: real] : ( Y4 = Z ) ) ).
% 5.12/5.45
% 5.12/5.45 % real.rel_eq_transfer
% 5.12/5.45 thf(fact_9703_inverse__real_Orsp,axiom,
% 5.12/5.45 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ( if_nat_rat @ ( vanishes @ X7 )
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X7 @ N4 ) ) )
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ( if_nat_rat @ ( vanishes @ X7 )
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X7 @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_real.rsp
% 5.12/5.45 thf(fact_9704_Real_Opositive__def,axiom,
% 5.12/5.45 ( positive2
% 5.12/5.45 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive_def
% 5.12/5.45 thf(fact_9705_times__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) ) )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % times_int.rsp
% 5.12/5.45 thf(fact_9706_intrel__iff,axiom,
% 5.12/5.45 ! [X: nat,Y: nat,U: nat,V: nat] :
% 5.12/5.45 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.12/5.45 = ( ( plus_plus_nat @ X @ V )
% 5.12/5.45 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % intrel_iff
% 5.12/5.45 thf(fact_9707_sup__nat__def,axiom,
% 5.12/5.45 sup_sup_nat = ord_max_nat ).
% 5.12/5.45
% 5.12/5.45 % sup_nat_def
% 5.12/5.45 thf(fact_9708_sup__int__def,axiom,
% 5.12/5.45 sup_sup_int = ord_max_int ).
% 5.12/5.45
% 5.12/5.45 % sup_int_def
% 5.12/5.45 thf(fact_9709_zero__int_Orsp,axiom,
% 5.12/5.45 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % zero_int.rsp
% 5.12/5.45 thf(fact_9710_int_Oabs__eq__iff,axiom,
% 5.12/5.45 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.12/5.45 ( ( ( abs_Integ @ X )
% 5.12/5.45 = ( abs_Integ @ Y ) )
% 5.12/5.45 = ( intrel @ X @ Y ) ) ).
% 5.12/5.45
% 5.12/5.45 % int.abs_eq_iff
% 5.12/5.45 thf(fact_9711_uminus__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.12/5.45 @ ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X2 ) )
% 5.12/5.45 @ ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_int.rsp
% 5.12/5.45 thf(fact_9712_nat_Orsp,axiom,
% 5.12/5.45 ( bNF_re8246922863344978751at_nat @ intrel
% 5.12/5.45 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.45 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.12/5.45 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 5.12/5.45
% 5.12/5.45 % nat.rsp
% 5.12/5.45 thf(fact_9713_one__int_Orsp,axiom,
% 5.12/5.45 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.12/5.45
% 5.12/5.45 % one_int.rsp
% 5.12/5.45 thf(fact_9714_intrel__def,axiom,
% 5.12/5.45 ( intrel
% 5.12/5.45 = ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] :
% 5.12/5.45 ( ( plus_plus_nat @ X2 @ V4 )
% 5.12/5.45 = ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % intrel_def
% 5.12/5.45 thf(fact_9715_less__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.12/5.45 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_int.rsp
% 5.12/5.45 thf(fact_9716_less__eq__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.12/5.45 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) )
% 5.12/5.45 @ ( produc8739625826339149834_nat_o
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc6081775807080527818_nat_o
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_eq_int.rsp
% 5.12/5.45 thf(fact_9717_int_Orel__eq__transfer,axiom,
% 5.12/5.45 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.12/5.45 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.12/5.45 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.45 @ intrel
% 5.12/5.45 @ ^ [Y4: int,Z: int] : ( Y4 = Z ) ) ).
% 5.12/5.45
% 5.12/5.45 % int.rel_eq_transfer
% 5.12/5.45 thf(fact_9718_minus__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) ) )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_int.rsp
% 5.12/5.45 thf(fact_9719_plus__int_Orsp,axiom,
% 5.12/5.45 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) )
% 5.12/5.45 @ ( produc27273713700761075at_nat
% 5.12/5.45 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.45 ( produc2626176000494625587at_nat
% 5.12/5.45 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % plus_int.rsp
% 5.12/5.45 thf(fact_9720_inverse__real_Oabs__eq,axiom,
% 5.12/5.45 ! [X: nat > rat] :
% 5.12/5.45 ( ( realrel @ X @ X )
% 5.12/5.45 => ( ( inverse_inverse_real @ ( real2 @ X ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ( if_nat_rat @ ( vanishes @ X )
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_real.abs_eq
% 5.12/5.45 thf(fact_9721_real_Oabs__induct,axiom,
% 5.12/5.45 ! [P: real > $o,X: real] :
% 5.12/5.45 ( ! [Y3: nat > rat] :
% 5.12/5.45 ( ( realrel @ Y3 @ Y3 )
% 5.12/5.45 => ( P @ ( real2 @ Y3 ) ) )
% 5.12/5.45 => ( P @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % real.abs_induct
% 5.12/5.45 thf(fact_9722_of__rat__Real,axiom,
% 5.12/5.45 ( field_7254667332652039916t_real
% 5.12/5.45 = ( ^ [X2: rat] :
% 5.12/5.45 ( real2
% 5.12/5.45 @ ^ [N4: nat] : X2 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % of_rat_Real
% 5.12/5.45 thf(fact_9723_zero__real__def,axiom,
% 5.12/5.45 ( zero_zero_real
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat ) ) ).
% 5.12/5.45
% 5.12/5.45 % zero_real_def
% 5.12/5.45 thf(fact_9724_one__real__def,axiom,
% 5.12/5.45 ( one_one_real
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : one_one_rat ) ) ).
% 5.12/5.45
% 5.12/5.45 % one_real_def
% 5.12/5.45 thf(fact_9725_of__int__Real,axiom,
% 5.12/5.45 ( ring_1_of_int_real
% 5.12/5.45 = ( ^ [X2: int] :
% 5.12/5.45 ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( ring_1_of_int_rat @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % of_int_Real
% 5.12/5.45 thf(fact_9726_of__nat__Real,axiom,
% 5.12/5.45 ( semiri5074537144036343181t_real
% 5.12/5.45 = ( ^ [X2: nat] :
% 5.12/5.45 ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( semiri681578069525770553at_rat @ X2 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % of_nat_Real
% 5.12/5.45 thf(fact_9727_uminus__real_Oabs__eq,axiom,
% 5.12/5.45 ! [X: nat > rat] :
% 5.12/5.45 ( ( realrel @ X @ X )
% 5.12/5.45 => ( ( uminus_uminus_real @ ( real2 @ X ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_real.abs_eq
% 5.12/5.45 thf(fact_9728_plus__real_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: nat > rat,X: nat > rat] :
% 5.12/5.45 ( ( realrel @ Xa @ Xa )
% 5.12/5.45 => ( ( realrel @ X @ X )
% 5.12/5.45 => ( ( plus_plus_real @ ( real2 @ Xa ) @ ( real2 @ X ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_rat @ ( Xa @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % plus_real.abs_eq
% 5.12/5.45 thf(fact_9729_times__real_Oabs__eq,axiom,
% 5.12/5.45 ! [Xa: nat > rat,X: nat > rat] :
% 5.12/5.45 ( ( realrel @ Xa @ Xa )
% 5.12/5.45 => ( ( realrel @ X @ X )
% 5.12/5.45 => ( ( times_times_real @ ( real2 @ Xa ) @ ( real2 @ X ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_rat @ ( Xa @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % times_real.abs_eq
% 5.12/5.45 thf(fact_9730_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.12/5.45 ! [I: nat,J2: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ ( suc @ I ) @ J2 )
% 5.12/5.45 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J2 ) )
% 5.12/5.45 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sorted_list_of_set_greaterThanAtMost
% 5.12/5.45 thf(fact_9731_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.12/5.45 ! [I: nat,J2: nat] :
% 5.12/5.45 ( ( ord_less_nat @ ( suc @ I ) @ J2 )
% 5.12/5.45 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J2 ) )
% 5.12/5.45 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % sorted_list_of_set_greaterThanLessThan
% 5.12/5.45 thf(fact_9732_Real_Opositive_Oabs__eq,axiom,
% 5.12/5.45 ! [X: nat > rat] :
% 5.12/5.45 ( ( realrel @ X @ X )
% 5.12/5.45 => ( ( positive2 @ ( real2 @ X ) )
% 5.12/5.45 = ( ? [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 & ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_rat @ R @ ( X @ N4 ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real.positive.abs_eq
% 5.12/5.45 thf(fact_9733_upto__aux__rec,axiom,
% 5.12/5.45 ( upto_aux
% 5.12/5.45 = ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % upto_aux_rec
% 5.12/5.45 thf(fact_9734_inverse__real__def,axiom,
% 5.12/5.45 ( inverse_inverse_real
% 5.12/5.45 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.12/5.45 @ ^ [X7: nat > rat] :
% 5.12/5.45 ( if_nat_rat @ ( vanishes @ X7 )
% 5.12/5.45 @ ^ [N4: nat] : zero_zero_rat
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % inverse_real_def
% 5.12/5.45 thf(fact_9735_uminus__real__def,axiom,
% 5.12/5.45 ( uminus_uminus_real
% 5.12/5.45 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.12/5.45 @ ^ [X7: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X7 @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % uminus_real_def
% 5.12/5.45 thf(fact_9736_le__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.12/5.45 = ( ! [R: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.45 => ? [K3: nat] :
% 5.12/5.45 ! [N4: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.45 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ ( plus_plus_rat @ ( Y7 @ N4 ) @ R ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % le_Real
% 5.12/5.45 thf(fact_9737_realrel__refl,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( realrel @ X8 @ X8 ) ) ).
% 5.12/5.45
% 5.12/5.45 % realrel_refl
% 5.12/5.45 thf(fact_9738_cauchy__add,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_add
% 5.12/5.45 thf(fact_9739_cauchy__const,axiom,
% 5.12/5.45 ! [X: rat] :
% 5.12/5.45 ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : X ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_const
% 5.12/5.45 thf(fact_9740_cauchy__minus,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_minus
% 5.12/5.45 thf(fact_9741_cauchy__mult,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_mult
% 5.12/5.45 thf(fact_9742_cauchy__diff,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_diff
% 5.12/5.45 thf(fact_9743_Real__induct,axiom,
% 5.12/5.45 ! [P: real > $o,X: real] :
% 5.12/5.45 ( ! [X10: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X10 )
% 5.12/5.45 => ( P @ ( real2 @ X10 ) ) )
% 5.12/5.45 => ( P @ X ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real_induct
% 5.12/5.45 thf(fact_9744_cr__real__eq,axiom,
% 5.12/5.45 ( pcr_real
% 5.12/5.45 = ( ^ [X2: nat > rat,Y6: real] :
% 5.12/5.45 ( ( cauchy @ X2 )
% 5.12/5.45 & ( ( real2 @ X2 )
% 5.12/5.45 = Y6 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cr_real_eq
% 5.12/5.45 thf(fact_9745_cauchy__inverse,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ~ ( vanishes @ X8 )
% 5.12/5.45 => ( cauchy
% 5.12/5.45 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_inverse
% 5.12/5.45 thf(fact_9746_cauchy__imp__bounded,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ? [B3: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.12/5.45 & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ B3 ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % cauchy_imp_bounded
% 5.12/5.45 thf(fact_9747_less__RealD,axiom,
% 5.12/5.45 ! [Y7: nat > rat,X: real] :
% 5.12/5.45 ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( ord_less_real @ X @ ( real2 @ Y7 ) )
% 5.12/5.45 => ? [N2: nat] : ( ord_less_real @ X @ ( field_7254667332652039916t_real @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % less_RealD
% 5.12/5.45 thf(fact_9748_le__RealI,axiom,
% 5.12/5.45 ! [Y7: nat > rat,X: real] :
% 5.12/5.45 ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ X @ ( field_7254667332652039916t_real @ ( Y7 @ N2 ) ) )
% 5.12/5.45 => ( ord_less_eq_real @ X @ ( real2 @ Y7 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % le_RealI
% 5.12/5.45 thf(fact_9749_Real__leI,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y: real] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X8 @ N2 ) ) @ Y )
% 5.12/5.45 => ( ord_less_eq_real @ ( real2 @ X8 ) @ Y ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % Real_leI
% 5.12/5.45 thf(fact_9750_minus__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( uminus_uminus_real @ ( real2 @ X8 ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % minus_Real
% 5.12/5.45 thf(fact_9751_add__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( plus_plus_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % add_Real
% 5.12/5.45 thf(fact_9752_mult__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % mult_Real
% 5.12/5.45 thf(fact_9753_diff__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( minus_minus_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.12/5.45 = ( real2
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % diff_Real
% 5.12/5.45 thf(fact_9754_realrelI,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) )
% 5.12/5.45 => ( realrel @ X8 @ Y7 ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % realrelI
% 5.12/5.45 thf(fact_9755_eq__Real,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ( ( real2 @ X8 )
% 5.12/5.45 = ( real2 @ Y7 ) )
% 5.12/5.45 = ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % eq_Real
% 5.12/5.45 thf(fact_9756_vanishes__diff__inverse,axiom,
% 5.12/5.45 ! [X8: nat > rat,Y7: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ~ ( vanishes @ X8 )
% 5.12/5.45 => ( ( cauchy @ Y7 )
% 5.12/5.45 => ( ~ ( vanishes @ Y7 )
% 5.12/5.45 => ( ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) )
% 5.12/5.45 => ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X8 @ N4 ) ) @ ( inverse_inverse_rat @ ( Y7 @ N4 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % vanishes_diff_inverse
% 5.12/5.45 thf(fact_9757_realrel__def,axiom,
% 5.12/5.45 ( realrel
% 5.12/5.45 = ( ^ [X7: nat > rat,Y8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X7 )
% 5.12/5.45 & ( cauchy @ Y8 )
% 5.12/5.45 & ( vanishes
% 5.12/5.45 @ ^ [N4: nat] : ( minus_minus_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ) ) ).
% 5.12/5.45
% 5.12/5.45 % realrel_def
% 5.12/5.45 thf(fact_9758_cauchy__not__vanishes__cases,axiom,
% 5.12/5.45 ! [X8: nat > rat] :
% 5.12/5.45 ( ( cauchy @ X8 )
% 5.12/5.45 => ( ~ ( vanishes @ X8 )
% 5.12/5.45 => ? [B3: rat] :
% 5.12/5.45 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.12/5.45 & ? [K2: nat] :
% 5.12/5.45 ( ! [N6: nat] :
% 5.12/5.45 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.12/5.46 => ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ ( X8 @ N6 ) ) ) )
% 5.12/5.46 | ! [N6: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.12/5.46 => ( ord_less_rat @ B3 @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cauchy_not_vanishes_cases
% 5.12/5.46 thf(fact_9759_positive__Real,axiom,
% 5.12/5.46 ! [X8: nat > rat] :
% 5.12/5.46 ( ( cauchy @ X8 )
% 5.12/5.46 => ( ( positive2 @ ( real2 @ X8 ) )
% 5.12/5.46 = ( ? [R: rat] :
% 5.12/5.46 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.46 & ? [K3: nat] :
% 5.12/5.46 ! [N4: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.46 => ( ord_less_rat @ R @ ( X8 @ N4 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % positive_Real
% 5.12/5.46 thf(fact_9760_cauchy__not__vanishes,axiom,
% 5.12/5.46 ! [X8: nat > rat] :
% 5.12/5.46 ( ( cauchy @ X8 )
% 5.12/5.46 => ( ~ ( vanishes @ X8 )
% 5.12/5.46 => ? [B3: rat] :
% 5.12/5.46 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.12/5.46 & ? [K2: nat] :
% 5.12/5.46 ! [N6: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.12/5.46 => ( ord_less_rat @ B3 @ ( abs_abs_rat @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cauchy_not_vanishes
% 5.12/5.46 thf(fact_9761_cauchy__def,axiom,
% 5.12/5.46 ( cauchy
% 5.12/5.46 = ( ^ [X7: nat > rat] :
% 5.12/5.46 ! [R: rat] :
% 5.12/5.46 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.46 => ? [K3: nat] :
% 5.12/5.46 ! [M5: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K3 @ M5 )
% 5.12/5.46 => ! [N4: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.46 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M5 ) @ ( X7 @ N4 ) ) ) @ R ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cauchy_def
% 5.12/5.46 thf(fact_9762_cauchyI,axiom,
% 5.12/5.46 ! [X8: nat > rat] :
% 5.12/5.46 ( ! [R3: rat] :
% 5.12/5.46 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.12/5.46 => ? [K4: nat] :
% 5.12/5.46 ! [M3: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K4 @ M3 )
% 5.12/5.46 => ! [N2: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.12/5.46 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N2 ) ) ) @ R3 ) ) ) )
% 5.12/5.46 => ( cauchy @ X8 ) ) ).
% 5.12/5.46
% 5.12/5.46 % cauchyI
% 5.12/5.46 thf(fact_9763_cauchyD,axiom,
% 5.12/5.46 ! [X8: nat > rat,R4: rat] :
% 5.12/5.46 ( ( cauchy @ X8 )
% 5.12/5.46 => ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 5.12/5.46 => ? [K2: nat] :
% 5.12/5.46 ! [M: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K2 @ M )
% 5.12/5.46 => ! [N6: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.12/5.46 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M ) @ ( X8 @ N6 ) ) ) @ R4 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cauchyD
% 5.12/5.46 thf(fact_9764_inverse__Real,axiom,
% 5.12/5.46 ! [X8: nat > rat] :
% 5.12/5.46 ( ( cauchy @ X8 )
% 5.12/5.46 => ( ( ( vanishes @ X8 )
% 5.12/5.46 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.12/5.46 = zero_zero_real ) )
% 5.12/5.46 & ( ~ ( vanishes @ X8 )
% 5.12/5.46 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.12/5.46 = ( real2
% 5.12/5.46 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % inverse_Real
% 5.12/5.46 thf(fact_9765_not__positive__Real,axiom,
% 5.12/5.46 ! [X8: nat > rat] :
% 5.12/5.46 ( ( cauchy @ X8 )
% 5.12/5.46 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 5.12/5.46 = ( ! [R: rat] :
% 5.12/5.46 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.12/5.46 => ? [K3: nat] :
% 5.12/5.46 ! [N4: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.12/5.46 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ R ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % not_positive_Real
% 5.12/5.46 thf(fact_9766_times__real__def,axiom,
% 5.12/5.46 ( times_times_real
% 5.12/5.46 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.12/5.46 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_real_def
% 5.12/5.46 thf(fact_9767_plus__real__def,axiom,
% 5.12/5.46 ( plus_plus_real
% 5.12/5.46 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.12/5.46 @ ^ [X7: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X7 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_real_def
% 5.12/5.46 thf(fact_9768_list__encode_Osimps_I2_J,axiom,
% 5.12/5.46 ! [X: nat,Xs: list_nat] :
% 5.12/5.46 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 5.12/5.46 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode.simps(2)
% 5.12/5.46 thf(fact_9769_cr__real__def,axiom,
% 5.12/5.46 ( cr_real
% 5.12/5.46 = ( ^ [X2: nat > rat,Y6: real] :
% 5.12/5.46 ( ( realrel @ X2 @ X2 )
% 5.12/5.46 & ( ( real2 @ X2 )
% 5.12/5.46 = Y6 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cr_real_def
% 5.12/5.46 thf(fact_9770_list__encode__eq,axiom,
% 5.12/5.46 ! [X: list_nat,Y: list_nat] :
% 5.12/5.46 ( ( ( nat_list_encode @ X )
% 5.12/5.46 = ( nat_list_encode @ Y ) )
% 5.12/5.46 = ( X = Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode_eq
% 5.12/5.46 thf(fact_9771_bij__list__encode,axiom,
% 5.12/5.46 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 5.12/5.46
% 5.12/5.46 % bij_list_encode
% 5.12/5.46 thf(fact_9772_inj__list__encode,axiom,
% 5.12/5.46 ! [A2: set_list_nat] : ( inj_on_list_nat_nat @ nat_list_encode @ A2 ) ).
% 5.12/5.46
% 5.12/5.46 % inj_list_encode
% 5.12/5.46 thf(fact_9773_surj__list__encode,axiom,
% 5.12/5.46 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 5.12/5.46 = top_top_set_nat ) ).
% 5.12/5.46
% 5.12/5.46 % surj_list_encode
% 5.12/5.46 thf(fact_9774_real_Opcr__cr__eq,axiom,
% 5.12/5.46 pcr_real = cr_real ).
% 5.12/5.46
% 5.12/5.46 % real.pcr_cr_eq
% 5.12/5.46 thf(fact_9775_list__encode_Oelims,axiom,
% 5.12/5.46 ! [X: list_nat,Y: nat] :
% 5.12/5.46 ( ( ( nat_list_encode @ X )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( ( X = nil_nat )
% 5.12/5.46 => ( Y != zero_zero_nat ) )
% 5.12/5.46 => ~ ! [X3: nat,Xs2: list_nat] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( cons_nat @ X3 @ Xs2 ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode.elims
% 5.12/5.46 thf(fact_9776_sorted__list__of__set__lessThan__Suc,axiom,
% 5.12/5.46 ! [K: nat] :
% 5.12/5.46 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.12/5.46 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % sorted_list_of_set_lessThan_Suc
% 5.12/5.46 thf(fact_9777_sorted__list__of__set__atMost__Suc,axiom,
% 5.12/5.46 ! [K: nat] :
% 5.12/5.46 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.12/5.46 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % sorted_list_of_set_atMost_Suc
% 5.12/5.46 thf(fact_9778_list__encode_Osimps_I1_J,axiom,
% 5.12/5.46 ( ( nat_list_encode @ nil_nat )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode.simps(1)
% 5.12/5.46 thf(fact_9779_list__encode_Ocases,axiom,
% 5.12/5.46 ! [X: list_nat] :
% 5.12/5.46 ( ( X != nil_nat )
% 5.12/5.46 => ~ ! [X3: nat,Xs2: list_nat] :
% 5.12/5.46 ( X
% 5.12/5.46 != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode.cases
% 5.12/5.46 thf(fact_9780_upto_Opsimps,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J2 ) )
% 5.12/5.46 => ( ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( upto @ I @ J2 )
% 5.12/5.46 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J2 ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( upto @ I @ J2 )
% 5.12/5.46 = nil_int ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto.psimps
% 5.12/5.46 thf(fact_9781_upto__Nil,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( ( upto @ I @ J2 )
% 5.12/5.46 = nil_int )
% 5.12/5.46 = ( ord_less_int @ J2 @ I ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_Nil
% 5.12/5.46 thf(fact_9782_upto__Nil2,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( nil_int
% 5.12/5.46 = ( upto @ I @ J2 ) )
% 5.12/5.46 = ( ord_less_int @ J2 @ I ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_Nil2
% 5.12/5.46 thf(fact_9783_upto__empty,axiom,
% 5.12/5.46 ! [J2: int,I: int] :
% 5.12/5.46 ( ( ord_less_int @ J2 @ I )
% 5.12/5.46 => ( ( upto @ I @ J2 )
% 5.12/5.46 = nil_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_empty
% 5.12/5.46 thf(fact_9784_nth__upto,axiom,
% 5.12/5.46 ! [I: int,K: nat,J2: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J2 )
% 5.12/5.46 => ( ( nth_int @ ( upto @ I @ J2 ) @ K )
% 5.12/5.46 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nth_upto
% 5.12/5.46 thf(fact_9785_length__upto,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( size_size_list_int @ ( upto @ I @ J2 ) )
% 5.12/5.46 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I ) @ one_one_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % length_upto
% 5.12/5.46 thf(fact_9786_upto__rec__numeral_I1_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 = nil_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec_numeral(1)
% 5.12/5.46 thf(fact_9787_upto__rec__numeral_I4_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 = nil_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec_numeral(4)
% 5.12/5.46 thf(fact_9788_upto__rec__numeral_I3_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 5.12/5.46 = nil_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec_numeral(3)
% 5.12/5.46 thf(fact_9789_upto__rec__numeral_I2_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.12/5.46 = nil_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec_numeral(2)
% 5.12/5.46 thf(fact_9790_upto__split2,axiom,
% 5.12/5.46 ! [I: int,J2: int,K: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( ord_less_eq_int @ J2 @ K )
% 5.12/5.46 => ( ( upto @ I @ K )
% 5.12/5.46 = ( append_int @ ( upto @ I @ J2 ) @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_split2
% 5.12/5.46 thf(fact_9791_upto__split1,axiom,
% 5.12/5.46 ! [I: int,J2: int,K: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( ord_less_eq_int @ J2 @ K )
% 5.12/5.46 => ( ( upto @ I @ K )
% 5.12/5.46 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( upto @ J2 @ K ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_split1
% 5.12/5.46 thf(fact_9792_atLeastLessThan__upto,axiom,
% 5.12/5.46 ( set_or4662586982721622107an_int
% 5.12/5.46 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % atLeastLessThan_upto
% 5.12/5.46 thf(fact_9793_greaterThanAtMost__upto,axiom,
% 5.12/5.46 ( set_or6656581121297822940st_int
% 5.12/5.46 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % greaterThanAtMost_upto
% 5.12/5.46 thf(fact_9794_upto__rec1,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( upto @ I @ J2 )
% 5.12/5.46 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec1
% 5.12/5.46 thf(fact_9795_upto_Oelims,axiom,
% 5.12/5.46 ! [X: int,Xa: int,Y: list_int] :
% 5.12/5.46 ( ( ( upto @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( ( ord_less_eq_int @ X @ Xa )
% 5.12/5.46 => ( Y
% 5.12/5.46 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.12/5.46 => ( Y = nil_int ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto.elims
% 5.12/5.46 thf(fact_9796_upto_Osimps,axiom,
% 5.12/5.46 ( upto
% 5.12/5.46 = ( ^ [I2: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J3 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto.simps
% 5.12/5.46 thf(fact_9797_upto__rec2,axiom,
% 5.12/5.46 ! [I: int,J2: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( upto @ I @ J2 )
% 5.12/5.46 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ nil_int ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_rec2
% 5.12/5.46 thf(fact_9798_greaterThanLessThan__upto,axiom,
% 5.12/5.46 ( set_or5832277885323065728an_int
% 5.12/5.46 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % greaterThanLessThan_upto
% 5.12/5.46 thf(fact_9799_upto__split3,axiom,
% 5.12/5.46 ! [I: int,J2: int,K: int] :
% 5.12/5.46 ( ( ord_less_eq_int @ I @ J2 )
% 5.12/5.46 => ( ( ord_less_eq_int @ J2 @ K )
% 5.12/5.46 => ( ( upto @ I @ K )
% 5.12/5.46 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto_split3
% 5.12/5.46 thf(fact_9800_upto_Opelims,axiom,
% 5.12/5.46 ! [X: int,Xa: int,Y: list_int] :
% 5.12/5.46 ( ( ( upto @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.12/5.46 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 5.12/5.46 => ( Y
% 5.12/5.46 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.12/5.46 => ( Y = nil_int ) ) )
% 5.12/5.46 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upto.pelims
% 5.12/5.46 thf(fact_9801_list__encode_Opelims,axiom,
% 5.12/5.46 ! [X: list_nat,Y: nat] :
% 5.12/5.46 ( ( ( nat_list_encode @ X )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.12/5.46 => ( ( ( X = nil_nat )
% 5.12/5.46 => ( ( Y = zero_zero_nat )
% 5.12/5.46 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.12/5.46 => ~ ! [X3: nat,Xs2: list_nat] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( cons_nat @ X3 @ Xs2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 5.12/5.46 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode.pelims
% 5.12/5.46 thf(fact_9802_upt__rec__numeral,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.46 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.46 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.46 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 5.12/5.46 = nil_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_rec_numeral
% 5.12/5.46 thf(fact_9803_tl__upt,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 5.12/5.46 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % tl_upt
% 5.12/5.46 thf(fact_9804_hd__upt,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.46 => ( ( hd_nat @ ( upt @ I @ J2 ) )
% 5.12/5.46 = I ) ) ).
% 5.12/5.46
% 5.12/5.46 % hd_upt
% 5.12/5.46 thf(fact_9805_length__upt,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( size_size_list_nat @ ( upt @ I @ J2 ) )
% 5.12/5.46 = ( minus_minus_nat @ J2 @ I ) ) ).
% 5.12/5.46
% 5.12/5.46 % length_upt
% 5.12/5.46 thf(fact_9806_upt__eq__Nil__conv,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ( upt @ I @ J2 )
% 5.12/5.46 = nil_nat )
% 5.12/5.46 = ( ( J2 = zero_zero_nat )
% 5.12/5.46 | ( ord_less_eq_nat @ J2 @ I ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_eq_Nil_conv
% 5.12/5.46 thf(fact_9807_nth__upt,axiom,
% 5.12/5.46 ! [I: nat,K: nat,J2: nat] :
% 5.12/5.46 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J2 )
% 5.12/5.46 => ( ( nth_nat @ ( upt @ I @ J2 ) @ K )
% 5.12/5.46 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nth_upt
% 5.12/5.46 thf(fact_9808_upt__0,axiom,
% 5.12/5.46 ! [I: nat] :
% 5.12/5.46 ( ( upt @ I @ zero_zero_nat )
% 5.12/5.46 = nil_nat ) ).
% 5.12/5.46
% 5.12/5.46 % upt_0
% 5.12/5.46 thf(fact_9809_upt__conv__Cons__Cons,axiom,
% 5.12/5.46 ! [M2: nat,N: nat,Ns: list_nat,Q5: nat] :
% 5.12/5.46 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 5.12/5.46 = ( upt @ M2 @ Q5 ) )
% 5.12/5.46 = ( ( cons_nat @ N @ Ns )
% 5.12/5.46 = ( upt @ ( suc @ M2 ) @ Q5 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_conv_Cons_Cons
% 5.12/5.46 thf(fact_9810_greaterThanAtMost__upt,axiom,
% 5.12/5.46 ( set_or6659071591806873216st_nat
% 5.12/5.46 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M5 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % greaterThanAtMost_upt
% 5.12/5.46 thf(fact_9811_atLeast__upt,axiom,
% 5.12/5.46 ( set_ord_lessThan_nat
% 5.12/5.46 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % atLeast_upt
% 5.12/5.46 thf(fact_9812_atLeastAtMost__upt,axiom,
% 5.12/5.46 ( set_or1269000886237332187st_nat
% 5.12/5.46 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M5 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % atLeastAtMost_upt
% 5.12/5.46 thf(fact_9813_greaterThanLessThan__upt,axiom,
% 5.12/5.46 ( set_or5834768355832116004an_nat
% 5.12/5.46 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M5 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % greaterThanLessThan_upt
% 5.12/5.46 thf(fact_9814_atMost__upto,axiom,
% 5.12/5.46 ( set_ord_atMost_nat
% 5.12/5.46 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % atMost_upto
% 5.12/5.46 thf(fact_9815_upt__conv__Cons,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.46 => ( ( upt @ I @ J2 )
% 5.12/5.46 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_conv_Cons
% 5.12/5.46 thf(fact_9816_upt__eq__Cons__conv,axiom,
% 5.12/5.46 ! [I: nat,J2: nat,X: nat,Xs: list_nat] :
% 5.12/5.46 ( ( ( upt @ I @ J2 )
% 5.12/5.46 = ( cons_nat @ X @ Xs ) )
% 5.12/5.46 = ( ( ord_less_nat @ I @ J2 )
% 5.12/5.46 & ( I = X )
% 5.12/5.46 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J2 )
% 5.12/5.46 = Xs ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_eq_Cons_conv
% 5.12/5.46 thf(fact_9817_upt__rec,axiom,
% 5.12/5.46 ( upt
% 5.12/5.46 = ( ^ [I2: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I2 @ J3 ) @ ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_rec
% 5.12/5.46 thf(fact_9818_upt__Suc,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.46 => ( ( upt @ I @ ( suc @ J2 ) )
% 5.12/5.46 = ( append_nat @ ( upt @ I @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 5.12/5.46 & ( ~ ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.46 => ( ( upt @ I @ ( suc @ J2 ) )
% 5.12/5.46 = nil_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_Suc
% 5.12/5.46 thf(fact_9819_upt__Suc__append,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ I @ J2 )
% 5.12/5.46 => ( ( upt @ I @ ( suc @ J2 ) )
% 5.12/5.46 = ( append_nat @ ( upt @ I @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % upt_Suc_append
% 5.12/5.46 thf(fact_9820_map__Suc__upt,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 5.12/5.46 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % map_Suc_upt
% 5.12/5.46 thf(fact_9821_sorted__wrt__upt,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % sorted_wrt_upt
% 5.12/5.46 thf(fact_9822_map__add__upt,axiom,
% 5.12/5.46 ! [N: nat,M2: nat] :
% 5.12/5.46 ( ( map_nat_nat
% 5.12/5.46 @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 5.12/5.46 @ ( upt @ zero_zero_nat @ M2 ) )
% 5.12/5.46 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % map_add_upt
% 5.12/5.46 thf(fact_9823_map__decr__upt,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( map_nat_nat
% 5.12/5.46 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 5.12/5.46 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 5.12/5.46 = ( upt @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % map_decr_upt
% 5.12/5.46 thf(fact_9824_sorted__wrt__less__idx,axiom,
% 5.12/5.46 ! [Ns: list_nat,I: nat] :
% 5.12/5.46 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.12/5.46 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.12/5.46 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % sorted_wrt_less_idx
% 5.12/5.46 thf(fact_9825_sorted__wrt__upto,axiom,
% 5.12/5.46 ! [I: int,J2: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % sorted_wrt_upto
% 5.12/5.46 thf(fact_9826_Max__divisors__self__nat,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( N != zero_zero_nat )
% 5.12/5.46 => ( ( lattic8265883725875713057ax_nat
% 5.12/5.46 @ ( collect_nat
% 5.12/5.46 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 5.12/5.46 = N ) ) ).
% 5.12/5.46
% 5.12/5.46 % Max_divisors_self_nat
% 5.12/5.46 thf(fact_9827_Max__divisors__self__int,axiom,
% 5.12/5.46 ! [N: int] :
% 5.12/5.46 ( ( N != zero_zero_int )
% 5.12/5.46 => ( ( lattic8263393255366662781ax_int
% 5.12/5.46 @ ( collect_int
% 5.12/5.46 @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 5.12/5.46 = ( abs_abs_int @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Max_divisors_self_int
% 5.12/5.46 thf(fact_9828_gcd__is__Max__divisors__int,axiom,
% 5.12/5.46 ! [N: int,M2: int] :
% 5.12/5.46 ( ( N != zero_zero_int )
% 5.12/5.46 => ( ( gcd_gcd_int @ M2 @ N )
% 5.12/5.46 = ( lattic8263393255366662781ax_int
% 5.12/5.46 @ ( collect_int
% 5.12/5.46 @ ^ [D4: int] :
% 5.12/5.46 ( ( dvd_dvd_int @ D4 @ M2 )
% 5.12/5.46 & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % gcd_is_Max_divisors_int
% 5.12/5.46 thf(fact_9829_card__le__Suc__Max,axiom,
% 5.12/5.46 ! [S3: set_nat] :
% 5.12/5.46 ( ( finite_finite_nat @ S3 )
% 5.12/5.46 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % card_le_Suc_Max
% 5.12/5.46 thf(fact_9830_Sup__nat__def,axiom,
% 5.12/5.46 ( complete_Sup_Sup_nat
% 5.12/5.46 = ( ^ [X7: set_nat] : ( if_nat @ ( X7 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X7 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Sup_nat_def
% 5.12/5.46 thf(fact_9831_divide__nat__def,axiom,
% 5.12/5.46 ( divide_divide_nat
% 5.12/5.46 = ( ^ [M5: nat,N4: nat] :
% 5.12/5.46 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 5.12/5.46 @ ( lattic8265883725875713057ax_nat
% 5.12/5.46 @ ( collect_nat
% 5.12/5.46 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M5 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % divide_nat_def
% 5.12/5.46 thf(fact_9832_gcd__is__Max__divisors__nat,axiom,
% 5.12/5.46 ! [N: nat,M2: nat] :
% 5.12/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.46 => ( ( gcd_gcd_nat @ M2 @ N )
% 5.12/5.46 = ( lattic8265883725875713057ax_nat
% 5.12/5.46 @ ( collect_nat
% 5.12/5.46 @ ^ [D4: nat] :
% 5.12/5.46 ( ( dvd_dvd_nat @ D4 @ M2 )
% 5.12/5.46 & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % gcd_is_Max_divisors_nat
% 5.12/5.46 thf(fact_9833_Gcd__eq__Max,axiom,
% 5.12/5.46 ! [M10: set_nat] :
% 5.12/5.46 ( ( finite_finite_nat @ M10 )
% 5.12/5.46 => ( ( M10 != bot_bot_set_nat )
% 5.12/5.46 => ( ~ ( member_nat @ zero_zero_nat @ M10 )
% 5.12/5.46 => ( ( gcd_Gcd_nat @ M10 )
% 5.12/5.46 = ( lattic8265883725875713057ax_nat
% 5.12/5.46 @ ( comple7806235888213564991et_nat
% 5.12/5.46 @ ( image_nat_set_nat
% 5.12/5.46 @ ^ [M5: nat] :
% 5.12/5.46 ( collect_nat
% 5.12/5.46 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M5 ) )
% 5.12/5.46 @ M10 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Gcd_eq_Max
% 5.12/5.46 thf(fact_9834_finite__le__enumerate,axiom,
% 5.12/5.46 ! [S3: set_nat,N: nat] :
% 5.12/5.46 ( ( finite_finite_nat @ S3 )
% 5.12/5.46 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 5.12/5.46 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % finite_le_enumerate
% 5.12/5.46 thf(fact_9835_Least__eq__0,axiom,
% 5.12/5.46 ! [P: nat > $o] :
% 5.12/5.46 ( ( P @ zero_zero_nat )
% 5.12/5.46 => ( ( ord_Least_nat @ P )
% 5.12/5.46 = zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % Least_eq_0
% 5.12/5.46 thf(fact_9836_Least__Suc2,axiom,
% 5.12/5.46 ! [P: nat > $o,N: nat,Q: nat > $o,M2: nat] :
% 5.12/5.46 ( ( P @ N )
% 5.12/5.46 => ( ( Q @ M2 )
% 5.12/5.46 => ( ~ ( P @ zero_zero_nat )
% 5.12/5.46 => ( ! [K2: nat] :
% 5.12/5.46 ( ( P @ ( suc @ K2 ) )
% 5.12/5.46 = ( Q @ K2 ) )
% 5.12/5.46 => ( ( ord_Least_nat @ P )
% 5.12/5.46 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Least_Suc2
% 5.12/5.46 thf(fact_9837_Least__Suc,axiom,
% 5.12/5.46 ! [P: nat > $o,N: nat] :
% 5.12/5.46 ( ( P @ N )
% 5.12/5.46 => ( ~ ( P @ zero_zero_nat )
% 5.12/5.46 => ( ( ord_Least_nat @ P )
% 5.12/5.46 = ( suc
% 5.12/5.46 @ ( ord_Least_nat
% 5.12/5.46 @ ^ [M5: nat] : ( P @ ( suc @ M5 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Least_Suc
% 5.12/5.46 thf(fact_9838_Sup__real__def,axiom,
% 5.12/5.46 ( comple1385675409528146559p_real
% 5.12/5.46 = ( ^ [X7: set_real] :
% 5.12/5.46 ( ord_Least_real
% 5.12/5.46 @ ^ [Z6: real] :
% 5.12/5.46 ! [X2: real] :
% 5.12/5.46 ( ( member_real @ X2 @ X7 )
% 5.12/5.46 => ( ord_less_eq_real @ X2 @ Z6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Sup_real_def
% 5.12/5.46 thf(fact_9839_continuous__on__arcosh,axiom,
% 5.12/5.46 ! [A2: set_real] :
% 5.12/5.46 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.12/5.46 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.12/5.46
% 5.12/5.46 % continuous_on_arcosh
% 5.12/5.46 thf(fact_9840_atLeast__0,axiom,
% 5.12/5.46 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.12/5.46 = top_top_set_nat ) ).
% 5.12/5.46
% 5.12/5.46 % atLeast_0
% 5.12/5.46 thf(fact_9841_atLeast__Suc__greaterThan,axiom,
% 5.12/5.46 ! [K: nat] :
% 5.12/5.46 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.12/5.46 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.12/5.46
% 5.12/5.46 % atLeast_Suc_greaterThan
% 5.12/5.46 thf(fact_9842_atLeast__Suc,axiom,
% 5.12/5.46 ! [K: nat] :
% 5.12/5.46 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.12/5.46 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % atLeast_Suc
% 5.12/5.46 thf(fact_9843_last__upt,axiom,
% 5.12/5.46 ! [I: nat,J2: nat] :
% 5.12/5.46 ( ( ord_less_nat @ I @ J2 )
% 5.12/5.46 => ( ( last_nat @ ( upt @ I @ J2 ) )
% 5.12/5.46 = ( minus_minus_nat @ J2 @ one_one_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % last_upt
% 5.12/5.46 thf(fact_9844_and__not__num_Opelims,axiom,
% 5.12/5.46 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.46 ( ( ( bit_and_not_num @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y = none_num )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ one ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y = none_num )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit0 @ M3 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit0 @ M3 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.12/5.46 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 5.12/5.46 @ ( bit_and_not_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ~ ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % and_not_num.pelims
% 5.12/5.46 thf(fact_9845_and__num_Opelims,axiom,
% 5.12/5.46 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.46 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ one ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y = none_num )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ one ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y = none_num )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ one ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ~ ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.12/5.46 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 5.12/5.46 @ ( bit_un7362597486090784418nd_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % and_num.pelims
% 5.12/5.46 thf(fact_9846_xor__num_Opelims,axiom,
% 5.12/5.46 ! [X: num,Xa: num,Y: option_num] :
% 5.12/5.46 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y = none_num )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit1 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ( ( X = one )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit0 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit1 @ M3 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit0 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ( ( Xa = one )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( bit0 @ M3 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 5.12/5.46 => ( ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit0 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.12/5.46 => ~ ! [M3: num] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( bit1 @ M3 ) )
% 5.12/5.46 => ! [N2: num] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( bit1 @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % xor_num.pelims
% 5.12/5.46 thf(fact_9847_pair__lessI2,axiom,
% 5.12/5.46 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.12/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.12/5.46 => ( ( ord_less_nat @ S @ T )
% 5.12/5.46 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % pair_lessI2
% 5.12/5.46 thf(fact_9848_pair__less__iff1,axiom,
% 5.12/5.46 ! [X: nat,Y: nat,Z2: nat] :
% 5.12/5.46 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z2 ) ) @ fun_pair_less )
% 5.12/5.46 = ( ord_less_nat @ Y @ Z2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % pair_less_iff1
% 5.12/5.46 thf(fact_9849_pair__lessI1,axiom,
% 5.12/5.46 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.12/5.46 ( ( ord_less_nat @ A @ B )
% 5.12/5.46 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 5.12/5.46
% 5.12/5.46 % pair_lessI1
% 5.12/5.46 thf(fact_9850_pair__leqI1,axiom,
% 5.12/5.46 ! [A: nat,B: nat,S: nat,T: nat] :
% 5.12/5.46 ( ( ord_less_nat @ A @ B )
% 5.12/5.46 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 5.12/5.46
% 5.12/5.46 % pair_leqI1
% 5.12/5.46 thf(fact_9851_gcd__nat_Oordering__top__axioms,axiom,
% 5.12/5.46 ( ordering_top_nat @ dvd_dvd_nat
% 5.12/5.46 @ ^ [M5: nat,N4: nat] :
% 5.12/5.46 ( ( dvd_dvd_nat @ M5 @ N4 )
% 5.12/5.46 & ( M5 != N4 ) )
% 5.12/5.46 @ zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % gcd_nat.ordering_top_axioms
% 5.12/5.46 thf(fact_9852_bot__nat__0_Oordering__top__axioms,axiom,
% 5.12/5.46 ( ordering_top_nat
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X2 )
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X2 )
% 5.12/5.46 @ zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % bot_nat_0.ordering_top_axioms
% 5.12/5.46 thf(fact_9853_set__encode__vimage__Suc,axiom,
% 5.12/5.46 ! [A2: set_nat] :
% 5.12/5.46 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 5.12/5.46 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % set_encode_vimage_Suc
% 5.12/5.46 thf(fact_9854_finite__vimage__Suc__iff,axiom,
% 5.12/5.46 ! [F4: set_nat] :
% 5.12/5.46 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F4 ) )
% 5.12/5.46 = ( finite_finite_nat @ F4 ) ) ).
% 5.12/5.46
% 5.12/5.46 % finite_vimage_Suc_iff
% 5.12/5.46 thf(fact_9855_vimage__Suc__insert__Suc,axiom,
% 5.12/5.46 ! [N: nat,A2: set_nat] :
% 5.12/5.46 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 5.12/5.46 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % vimage_Suc_insert_Suc
% 5.12/5.46 thf(fact_9856_vimage__Suc__insert__0,axiom,
% 5.12/5.46 ! [A2: set_nat] :
% 5.12/5.46 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 5.12/5.46 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % vimage_Suc_insert_0
% 5.12/5.46 thf(fact_9857_set__decode__div__2,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.12/5.46 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % set_decode_div_2
% 5.12/5.46 thf(fact_9858_abs__division__segment,axiom,
% 5.12/5.46 ! [K: int] :
% 5.12/5.46 ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 5.12/5.46 = one_one_int ) ).
% 5.12/5.46
% 5.12/5.46 % abs_division_segment
% 5.12/5.46 thf(fact_9859_division__segment__nat__def,axiom,
% 5.12/5.46 ( euclid3398187327856392827nt_nat
% 5.12/5.46 = ( ^ [N4: nat] : one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % division_segment_nat_def
% 5.12/5.46 thf(fact_9860_division__segment__eq__sgn,axiom,
% 5.12/5.46 ! [K: int] :
% 5.12/5.46 ( ( K != zero_zero_int )
% 5.12/5.46 => ( ( euclid3395696857347342551nt_int @ K )
% 5.12/5.46 = ( sgn_sgn_int @ K ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % division_segment_eq_sgn
% 5.12/5.46 thf(fact_9861_division__segment__int__def,axiom,
% 5.12/5.46 ( euclid3395696857347342551nt_int
% 5.12/5.46 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % division_segment_int_def
% 5.12/5.46 thf(fact_9862_transp__realrel,axiom,
% 5.12/5.46 transp_nat_rat @ realrel ).
% 5.12/5.46
% 5.12/5.46 % transp_realrel
% 5.12/5.46 thf(fact_9863_pred__nat__def,axiom,
% 5.12/5.46 ( pred_nat
% 5.12/5.46 = ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [M5: nat,N4: nat] :
% 5.12/5.46 ( N4
% 5.12/5.46 = ( suc @ M5 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % pred_nat_def
% 5.12/5.46 thf(fact_9864_less__enat__def,axiom,
% 5.12/5.46 ( ord_le72135733267957522d_enat
% 5.12/5.46 = ( ^ [M5: extended_enat,N4: extended_enat] :
% 5.12/5.46 ( extended_case_enat_o
% 5.12/5.46 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N4 )
% 5.12/5.46 @ $false
% 5.12/5.46 @ M5 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_enat_def
% 5.12/5.46 thf(fact_9865_Divides_Oadjust__div__def,axiom,
% 5.12/5.46 ( adjust_div
% 5.12/5.46 = ( produc8211389475949308722nt_int
% 5.12/5.46 @ ^ [Q4: int,R: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Divides.adjust_div_def
% 5.12/5.46 thf(fact_9866_strict__mono__imp__increasing,axiom,
% 5.12/5.46 ! [F: nat > nat,N: nat] :
% 5.12/5.46 ( ( order_5726023648592871131at_nat @ F )
% 5.12/5.46 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % strict_mono_imp_increasing
% 5.12/5.46 thf(fact_9867_rat__floor__code,axiom,
% 5.12/5.46 ( archim3151403230148437115or_rat
% 5.12/5.46 = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % rat_floor_code
% 5.12/5.46 thf(fact_9868_prod__decode__triangle__add,axiom,
% 5.12/5.46 ! [K: nat,M2: nat] :
% 5.12/5.46 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M2 ) )
% 5.12/5.46 = ( nat_prod_decode_aux @ K @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % prod_decode_triangle_add
% 5.12/5.46 thf(fact_9869_prod__decode__eq,axiom,
% 5.12/5.46 ! [X: nat,Y: nat] :
% 5.12/5.46 ( ( ( nat_prod_decode @ X )
% 5.12/5.46 = ( nat_prod_decode @ Y ) )
% 5.12/5.46 = ( X = Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % prod_decode_eq
% 5.12/5.46 thf(fact_9870_prod__decode__inverse,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( nat_prod_encode @ ( nat_prod_decode @ N ) )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % prod_decode_inverse
% 5.12/5.46 thf(fact_9871_prod__encode__inverse,axiom,
% 5.12/5.46 ! [X: product_prod_nat_nat] :
% 5.12/5.46 ( ( nat_prod_decode @ ( nat_prod_encode @ X ) )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 % prod_encode_inverse
% 5.12/5.46 thf(fact_9872_tanh__real__strict__mono,axiom,
% 5.12/5.46 order_7092887310737990675l_real @ tanh_real ).
% 5.12/5.46
% 5.12/5.46 % tanh_real_strict_mono
% 5.12/5.46 thf(fact_9873_sinh__real__strict__mono,axiom,
% 5.12/5.46 order_7092887310737990675l_real @ sinh_real ).
% 5.12/5.46
% 5.12/5.46 % sinh_real_strict_mono
% 5.12/5.46 thf(fact_9874_inj__prod__decode,axiom,
% 5.12/5.46 ! [A2: set_nat] : ( inj_on5538052773655684606at_nat @ nat_prod_decode @ A2 ) ).
% 5.12/5.46
% 5.12/5.46 % inj_prod_decode
% 5.12/5.46 thf(fact_9875_prod__decode__def,axiom,
% 5.12/5.46 ( nat_prod_decode
% 5.12/5.46 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % prod_decode_def
% 5.12/5.46 thf(fact_9876_bij__prod__decode,axiom,
% 5.12/5.46 bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 5.12/5.46
% 5.12/5.46 % bij_prod_decode
% 5.12/5.46 thf(fact_9877_surj__prod__decode,axiom,
% 5.12/5.46 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 5.12/5.46 = top_to4669805908274784177at_nat ) ).
% 5.12/5.46
% 5.12/5.46 % surj_prod_decode
% 5.12/5.46 thf(fact_9878_list__decode_Opinduct,axiom,
% 5.12/5.46 ! [A0: nat,P: nat > $o] :
% 5.12/5.46 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 5.12/5.46 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.12/5.46 => ( P @ zero_zero_nat ) )
% 5.12/5.46 => ( ! [N2: nat] :
% 5.12/5.46 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 5.12/5.46 => ( ! [X4: nat,Y5: nat] :
% 5.12/5.46 ( ( ( product_Pair_nat_nat @ X4 @ Y5 )
% 5.12/5.46 = ( nat_prod_decode @ N2 ) )
% 5.12/5.46 => ( P @ Y5 ) )
% 5.12/5.46 => ( P @ ( suc @ N2 ) ) ) )
% 5.12/5.46 => ( P @ A0 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.pinduct
% 5.12/5.46 thf(fact_9879_list__decode_Oelims,axiom,
% 5.12/5.46 ! [X: nat,Y: list_nat] :
% 5.12/5.46 ( ( ( nat_list_decode @ X )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( ( X = zero_zero_nat )
% 5.12/5.46 => ( Y != nil_nat ) )
% 5.12/5.46 => ~ ! [N2: nat] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( suc @ N2 ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 != ( produc2761476792215241774st_nat
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( cons_nat @ X2 @ ( nat_list_decode @ Y6 ) )
% 5.12/5.46 @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.elims
% 5.12/5.46 thf(fact_9880_list__decode__inverse,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( nat_list_encode @ ( nat_list_decode @ N ) )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode_inverse
% 5.12/5.46 thf(fact_9881_list__encode__inverse,axiom,
% 5.12/5.46 ! [X: list_nat] :
% 5.12/5.46 ( ( nat_list_decode @ ( nat_list_encode @ X ) )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 % list_encode_inverse
% 5.12/5.46 thf(fact_9882_list__decode_Opsimps_I1_J,axiom,
% 5.12/5.46 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.12/5.46 => ( ( nat_list_decode @ zero_zero_nat )
% 5.12/5.46 = nil_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.psimps(1)
% 5.12/5.46 thf(fact_9883_inj__list__decode,axiom,
% 5.12/5.46 ! [A2: set_nat] : ( inj_on_nat_list_nat @ nat_list_decode @ A2 ) ).
% 5.12/5.46
% 5.12/5.46 % inj_list_decode
% 5.12/5.46 thf(fact_9884_list__decode__eq,axiom,
% 5.12/5.46 ! [X: nat,Y: nat] :
% 5.12/5.46 ( ( ( nat_list_decode @ X )
% 5.12/5.46 = ( nat_list_decode @ Y ) )
% 5.12/5.46 = ( X = Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode_eq
% 5.12/5.46 thf(fact_9885_list__decode_Osimps_I1_J,axiom,
% 5.12/5.46 ( ( nat_list_decode @ zero_zero_nat )
% 5.12/5.46 = nil_nat ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.simps(1)
% 5.12/5.46 thf(fact_9886_list__decode_Opsimps_I2_J,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 5.12/5.46 => ( ( nat_list_decode @ ( suc @ N ) )
% 5.12/5.46 = ( produc2761476792215241774st_nat
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( cons_nat @ X2 @ ( nat_list_decode @ Y6 ) )
% 5.12/5.46 @ ( nat_prod_decode @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.psimps(2)
% 5.12/5.46 thf(fact_9887_bij__list__decode,axiom,
% 5.12/5.46 bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 5.12/5.46
% 5.12/5.46 % bij_list_decode
% 5.12/5.46 thf(fact_9888_surj__list__decode,axiom,
% 5.12/5.46 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 5.12/5.46 = top_top_set_list_nat ) ).
% 5.12/5.46
% 5.12/5.46 % surj_list_decode
% 5.12/5.46 thf(fact_9889_list__decode_Osimps_I2_J,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( nat_list_decode @ ( suc @ N ) )
% 5.12/5.46 = ( produc2761476792215241774st_nat
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( cons_nat @ X2 @ ( nat_list_decode @ Y6 ) )
% 5.12/5.46 @ ( nat_prod_decode @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.simps(2)
% 5.12/5.46 thf(fact_9890_list__decode_Opelims,axiom,
% 5.12/5.46 ! [X: nat,Y: list_nat] :
% 5.12/5.46 ( ( ( nat_list_decode @ X )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 5.12/5.46 => ( ( ( X = zero_zero_nat )
% 5.12/5.46 => ( ( Y = nil_nat )
% 5.12/5.46 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 5.12/5.46 => ~ ! [N2: nat] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( suc @ N2 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( produc2761476792215241774st_nat
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] : ( cons_nat @ X2 @ ( nat_list_decode @ Y6 ) )
% 5.12/5.46 @ ( nat_prod_decode @ N2 ) ) )
% 5.12/5.46 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % list_decode.pelims
% 5.12/5.46 thf(fact_9891_compute__powr__real,axiom,
% 5.12/5.46 ( powr_real2
% 5.12/5.46 = ( ^ [B2: real,I2: real] :
% 5.12/5.46 ( if_real @ ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.12/5.46 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.12/5.46 @ ^ [Uu3: product_unit] : ( powr_real2 @ B2 @ I2 ) )
% 5.12/5.46 @ ( if_real
% 5.12/5.46 @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I2 ) )
% 5.12/5.46 = I2 )
% 5.12/5.46 @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I2 ) @ ( power_power_real @ B2 @ ( nat2 @ ( archim6058952711729229775r_real @ I2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B2 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I2 ) ) ) ) ) )
% 5.12/5.46 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.12/5.46 @ ^ [Uu3: product_unit] : ( powr_real2 @ B2 @ I2 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % compute_powr_real
% 5.12/5.46 thf(fact_9892_powr__real__def,axiom,
% 5.12/5.46 powr_real2 = powr_real ).
% 5.12/5.46
% 5.12/5.46 % powr_real_def
% 5.12/5.46 thf(fact_9893_integer__of__nat_Orep__eq,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( code_int_of_integer @ ( code_integer_of_nat @ X ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ X ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat.rep_eq
% 5.12/5.46 thf(fact_9894_int__of__integer__integer__of__nat,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % int_of_integer_integer_of_nat
% 5.12/5.46 thf(fact_9895_integer__of__nat__0,axiom,
% 5.12/5.46 ( ( code_integer_of_nat @ zero_zero_nat )
% 5.12/5.46 = zero_z3403309356797280102nteger ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat_0
% 5.12/5.46 thf(fact_9896_integer__of__nat_Oabs__eq,axiom,
% 5.12/5.46 ( code_integer_of_nat
% 5.12/5.46 = ( ^ [X2: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat.abs_eq
% 5.12/5.46 thf(fact_9897_integer__of__nat__1,axiom,
% 5.12/5.46 ( ( code_integer_of_nat @ one_one_nat )
% 5.12/5.46 = one_one_Code_integer ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat_1
% 5.12/5.46 thf(fact_9898_integer__of__nat__def,axiom,
% 5.12/5.46 ( code_integer_of_nat
% 5.12/5.46 = ( map_fu6290471996055670595nteger @ id_nat @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat_def
% 5.12/5.46 thf(fact_9899_pairs__le__eq__Sigma,axiom,
% 5.12/5.46 ! [M2: nat] :
% 5.12/5.46 ( ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [I2: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ J3 ) @ M2 ) ) )
% 5.12/5.46 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 5.12/5.46 @ ^ [R: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % pairs_le_eq_Sigma
% 5.12/5.46 thf(fact_9900_product__atMost__eq__Un,axiom,
% 5.12/5.46 ! [A2: set_nat,M2: nat] :
% 5.12/5.46 ( ( produc457027306803732586at_nat @ A2
% 5.12/5.46 @ ^ [Uu3: nat] : ( set_ord_atMost_nat @ M2 ) )
% 5.12/5.46 = ( sup_su6327502436637775413at_nat
% 5.12/5.46 @ ( produc457027306803732586at_nat @ A2
% 5.12/5.46 @ ^ [I2: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ I2 ) ) )
% 5.12/5.46 @ ( produc457027306803732586at_nat @ A2
% 5.12/5.46 @ ^ [I2: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M2 @ I2 ) @ M2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % product_atMost_eq_Un
% 5.12/5.46 thf(fact_9901_filtermap__ln__at__right,axiom,
% 5.12/5.46 ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.12/5.46 = at_bot_real ) ).
% 5.12/5.46
% 5.12/5.46 % filtermap_ln_at_right
% 5.12/5.46 thf(fact_9902_Gcd__int__set__eq__fold,axiom,
% 5.12/5.46 ! [Xs: list_int] :
% 5.12/5.46 ( ( gcd_Gcd_int @ ( set_int2 @ Xs ) )
% 5.12/5.46 = ( fold_int_int @ gcd_gcd_int @ Xs @ zero_zero_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % Gcd_int_set_eq_fold
% 5.12/5.46 thf(fact_9903_filtermap__ln__at__top,axiom,
% 5.12/5.46 ( ( filtermap_real_real @ ln_ln_real @ at_top_real )
% 5.12/5.46 = at_top_real ) ).
% 5.12/5.46
% 5.12/5.46 % filtermap_ln_at_top
% 5.12/5.46 thf(fact_9904_filtermap__exp__at__top,axiom,
% 5.12/5.46 ( ( filtermap_real_real @ exp_real @ at_top_real )
% 5.12/5.46 = at_top_real ) ).
% 5.12/5.46
% 5.12/5.46 % filtermap_exp_at_top
% 5.12/5.46 thf(fact_9905_filtermap__at__right__shift,axiom,
% 5.12/5.46 ! [D: real,A: real] :
% 5.12/5.46 ( ( filtermap_real_real
% 5.12/5.46 @ ^ [X2: real] : ( minus_minus_real @ X2 @ D )
% 5.12/5.46 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.12/5.46 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % filtermap_at_right_shift
% 5.12/5.46 thf(fact_9906_at__right__minus,axiom,
% 5.12/5.46 ! [A: real] :
% 5.12/5.46 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.12/5.46 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5984915006950818249n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % at_right_minus
% 5.12/5.46 thf(fact_9907_at__left__minus,axiom,
% 5.12/5.46 ! [A: real] :
% 5.12/5.46 ( ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) )
% 5.12/5.46 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % at_left_minus
% 5.12/5.46 thf(fact_9908_less__than__iff,axiom,
% 5.12/5.46 ! [X: nat,Y: nat] :
% 5.12/5.46 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 5.12/5.46 = ( ord_less_nat @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_than_iff
% 5.12/5.46 thf(fact_9909_elimnum,axiom,
% 5.12/5.46 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.12/5.46 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.12/5.46 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.12/5.46 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % elimnum
% 5.12/5.46 thf(fact_9910_idiff__enat__0,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 5.12/5.46 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_enat_0
% 5.12/5.46 thf(fact_9911_idiff__enat__0__right,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_enat_0_right
% 5.12/5.46 thf(fact_9912_idiff__enat__enat,axiom,
% 5.12/5.46 ! [A: nat,B: nat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
% 5.12/5.46 = ( extended_enat2 @ ( minus_minus_nat @ A @ B ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_enat_enat
% 5.12/5.46 thf(fact_9913_enat__ord__simps_I2_J,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 5.12/5.46 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_ord_simps(2)
% 5.12/5.46 thf(fact_9914_numeral__less__enat__iff,axiom,
% 5.12/5.46 ! [M2: num,N: nat] :
% 5.12/5.46 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 5.12/5.46 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % numeral_less_enat_iff
% 5.12/5.46 thf(fact_9915_enat__0__iff_I2_J,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( zero_z5237406670263579293d_enat
% 5.12/5.46 = ( extended_enat2 @ X ) )
% 5.12/5.46 = ( X = zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_0_iff(2)
% 5.12/5.46 thf(fact_9916_enat__0__iff_I1_J,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( ( extended_enat2 @ X )
% 5.12/5.46 = zero_z5237406670263579293d_enat )
% 5.12/5.46 = ( X = zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_0_iff(1)
% 5.12/5.46 thf(fact_9917_zero__enat__def,axiom,
% 5.12/5.46 ( zero_z5237406670263579293d_enat
% 5.12/5.46 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % zero_enat_def
% 5.12/5.46 thf(fact_9918_enat__1__iff_I2_J,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( one_on7984719198319812577d_enat
% 5.12/5.46 = ( extended_enat2 @ X ) )
% 5.12/5.46 = ( X = one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_1_iff(2)
% 5.12/5.46 thf(fact_9919_enat__1__iff_I1_J,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( ( extended_enat2 @ X )
% 5.12/5.46 = one_on7984719198319812577d_enat )
% 5.12/5.46 = ( X = one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_1_iff(1)
% 5.12/5.46 thf(fact_9920_one__enat__def,axiom,
% 5.12/5.46 ( one_on7984719198319812577d_enat
% 5.12/5.46 = ( extended_enat2 @ one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % one_enat_def
% 5.12/5.46 thf(fact_9921_VEBT__internal_Oelim__dead_Osimps_I1_J,axiom,
% 5.12/5.46 ! [A: $o,B: $o,Uu: extended_enat] :
% 5.12/5.46 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ Uu )
% 5.12/5.46 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.simps(1)
% 5.12/5.46 thf(fact_9922_less__enatE,axiom,
% 5.12/5.46 ! [N: extended_enat,M2: nat] :
% 5.12/5.46 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M2 ) )
% 5.12/5.46 => ~ ! [K2: nat] :
% 5.12/5.46 ( ( N
% 5.12/5.46 = ( extended_enat2 @ K2 ) )
% 5.12/5.46 => ~ ( ord_less_nat @ K2 @ M2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_enatE
% 5.12/5.46 thf(fact_9923_Suc__ile__eq,axiom,
% 5.12/5.46 ! [M2: nat,N: extended_enat] :
% 5.12/5.46 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N )
% 5.12/5.46 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % Suc_ile_eq
% 5.12/5.46 thf(fact_9924_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 5.12/5.46 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 5.12/5.46 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ L ) )
% 5.12/5.46 = ( vEBT_Node @ Info @ Deg
% 5.12/5.46 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList ) )
% 5.12/5.46 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.simps(3)
% 5.12/5.46 thf(fact_9925_Gcd__nat__set__eq__fold,axiom,
% 5.12/5.46 ! [Xs: list_nat] :
% 5.12/5.46 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 5.12/5.46 = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % Gcd_nat_set_eq_fold
% 5.12/5.46 thf(fact_9926_VEBT__internal_Oelim__dead_Oelims,axiom,
% 5.12/5.46 ! [X: vEBT_VEBT,Xa: extended_enat,Y: vEBT_VEBT] :
% 5.12/5.46 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ! [A4: $o,B3: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 != ( vEBT_Leaf @ A4 @ B3 ) ) )
% 5.12/5.46 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.46 => ( ( Xa = extend5688581933313929465d_enat )
% 5.12/5.46 => ( Y
% 5.12/5.46 != ( vEBT_Node @ Info2 @ Deg2
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList2 )
% 5.12/5.46 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 5.12/5.46 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.46 => ! [L3: nat] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( extended_enat2 @ L3 ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 != ( vEBT_Node @ Info2 @ Deg2
% 5.12/5.46 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList2 ) )
% 5.12/5.46 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.elims
% 5.12/5.46 thf(fact_9927_elimcomplete,axiom,
% 5.12/5.46 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.12/5.46 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.12/5.46 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 5.12/5.46 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % elimcomplete
% 5.12/5.46 thf(fact_9928_idiff__infinity,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ extend5688581933313929465d_enat @ N )
% 5.12/5.46 = extend5688581933313929465d_enat ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_infinity
% 5.12/5.46 thf(fact_9929_add__diff__cancel__enat,axiom,
% 5.12/5.46 ! [X: extended_enat,Y: extended_enat] :
% 5.12/5.46 ( ( X != extend5688581933313929465d_enat )
% 5.12/5.46 => ( ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ X )
% 5.12/5.46 = Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % add_diff_cancel_enat
% 5.12/5.46 thf(fact_9930_idiff__0,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.12/5.46 = zero_z5237406670263579293d_enat ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_0
% 5.12/5.46 thf(fact_9931_idiff__0__right,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_0_right
% 5.12/5.46 thf(fact_9932_idiff__self,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( N != extend5688581933313929465d_enat )
% 5.12/5.46 => ( ( minus_3235023915231533773d_enat @ N @ N )
% 5.12/5.46 = zero_z5237406670263579293d_enat ) ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_self
% 5.12/5.46 thf(fact_9933_times__enat__simps_I3_J,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( ( N = zero_zero_nat )
% 5.12/5.46 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.12/5.46 = zero_z5237406670263579293d_enat ) )
% 5.12/5.46 & ( ( N != zero_zero_nat )
% 5.12/5.46 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.12/5.46 = extend5688581933313929465d_enat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_enat_simps(3)
% 5.12/5.46 thf(fact_9934_times__enat__simps_I4_J,axiom,
% 5.12/5.46 ! [M2: nat] :
% 5.12/5.46 ( ( ( M2 = zero_zero_nat )
% 5.12/5.46 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 5.12/5.46 = zero_z5237406670263579293d_enat ) )
% 5.12/5.46 & ( ( M2 != zero_zero_nat )
% 5.12/5.46 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 5.12/5.46 = extend5688581933313929465d_enat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_enat_simps(4)
% 5.12/5.46 thf(fact_9935_idiff__infinity__right,axiom,
% 5.12/5.46 ! [A: nat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ extend5688581933313929465d_enat )
% 5.12/5.46 = zero_z5237406670263579293d_enat ) ).
% 5.12/5.46
% 5.12/5.46 % idiff_infinity_right
% 5.12/5.46 thf(fact_9936_infinity__ne__i1,axiom,
% 5.12/5.46 extend5688581933313929465d_enat != one_on7984719198319812577d_enat ).
% 5.12/5.46
% 5.12/5.46 % infinity_ne_i1
% 5.12/5.46 thf(fact_9937_zero__one__enat__neq_I1_J,axiom,
% 5.12/5.46 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.12/5.46
% 5.12/5.46 % zero_one_enat_neq(1)
% 5.12/5.46 thf(fact_9938_add__diff__assoc__enat,axiom,
% 5.12/5.46 ! [Z2: extended_enat,Y: extended_enat,X: extended_enat] :
% 5.12/5.46 ( ( ord_le2932123472753598470d_enat @ Z2 @ Y )
% 5.12/5.46 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z2 ) )
% 5.12/5.46 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % add_diff_assoc_enat
% 5.12/5.46 thf(fact_9939_VEBT__internal_Oelim__dead_Ocases,axiom,
% 5.12/5.46 ! [X: produc7272778201969148633d_enat] :
% 5.12/5.46 ( ! [A4: $o,B3: $o,Uu2: extended_enat] :
% 5.12/5.46 ( X
% 5.12/5.46 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A4 @ B3 ) @ Uu2 ) )
% 5.12/5.46 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.46 ( X
% 5.12/5.46 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 5.12/5.46 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,L3: nat] :
% 5.12/5.46 ( X
% 5.12/5.46 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L3 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.cases
% 5.12/5.46 thf(fact_9940_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 5.12/5.46 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.12/5.46 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 5.12/5.46 = ( vEBT_Node @ Info @ Deg
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList )
% 5.12/5.46 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.simps(2)
% 5.12/5.46 thf(fact_9941_VEBT__internal_Oelim__dead_Opelims,axiom,
% 5.12/5.46 ! [X: vEBT_VEBT,Xa: extended_enat,Y: vEBT_VEBT] :
% 5.12/5.46 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X @ Xa ) )
% 5.12/5.46 => ( ! [A4: $o,B3: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.12/5.46 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) ) ) )
% 5.12/5.46 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.46 => ( ( Xa = extend5688581933313929465d_enat )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList2 )
% 5.12/5.46 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 5.12/5.46 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 5.12/5.46 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.12/5.46 => ! [L3: nat] :
% 5.12/5.46 ( ( Xa
% 5.12/5.46 = ( extended_enat2 @ L3 ) )
% 5.12/5.46 => ( ( Y
% 5.12/5.46 = ( vEBT_Node @ Info2 @ Deg2
% 5.12/5.46 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.12/5.46 @ ( map_VE8901447254227204932T_VEBT
% 5.12/5.46 @ ^ [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 ) ) ) ) ) )
% 5.12/5.46 @ TreeList2 ) )
% 5.12/5.46 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.12/5.46 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.elim_dead.pelims
% 5.12/5.46 thf(fact_9942_diff__enat__def,axiom,
% 5.12/5.46 ( minus_3235023915231533773d_enat
% 5.12/5.46 = ( ^ [A3: extended_enat,B2: extended_enat] :
% 5.12/5.46 ( extend3600170679010898289d_enat
% 5.12/5.46 @ ^ [X2: nat] :
% 5.12/5.46 ( extend3600170679010898289d_enat
% 5.12/5.46 @ ^ [Y6: nat] : ( extended_enat2 @ ( minus_minus_nat @ X2 @ Y6 ) )
% 5.12/5.46 @ zero_z5237406670263579293d_enat
% 5.12/5.46 @ B2 )
% 5.12/5.46 @ extend5688581933313929465d_enat
% 5.12/5.46 @ A3 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % diff_enat_def
% 5.12/5.46 thf(fact_9943_times__enat__def,axiom,
% 5.12/5.46 ( times_7803423173614009249d_enat
% 5.12/5.46 = ( ^ [M5: extended_enat,N4: extended_enat] :
% 5.12/5.46 ( extend3600170679010898289d_enat
% 5.12/5.46 @ ^ [O: nat] :
% 5.12/5.46 ( extend3600170679010898289d_enat
% 5.12/5.46 @ ^ [P6: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P6 ) )
% 5.12/5.46 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.12/5.46 @ N4 )
% 5.12/5.46 @ ( if_Extended_enat @ ( N4 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.12/5.46 @ M5 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_enat_def
% 5.12/5.46 thf(fact_9944_eSuc__def,axiom,
% 5.12/5.46 ( extended_eSuc
% 5.12/5.46 = ( extend3600170679010898289d_enat
% 5.12/5.46 @ ^ [N4: nat] : ( extended_enat2 @ ( suc @ N4 ) )
% 5.12/5.46 @ extend5688581933313929465d_enat ) ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_def
% 5.12/5.46 thf(fact_9945_binomial__def,axiom,
% 5.12/5.46 ( binomial
% 5.12/5.46 = ( ^ [N4: nat,K3: nat] :
% 5.12/5.46 ( finite_card_set_nat
% 5.12/5.46 @ ( collect_set_nat
% 5.12/5.46 @ ^ [K7: set_nat] :
% 5.12/5.46 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 5.12/5.46 & ( ( finite_card_nat @ K7 )
% 5.12/5.46 = K3 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % binomial_def
% 5.12/5.46 thf(fact_9946_eSuc__minus__eSuc,axiom,
% 5.12/5.46 ! [N: extended_enat,M2: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M2 ) )
% 5.12/5.46 = ( minus_3235023915231533773d_enat @ N @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_minus_eSuc
% 5.12/5.46 thf(fact_9947_eSuc__minus__1,axiom,
% 5.12/5.46 ! [N: extended_enat] :
% 5.12/5.46 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ one_on7984719198319812577d_enat )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_minus_1
% 5.12/5.46 thf(fact_9948_enat__eSuc__iff,axiom,
% 5.12/5.46 ! [Y: nat,X: extended_enat] :
% 5.12/5.46 ( ( ( extended_enat2 @ Y )
% 5.12/5.46 = ( extended_eSuc @ X ) )
% 5.12/5.46 = ( ? [N4: nat] :
% 5.12/5.46 ( ( Y
% 5.12/5.46 = ( suc @ N4 ) )
% 5.12/5.46 & ( ( extended_enat2 @ N4 )
% 5.12/5.46 = X ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % enat_eSuc_iff
% 5.12/5.46 thf(fact_9949_eSuc__enat__iff,axiom,
% 5.12/5.46 ! [X: extended_enat,Y: nat] :
% 5.12/5.46 ( ( ( extended_eSuc @ X )
% 5.12/5.46 = ( extended_enat2 @ Y ) )
% 5.12/5.46 = ( ? [N4: nat] :
% 5.12/5.46 ( ( Y
% 5.12/5.46 = ( suc @ N4 ) )
% 5.12/5.46 & ( X
% 5.12/5.46 = ( extended_enat2 @ N4 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_enat_iff
% 5.12/5.46 thf(fact_9950_eSuc__enat,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 5.12/5.46 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_enat
% 5.12/5.46 thf(fact_9951_one__eSuc,axiom,
% 5.12/5.46 ( one_on7984719198319812577d_enat
% 5.12/5.46 = ( extended_eSuc @ zero_z5237406670263579293d_enat ) ) ).
% 5.12/5.46
% 5.12/5.46 % one_eSuc
% 5.12/5.46 thf(fact_9952_eSuc__plus__1,axiom,
% 5.12/5.46 ( extended_eSuc
% 5.12/5.46 = ( ^ [N4: extended_enat] : ( plus_p3455044024723400733d_enat @ N4 @ one_on7984719198319812577d_enat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % eSuc_plus_1
% 5.12/5.46 thf(fact_9953_plus__1__eSuc_I1_J,axiom,
% 5.12/5.46 ! [Q5: extended_enat] :
% 5.12/5.46 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ Q5 )
% 5.12/5.46 = ( extended_eSuc @ Q5 ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_1_eSuc(1)
% 5.12/5.46 thf(fact_9954_plus__1__eSuc_I2_J,axiom,
% 5.12/5.46 ! [Q5: extended_enat] :
% 5.12/5.46 ( ( plus_p3455044024723400733d_enat @ Q5 @ one_on7984719198319812577d_enat )
% 5.12/5.46 = ( extended_eSuc @ Q5 ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_1_eSuc(2)
% 5.12/5.46 thf(fact_9955_Quotient__real,axiom,
% 5.12/5.46 quotie3684837364556693515t_real @ realrel @ real2 @ rep_real @ cr_real ).
% 5.12/5.46
% 5.12/5.46 % Quotient_real
% 5.12/5.46 thf(fact_9956_UNIV__char__of__nat,axiom,
% 5.12/5.46 ( top_top_set_char
% 5.12/5.46 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % UNIV_char_of_nat
% 5.12/5.46 thf(fact_9957_inj__on__char__of__nat,axiom,
% 5.12/5.46 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % inj_on_char_of_nat
% 5.12/5.46 thf(fact_9958_range__nat__of__char,axiom,
% 5.12/5.46 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.12/5.46 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % range_nat_of_char
% 5.12/5.46 thf(fact_9959_char_Osize_I2_J,axiom,
% 5.12/5.46 ! [X1: $o,X23: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.12/5.46 ( ( size_size_char @ ( char2 @ X1 @ X23 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % char.size(2)
% 5.12/5.46 thf(fact_9960_nat__of__char__less__256,axiom,
% 5.12/5.46 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_char_less_256
% 5.12/5.46 thf(fact_9961_char_Osize__gen,axiom,
% 5.12/5.46 ! [X1: $o,X23: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.12/5.46 ( ( size_char @ ( char2 @ X1 @ X23 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % char.size_gen
% 5.12/5.46 thf(fact_9962_cr__int__def,axiom,
% 5.12/5.46 ( cr_int
% 5.12/5.46 = ( ^ [X2: product_prod_nat_nat] :
% 5.12/5.46 ( ^ [Y4: int,Z: int] : ( Y4 = Z )
% 5.12/5.46 @ ( abs_Integ @ X2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % cr_int_def
% 5.12/5.46 thf(fact_9963_int_Opcr__cr__eq,axiom,
% 5.12/5.46 pcr_int = cr_int ).
% 5.12/5.46
% 5.12/5.46 % int.pcr_cr_eq
% 5.12/5.46 thf(fact_9964_less__eq,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.12/5.46 = ( ord_less_nat @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq
% 5.12/5.46 thf(fact_9965_Quotient__int,axiom,
% 5.12/5.46 quotie1194848508323700631at_int @ intrel @ abs_Integ @ rep_Integ @ cr_int ).
% 5.12/5.46
% 5.12/5.46 % Quotient_int
% 5.12/5.46 thf(fact_9966_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 5.12/5.46 semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % gcd_nat.semilattice_neutr_axioms
% 5.12/5.46 thf(fact_9967_max__nat_Osemilattice__neutr__axioms,axiom,
% 5.12/5.46 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % max_nat.semilattice_neutr_axioms
% 5.12/5.46 thf(fact_9968_uminus__integer__def,axiom,
% 5.12/5.46 ( uminus1351360451143612070nteger
% 5.12/5.46 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % uminus_integer_def
% 5.12/5.46 thf(fact_9969_natLess__def,axiom,
% 5.12/5.46 ( bNF_Ca8459412986667044542atLess
% 5.12/5.46 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLess_def
% 5.12/5.46 thf(fact_9970_Restr__natLeq,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.12/5.46 @ ( produc457027306803732586at_nat
% 5.12/5.46 @ ( collect_nat
% 5.12/5.46 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 5.12/5.46 @ ^ [Uu3: nat] :
% 5.12/5.46 ( collect_nat
% 5.12/5.46 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) )
% 5.12/5.46 = ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Restr_natLeq
% 5.12/5.46 thf(fact_9971_divide__integer__def,axiom,
% 5.12/5.46 ( divide6298287555418463151nteger
% 5.12/5.46 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ divide_divide_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % divide_integer_def
% 5.12/5.46 thf(fact_9972_minus__integer__def,axiom,
% 5.12/5.46 ( minus_8373710615458151222nteger
% 5.12/5.46 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ minus_minus_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_integer_def
% 5.12/5.46 thf(fact_9973_Restr__natLeq2,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.12/5.46 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.12/5.46 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.12/5.46 = ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Restr_natLeq2
% 5.12/5.46 thf(fact_9974_natLeq__underS__less,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.12/5.46 = ( collect_nat
% 5.12/5.46 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLeq_underS_less
% 5.12/5.46 thf(fact_9975_sub_Oabs__eq,axiom,
% 5.12/5.46 ( code_sub
% 5.12/5.46 = ( ^ [Xa4: num,X2: num] : ( code_integer_of_int @ ( minus_minus_int @ ( numeral_numeral_int @ Xa4 ) @ ( numeral_numeral_int @ X2 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % sub.abs_eq
% 5.12/5.46 thf(fact_9976_sub_Orep__eq,axiom,
% 5.12/5.46 ! [X: num,Xa: num] :
% 5.12/5.46 ( ( code_int_of_integer @ ( code_sub @ X @ Xa ) )
% 5.12/5.46 = ( minus_minus_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Xa ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % sub.rep_eq
% 5.12/5.46 thf(fact_9977_Code__Numeral_Osub__code_I9_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.46 = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M2 @ N ) ) @ one_one_Code_integer ) ) ).
% 5.12/5.46
% 5.12/5.46 % Code_Numeral.sub_code(9)
% 5.12/5.46 thf(fact_9978_Code__Numeral_Osub__code_I8_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 5.12/5.46 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M2 @ N ) ) @ one_one_Code_integer ) ) ).
% 5.12/5.46
% 5.12/5.46 % Code_Numeral.sub_code(8)
% 5.12/5.46 thf(fact_9979_gcd__nat_Omonoid__axioms,axiom,
% 5.12/5.46 monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % gcd_nat.monoid_axioms
% 5.12/5.46 thf(fact_9980_max__nat_Omonoid__axioms,axiom,
% 5.12/5.46 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % max_nat.monoid_axioms
% 5.12/5.46 thf(fact_9981_convergent__realpow,axiom,
% 5.12/5.46 ! [X: real] :
% 5.12/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.12/5.46 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.12/5.46 => ( topolo7531315842566124627t_real @ ( power_power_real @ X ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % convergent_realpow
% 5.12/5.46 thf(fact_9982_lcm__altdef__int,axiom,
% 5.12/5.46 ( gcd_lcm_int
% 5.12/5.46 = ( ^ [A3: int,B2: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A3 ) @ ( abs_abs_int @ B2 ) ) @ ( gcd_gcd_int @ A3 @ B2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_altdef_int
% 5.12/5.46 thf(fact_9983_lcm__0__iff__int,axiom,
% 5.12/5.46 ! [M2: int,N: int] :
% 5.12/5.46 ( ( ( gcd_lcm_int @ M2 @ N )
% 5.12/5.46 = zero_zero_int )
% 5.12/5.46 = ( ( M2 = zero_zero_int )
% 5.12/5.46 | ( N = zero_zero_int ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_0_iff_int
% 5.12/5.46 thf(fact_9984_lcm__1__iff__int,axiom,
% 5.12/5.46 ! [M2: int,N: int] :
% 5.12/5.46 ( ( ( gcd_lcm_int @ M2 @ N )
% 5.12/5.46 = one_one_int )
% 5.12/5.46 = ( ( ( M2 = one_one_int )
% 5.12/5.46 | ( M2
% 5.12/5.46 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.12/5.46 & ( ( N = one_one_int )
% 5.12/5.46 | ( N
% 5.12/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_1_iff_int
% 5.12/5.46 thf(fact_9985_lcm__neg1__int,axiom,
% 5.12/5.46 ! [X: int,Y: int] :
% 5.12/5.46 ( ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.12/5.46 = ( gcd_lcm_int @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_neg1_int
% 5.12/5.46 thf(fact_9986_lcm__neg2__int,axiom,
% 5.12/5.46 ! [X: int,Y: int] :
% 5.12/5.46 ( ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.12/5.46 = ( gcd_lcm_int @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_neg2_int
% 5.12/5.46 thf(fact_9987_lcm__pos__int,axiom,
% 5.12/5.46 ! [M2: int,N: int] :
% 5.12/5.46 ( ( M2 != zero_zero_int )
% 5.12/5.46 => ( ( N != zero_zero_int )
% 5.12/5.46 => ( ord_less_int @ zero_zero_int @ ( gcd_lcm_int @ M2 @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_pos_int
% 5.12/5.46 thf(fact_9988_lcm__unique__int,axiom,
% 5.12/5.46 ! [D: int,A: int,B: int] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.12/5.46 & ( dvd_dvd_int @ A @ D )
% 5.12/5.46 & ( dvd_dvd_int @ B @ D )
% 5.12/5.46 & ! [E3: int] :
% 5.12/5.46 ( ( ( dvd_dvd_int @ A @ E3 )
% 5.12/5.46 & ( dvd_dvd_int @ B @ E3 ) )
% 5.12/5.46 => ( dvd_dvd_int @ D @ E3 ) ) )
% 5.12/5.46 = ( D
% 5.12/5.46 = ( gcd_lcm_int @ A @ B ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_unique_int
% 5.12/5.46 thf(fact_9989_lcm__ge__0__int,axiom,
% 5.12/5.46 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_lcm_int @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_ge_0_int
% 5.12/5.46 thf(fact_9990_lcm__cases__int,axiom,
% 5.12/5.46 ! [X: int,Y: int,P: int > $o] :
% 5.12/5.46 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.46 => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) )
% 5.12/5.46 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.12/5.46 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.12/5.46 => ( P @ ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.12/5.46 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.12/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.12/5.46 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 5.12/5.46 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.12/5.46 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.12/5.46 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.12/5.46 => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_cases_int
% 5.12/5.46 thf(fact_9991_Lcm__int__set__eq__fold,axiom,
% 5.12/5.46 ! [Xs: list_int] :
% 5.12/5.46 ( ( gcd_Lcm_int @ ( set_int2 @ Xs ) )
% 5.12/5.46 = ( fold_int_int @ gcd_lcm_int @ Xs @ one_one_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_int_set_eq_fold
% 5.12/5.46 thf(fact_9992_lcm__0__iff__nat,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( ( gcd_lcm_nat @ M2 @ N )
% 5.12/5.46 = zero_zero_nat )
% 5.12/5.46 = ( ( M2 = zero_zero_nat )
% 5.12/5.46 | ( N = zero_zero_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_0_iff_nat
% 5.12/5.46 thf(fact_9993_lcm__1__iff__nat,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( ( gcd_lcm_nat @ M2 @ N )
% 5.12/5.46 = ( suc @ zero_zero_nat ) )
% 5.12/5.46 = ( ( M2
% 5.12/5.46 = ( suc @ zero_zero_nat ) )
% 5.12/5.46 & ( N
% 5.12/5.46 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_1_iff_nat
% 5.12/5.46 thf(fact_9994_lcm__int__int__eq,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_int_int_eq
% 5.12/5.46 thf(fact_9995_lcm__nat__abs__right__eq,axiom,
% 5.12/5.46 ! [N: nat,K: int] :
% 5.12/5.46 ( ( gcd_lcm_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.12/5.46 = ( nat2 @ ( gcd_lcm_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_nat_abs_right_eq
% 5.12/5.46 thf(fact_9996_lcm__nat__abs__left__eq,axiom,
% 5.12/5.46 ! [K: int,N: nat] :
% 5.12/5.46 ( ( gcd_lcm_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.12/5.46 = ( nat2 @ ( gcd_lcm_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_nat_abs_left_eq
% 5.12/5.46 thf(fact_9997_lcm__nat__def,axiom,
% 5.12/5.46 ( gcd_lcm_nat
% 5.12/5.46 = ( ^ [X2: nat,Y6: nat] : ( divide_divide_nat @ ( times_times_nat @ X2 @ Y6 ) @ ( gcd_gcd_nat @ X2 @ Y6 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_nat_def
% 5.12/5.46 thf(fact_9998_lcm__pos__nat,axiom,
% 5.12/5.46 ! [M2: nat,N: nat] :
% 5.12/5.46 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.12/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.46 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M2 @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_pos_nat
% 5.12/5.46 thf(fact_9999_Lcm__int__greater__eq__0,axiom,
% 5.12/5.46 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Lcm_int @ K5 ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_int_greater_eq_0
% 5.12/5.46 thf(fact_10000_lcm__code__integer,axiom,
% 5.12/5.46 ( gcd_lcm_Code_integer
% 5.12/5.46 = ( ^ [A3: code_integer,B2: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A3 ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( gcd_gcd_Code_integer @ A3 @ B2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_code_integer
% 5.12/5.46 thf(fact_10001_lcm__int__def,axiom,
% 5.12/5.46 ( gcd_lcm_int
% 5.12/5.46 = ( ^ [X2: int,Y6: int] : ( semiri1314217659103216013at_int @ ( gcd_lcm_nat @ ( nat2 @ ( abs_abs_int @ X2 ) ) @ ( nat2 @ ( abs_abs_int @ Y6 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % lcm_int_def
% 5.12/5.46 thf(fact_10002_Lcm__int__def,axiom,
% 5.12/5.46 ( gcd_Lcm_int
% 5.12/5.46 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_int_def
% 5.12/5.46 thf(fact_10003_Lcm__int__eq,axiom,
% 5.12/5.46 ! [N5: set_nat] :
% 5.12/5.46 ( ( gcd_Lcm_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ N5 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_int_eq
% 5.12/5.46 thf(fact_10004_Lcm__eq__0__I__nat,axiom,
% 5.12/5.46 ! [A2: set_nat] :
% 5.12/5.46 ( ( member_nat @ zero_zero_nat @ A2 )
% 5.12/5.46 => ( ( gcd_Lcm_nat @ A2 )
% 5.12/5.46 = zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_eq_0_I_nat
% 5.12/5.46 thf(fact_10005_Lcm__0__iff__nat,axiom,
% 5.12/5.46 ! [A2: set_nat] :
% 5.12/5.46 ( ( finite_finite_nat @ A2 )
% 5.12/5.46 => ( ( ( gcd_Lcm_nat @ A2 )
% 5.12/5.46 = zero_zero_nat )
% 5.12/5.46 = ( member_nat @ zero_zero_nat @ A2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_0_iff_nat
% 5.12/5.46 thf(fact_10006_Lcm__nat__empty,axiom,
% 5.12/5.46 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 5.12/5.46 = one_one_nat ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_nat_empty
% 5.12/5.46 thf(fact_10007_Lcm__nat__infinite,axiom,
% 5.12/5.46 ! [M10: set_nat] :
% 5.12/5.46 ( ~ ( finite_finite_nat @ M10 )
% 5.12/5.46 => ( ( gcd_Lcm_nat @ M10 )
% 5.12/5.46 = zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_nat_infinite
% 5.12/5.46 thf(fact_10008_Lcm__nat__set__eq__fold,axiom,
% 5.12/5.46 ! [Xs: list_nat] :
% 5.12/5.46 ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 5.12/5.46 = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_nat_set_eq_fold
% 5.12/5.46 thf(fact_10009_Lcm__eq__Max__nat,axiom,
% 5.12/5.46 ! [M10: set_nat] :
% 5.12/5.46 ( ( finite_finite_nat @ M10 )
% 5.12/5.46 => ( ( M10 != bot_bot_set_nat )
% 5.12/5.46 => ( ~ ( member_nat @ zero_zero_nat @ M10 )
% 5.12/5.46 => ( ! [M3: nat,N2: nat] :
% 5.12/5.46 ( ( member_nat @ M3 @ M10 )
% 5.12/5.46 => ( ( member_nat @ N2 @ M10 )
% 5.12/5.46 => ( member_nat @ ( gcd_lcm_nat @ M3 @ N2 ) @ M10 ) ) )
% 5.12/5.46 => ( ( gcd_Lcm_nat @ M10 )
% 5.12/5.46 = ( lattic8265883725875713057ax_nat @ M10 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_eq_Max_nat
% 5.12/5.46 thf(fact_10010_Lcm__nat__def,axiom,
% 5.12/5.46 ( gcd_Lcm_nat
% 5.12/5.46 = ( ^ [M7: set_nat] : ( if_nat @ ( finite_finite_nat @ M7 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M7 ) @ zero_zero_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Lcm_nat_def
% 5.12/5.46 thf(fact_10011_unit__factor__simps_I1_J,axiom,
% 5.12/5.46 ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % unit_factor_simps(1)
% 5.12/5.46 thf(fact_10012_unit__factor__simps_I2_J,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 5.12/5.46 = one_one_nat ) ).
% 5.12/5.46
% 5.12/5.46 % unit_factor_simps(2)
% 5.12/5.46 thf(fact_10013_unit__factor__nat__def,axiom,
% 5.12/5.46 ( unit_f2748546683901255202or_nat
% 5.12/5.46 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % unit_factor_nat_def
% 5.12/5.46 thf(fact_10014_gcd__nat_Ocomm__monoid__axioms,axiom,
% 5.12/5.46 comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % gcd_nat.comm_monoid_axioms
% 5.12/5.46 thf(fact_10015_max__nat_Ocomm__monoid__axioms,axiom,
% 5.12/5.46 comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 5.12/5.46
% 5.12/5.46 % max_nat.comm_monoid_axioms
% 5.12/5.46 thf(fact_10016_times__num__def,axiom,
% 5.12/5.46 ( times_times_num
% 5.12/5.46 = ( ^ [M5: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M5 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_num_def
% 5.12/5.46 thf(fact_10017_less__eq__num__def,axiom,
% 5.12/5.46 ( ord_less_eq_num
% 5.12/5.46 = ( ^ [M5: num,N4: num] : ( ord_less_eq_nat @ ( nat_of_num @ M5 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_num_def
% 5.12/5.46 thf(fact_10018_nat__of__num__code_I1_J,axiom,
% 5.12/5.46 ( ( nat_of_num @ one )
% 5.12/5.46 = one_one_nat ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_code(1)
% 5.12/5.46 thf(fact_10019_nat__of__num__neq__0,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( nat_of_num @ X )
% 5.12/5.46 != zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_neq_0
% 5.12/5.46 thf(fact_10020_nat__of__num__pos,axiom,
% 5.12/5.46 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_pos
% 5.12/5.46 thf(fact_10021_nat__of__num__inc,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( nat_of_num @ ( inc @ X ) )
% 5.12/5.46 = ( suc @ ( nat_of_num @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_inc
% 5.12/5.46 thf(fact_10022_num__eq__iff,axiom,
% 5.12/5.46 ( ( ^ [Y4: num,Z: num] : ( Y4 = Z ) )
% 5.12/5.46 = ( ^ [X2: num,Y6: num] :
% 5.12/5.46 ( ( nat_of_num @ X2 )
% 5.12/5.46 = ( nat_of_num @ Y6 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % num_eq_iff
% 5.12/5.46 thf(fact_10023_nat__of__num__numeral,axiom,
% 5.12/5.46 nat_of_num = numeral_numeral_nat ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_numeral
% 5.12/5.46 thf(fact_10024_nat__of__num__inverse,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( num_of_nat @ ( nat_of_num @ X ) )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_inverse
% 5.12/5.46 thf(fact_10025_less__num__def,axiom,
% 5.12/5.46 ( ord_less_num
% 5.12/5.46 = ( ^ [M5: num,N4: num] : ( ord_less_nat @ ( nat_of_num @ M5 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_num_def
% 5.12/5.46 thf(fact_10026_nat__of__num__code_I2_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( nat_of_num @ ( bit0 @ N ) )
% 5.12/5.46 = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_code(2)
% 5.12/5.46 thf(fact_10027_nat__of__num_Osimps_I2_J,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( nat_of_num @ ( bit0 @ X ) )
% 5.12/5.46 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num.simps(2)
% 5.12/5.46 thf(fact_10028_nat__of__num__add,axiom,
% 5.12/5.46 ! [X: num,Y: num] :
% 5.12/5.46 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 5.12/5.46 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_add
% 5.12/5.46 thf(fact_10029_nat__of__num__mult,axiom,
% 5.12/5.46 ! [X: num,Y: num] :
% 5.12/5.46 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 5.12/5.46 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_mult
% 5.12/5.46 thf(fact_10030_nat__of__num__sqr,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( nat_of_num @ ( sqr @ X ) )
% 5.12/5.46 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_sqr
% 5.12/5.46 thf(fact_10031_nat__of__num_Osimps_I1_J,axiom,
% 5.12/5.46 ( ( nat_of_num @ one )
% 5.12/5.46 = ( suc @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num.simps(1)
% 5.12/5.46 thf(fact_10032_nat__of__num_Osimps_I3_J,axiom,
% 5.12/5.46 ! [X: num] :
% 5.12/5.46 ( ( nat_of_num @ ( bit1 @ X ) )
% 5.12/5.46 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num.simps(3)
% 5.12/5.46 thf(fact_10033_num__of__nat__inverse,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.12/5.46 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 5.12/5.46 = N ) ) ).
% 5.12/5.46
% 5.12/5.46 % num_of_nat_inverse
% 5.12/5.46 thf(fact_10034_nat__of__num__code_I3_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( nat_of_num @ ( bit1 @ N ) )
% 5.12/5.46 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_of_num_code(3)
% 5.12/5.46 thf(fact_10035_plus__num__def,axiom,
% 5.12/5.46 ( plus_plus_num
% 5.12/5.46 = ( ^ [M5: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M5 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_num_def
% 5.12/5.46 thf(fact_10036_real__floor__code,axiom,
% 5.12/5.46 ! [X: rat] :
% 5.12/5.46 ( ( archim6058952711729229775r_real @ ( ratreal @ X ) )
% 5.12/5.46 = ( archim3151403230148437115or_rat @ X ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_floor_code
% 5.12/5.46 thf(fact_10037_real__minus__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( minus_minus_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ratreal @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_minus_code
% 5.12/5.46 thf(fact_10038_real__inverse__code,axiom,
% 5.12/5.46 ! [X: rat] :
% 5.12/5.46 ( ( inverse_inverse_real @ ( ratreal @ X ) )
% 5.12/5.46 = ( ratreal @ ( inverse_inverse_rat @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_inverse_code
% 5.12/5.46 thf(fact_10039_real__plus__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( plus_plus_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ratreal @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_plus_code
% 5.12/5.46 thf(fact_10040_real__times__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( times_times_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ratreal @ ( times_times_rat @ X @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_times_code
% 5.12/5.46 thf(fact_10041_one__real__code,axiom,
% 5.12/5.46 ( one_one_real
% 5.12/5.46 = ( ratreal @ one_one_rat ) ) ).
% 5.12/5.46
% 5.12/5.46 % one_real_code
% 5.12/5.46 thf(fact_10042_real__uminus__code,axiom,
% 5.12/5.46 ! [X: rat] :
% 5.12/5.46 ( ( uminus_uminus_real @ ( ratreal @ X ) )
% 5.12/5.46 = ( ratreal @ ( uminus_uminus_rat @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_uminus_code
% 5.12/5.46 thf(fact_10043_Ratreal__def,axiom,
% 5.12/5.46 ratreal = field_7254667332652039916t_real ).
% 5.12/5.46
% 5.12/5.46 % Ratreal_def
% 5.12/5.46 thf(fact_10044_real__less__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( ord_less_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ord_less_rat @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_less_code
% 5.12/5.46 thf(fact_10045_zero__real__code,axiom,
% 5.12/5.46 ( zero_zero_real
% 5.12/5.46 = ( ratreal @ zero_zero_rat ) ) ).
% 5.12/5.46
% 5.12/5.46 % zero_real_code
% 5.12/5.46 thf(fact_10046_real__less__eq__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( ord_less_eq_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_less_eq_code
% 5.12/5.46 thf(fact_10047_real__divide__code,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( divide_divide_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 5.12/5.46 = ( ratreal @ ( divide_divide_rat @ X @ Y ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % real_divide_code
% 5.12/5.46 thf(fact_10048_natLeq__on__wo__rel,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( bNF_We3818239936649020644el_nat
% 5.12/5.46 @ ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLeq_on_wo_rel
% 5.12/5.46 thf(fact_10049_natLeq__natLess__Id,axiom,
% 5.12/5.46 ( bNF_Ca8459412986667044542atLess
% 5.12/5.46 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLeq_natLess_Id
% 5.12/5.46 thf(fact_10050_Field__natLeq__on,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( ( field_nat
% 5.12/5.46 @ ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) )
% 5.12/5.46 = ( collect_nat
% 5.12/5.46 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Field_natLeq_on
% 5.12/5.46 thf(fact_10051_wf__less,axiom,
% 5.12/5.46 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % wf_less
% 5.12/5.46 thf(fact_10052_wf__int__ge__less__than,axiom,
% 5.12/5.46 ! [D: int] : ( wf_int @ ( int_ge_less_than @ D ) ) ).
% 5.12/5.46
% 5.12/5.46 % wf_int_ge_less_than
% 5.12/5.46 thf(fact_10053_wf__int__ge__less__than2,axiom,
% 5.12/5.46 ! [D: int] : ( wf_int @ ( int_ge_less_than2 @ D ) ) ).
% 5.12/5.46
% 5.12/5.46 % wf_int_ge_less_than2
% 5.12/5.46 thf(fact_10054_natLeq__on__Well__order,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( order_2888998067076097458on_nat
% 5.12/5.46 @ ( field_nat
% 5.12/5.46 @ ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) )
% 5.12/5.46 @ ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLeq_on_Well_order
% 5.12/5.46 thf(fact_10055_natLeq__on__well__order__on,axiom,
% 5.12/5.46 ! [N: nat] :
% 5.12/5.46 ( order_2888998067076097458on_nat
% 5.12/5.46 @ ( collect_nat
% 5.12/5.46 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 5.12/5.46 @ ( collec3392354462482085612at_nat
% 5.12/5.46 @ ( produc6081775807080527818_nat_o
% 5.12/5.46 @ ^ [X2: nat,Y6: nat] :
% 5.12/5.46 ( ( ord_less_nat @ X2 @ N )
% 5.12/5.46 & ( ord_less_nat @ Y6 @ N )
% 5.12/5.46 & ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natLeq_on_well_order_on
% 5.12/5.46 thf(fact_10056_natural__decr,axiom,
% 5.12/5.46 ! [N: code_natural] :
% 5.12/5.46 ( ( N != zero_z2226904508553997617atural )
% 5.12/5.46 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % natural_decr
% 5.12/5.46 thf(fact_10057_minus__natural_Orep__eq,axiom,
% 5.12/5.46 ! [X: code_natural,Xa: code_natural] :
% 5.12/5.46 ( ( code_nat_of_natural @ ( minus_7197305767214868737atural @ X @ Xa ) )
% 5.12/5.46 = ( minus_minus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_natural.rep_eq
% 5.12/5.46 thf(fact_10058_one__natural_Orep__eq,axiom,
% 5.12/5.46 ( ( code_nat_of_natural @ one_one_Code_natural )
% 5.12/5.46 = one_one_nat ) ).
% 5.12/5.46
% 5.12/5.46 % one_natural.rep_eq
% 5.12/5.46 thf(fact_10059_divide__natural_Orep__eq,axiom,
% 5.12/5.46 ! [X: code_natural,Xa: code_natural] :
% 5.12/5.46 ( ( code_nat_of_natural @ ( divide5121882707175180666atural @ X @ Xa ) )
% 5.12/5.46 = ( divide_divide_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % divide_natural.rep_eq
% 5.12/5.46 thf(fact_10060_zero__natural_Orep__eq,axiom,
% 5.12/5.46 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % zero_natural.rep_eq
% 5.12/5.46 thf(fact_10061_natural__zero__minus__one,axiom,
% 5.12/5.46 ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 5.12/5.46 = zero_z2226904508553997617atural ) ).
% 5.12/5.46
% 5.12/5.46 % natural_zero_minus_one
% 5.12/5.46 thf(fact_10062_less__natural_Orep__eq,axiom,
% 5.12/5.46 ( ord_le5570908160329646204atural
% 5.12/5.46 = ( ^ [X2: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X2 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_natural.rep_eq
% 5.12/5.46 thf(fact_10063_int__of__integer__of__natural,axiom,
% 5.12/5.46 ! [N: code_natural] :
% 5.12/5.46 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ N ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % int_of_integer_of_natural
% 5.12/5.46 thf(fact_10064_integer__of__natural_Orep__eq,axiom,
% 5.12/5.46 ! [X: code_natural] :
% 5.12/5.46 ( ( code_int_of_integer @ ( code_i5400310926305786745atural @ X ) )
% 5.12/5.46 = ( semiri1314217659103216013at_int @ ( code_nat_of_natural @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_natural.rep_eq
% 5.12/5.46 thf(fact_10065_log_Osimps,axiom,
% 5.12/5.46 ( log
% 5.12/5.46 = ( ^ [B2: code_natural,I2: code_natural] :
% 5.12/5.46 ( if_Code_natural
% 5.12/5.46 @ ( ( ord_le1926595141338095240atural @ B2 @ one_one_Code_natural )
% 5.12/5.46 | ( ord_le5570908160329646204atural @ I2 @ B2 ) )
% 5.12/5.46 @ one_one_Code_natural
% 5.12/5.46 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B2 @ ( divide5121882707175180666atural @ I2 @ B2 ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % log.simps
% 5.12/5.46 thf(fact_10066_log_Oelims,axiom,
% 5.12/5.46 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 5.12/5.46 ( ( ( log @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.12/5.46 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.12/5.46 => ( Y = one_one_Code_natural ) )
% 5.12/5.46 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.12/5.46 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % log.elims
% 5.12/5.46 thf(fact_10067_minus__shift__def,axiom,
% 5.12/5.46 ( minus_shift
% 5.12/5.46 = ( ^ [R: code_natural,K3: code_natural,L2: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K3 @ L2 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R @ K3 ) @ L2 ) @ ( minus_7197305767214868737atural @ K3 @ L2 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_shift_def
% 5.12/5.46 thf(fact_10068_next_Osimps,axiom,
% 5.12/5.46 ! [V: code_natural,W: code_natural] :
% 5.12/5.46 ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 5.12/5.46 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % next.simps
% 5.12/5.46 thf(fact_10069_Random_Orange__def,axiom,
% 5.12/5.46 ( range
% 5.12/5.46 = ( ^ [K3: code_natural] :
% 5.12/5.46 ( produc5538323210962509403atural
% 5.12/5.46 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K3 )
% 5.12/5.46 @ ^ [L2: code_natural] :
% 5.12/5.46 ( produc5538323210962509403atural @ next
% 5.12/5.46 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V4 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.12/5.46 @ one_one_Code_natural )
% 5.12/5.46 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V4 @ K3 ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Random.range_def
% 5.12/5.46 thf(fact_10070_inc__shift__def,axiom,
% 5.12/5.46 ( inc_shift
% 5.12/5.46 = ( ^ [V4: code_natural,K3: code_natural] : ( if_Code_natural @ ( V4 = K3 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K3 @ one_one_Code_natural ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % inc_shift_def
% 5.12/5.46 thf(fact_10071_log_Opelims,axiom,
% 5.12/5.46 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 5.12/5.46 ( ( ( log @ X @ Xa )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 5.12/5.46 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.12/5.46 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.12/5.46 => ( Y = one_one_Code_natural ) )
% 5.12/5.46 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.12/5.46 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 5.12/5.46 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % log.pelims
% 5.12/5.46 thf(fact_10072_integer__of__natural__def,axiom,
% 5.12/5.46 ( code_i5400310926305786745atural
% 5.12/5.46 = ( map_fu2787874002554666395nteger @ code_nat_of_natural @ code_integer_of_int @ semiri1314217659103216013at_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_natural_def
% 5.12/5.46 thf(fact_10073_zero__natural__def,axiom,
% 5.12/5.46 ( zero_z2226904508553997617atural
% 5.12/5.46 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % zero_natural_def
% 5.12/5.46 thf(fact_10074_minus__natural_Oabs__eq,axiom,
% 5.12/5.46 ! [Xa: nat,X: nat] :
% 5.12/5.46 ( ( minus_7197305767214868737atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 5.12/5.46 = ( code_natural_of_nat @ ( minus_minus_nat @ Xa @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_natural.abs_eq
% 5.12/5.46 thf(fact_10075_divide__natural_Oabs__eq,axiom,
% 5.12/5.46 ! [Xa: nat,X: nat] :
% 5.12/5.46 ( ( divide5121882707175180666atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 5.12/5.46 = ( code_natural_of_nat @ ( divide_divide_nat @ Xa @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % divide_natural.abs_eq
% 5.12/5.46 thf(fact_10076_less__natural_Oabs__eq,axiom,
% 5.12/5.46 ! [Xa: nat,X: nat] :
% 5.12/5.46 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 5.12/5.46 = ( ord_less_nat @ Xa @ X ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_natural.abs_eq
% 5.12/5.46 thf(fact_10077_one__natural__def,axiom,
% 5.12/5.46 ( one_one_Code_natural
% 5.12/5.46 = ( code_natural_of_nat @ one_one_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % one_natural_def
% 5.12/5.46 thf(fact_10078_integer__of__natural_Oabs__eq,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( code_i5400310926305786745atural @ ( code_natural_of_nat @ X ) )
% 5.12/5.46 = ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_natural.abs_eq
% 5.12/5.46 thf(fact_10079_Suc_Orep__eq,axiom,
% 5.12/5.46 ! [X: code_natural] :
% 5.12/5.46 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 5.12/5.46 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Suc.rep_eq
% 5.12/5.46 thf(fact_10080_Suc__natural__minus__one,axiom,
% 5.12/5.46 ! [N: code_natural] :
% 5.12/5.46 ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 5.12/5.46 = N ) ).
% 5.12/5.46
% 5.12/5.46 % Suc_natural_minus_one
% 5.12/5.46 thf(fact_10081_Suc_Oabs__eq,axiom,
% 5.12/5.46 ! [X: nat] :
% 5.12/5.46 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 5.12/5.46 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Suc.abs_eq
% 5.12/5.46 thf(fact_10082_Code__Numeral_OSuc__def,axiom,
% 5.12/5.46 ( code_Suc
% 5.12/5.46 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 5.12/5.46
% 5.12/5.46 % Code_Numeral.Suc_def
% 5.12/5.46 thf(fact_10083_divide__natural__def,axiom,
% 5.12/5.46 ( divide5121882707175180666atural
% 5.12/5.46 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ divide_divide_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % divide_natural_def
% 5.12/5.46 thf(fact_10084_minus__natural__def,axiom,
% 5.12/5.46 ( minus_7197305767214868737atural
% 5.12/5.46 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ minus_minus_nat ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_natural_def
% 5.12/5.46 thf(fact_10085_Quotient3__int,axiom,
% 5.12/5.46 quotie6776551016481293500at_int @ intrel @ abs_Integ @ rep_Integ ).
% 5.12/5.46
% 5.12/5.46 % Quotient3_int
% 5.12/5.46 thf(fact_10086_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.12/5.46 ! [X: vEBT_VEBT,Y: $o] :
% 5.12/5.46 ( ( ( vEBT_VEBT_minNull @ X )
% 5.12/5.46 = Y )
% 5.12/5.46 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.12/5.46 => ( ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.12/5.46 => ( ! [Uv2: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.12/5.46 => ( ~ Y
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.12/5.46 => ( ! [Uu2: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.12/5.46 => ( ~ Y
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.12/5.46 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) )
% 5.12/5.46 => ( Y
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) ) ) )
% 5.12/5.46 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.12/5.46 => ( ~ Y
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.minNull.pelims(1)
% 5.12/5.46 thf(fact_10087_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.12/5.46 ! [X: vEBT_VEBT] :
% 5.12/5.46 ( ( vEBT_VEBT_minNull @ X )
% 5.12/5.46 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.12/5.46 => ( ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ $false @ $false ) )
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.12/5.46 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) )
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.minNull.pelims(2)
% 5.12/5.46 thf(fact_10088_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.12/5.46 ! [X: vEBT_VEBT] :
% 5.12/5.46 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.12/5.46 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.12/5.46 => ( ! [Uv2: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.12/5.46 => ( ! [Uu2: $o] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.12/5.46 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.12/5.46 ( ( X
% 5.12/5.46 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.12/5.46 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % VEBT_internal.minNull.pelims(3)
% 5.12/5.46 thf(fact_10089_sub_Otransfer,axiom,
% 5.12/5.46 ( bNF_re7876454716742015248nteger
% 5.12/5.46 @ ^ [Y4: num,Z: num] : ( Y4 = Z )
% 5.12/5.46 @ ( bNF_re6501075790457514782nteger
% 5.12/5.46 @ ^ [Y4: num,Z: num] : ( Y4 = Z )
% 5.12/5.46 @ code_pcr_integer )
% 5.12/5.46 @ ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) )
% 5.12/5.46 @ code_sub ) ).
% 5.12/5.46
% 5.12/5.46 % sub.transfer
% 5.12/5.46 thf(fact_10090_one__integer_Otransfer,axiom,
% 5.12/5.46 code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 5.12/5.46
% 5.12/5.46 % one_integer.transfer
% 5.12/5.46 thf(fact_10091_less__integer_Otransfer,axiom,
% 5.12/5.46 ( bNF_re6321650412969554871eger_o @ code_pcr_integer
% 5.12/5.46 @ ( bNF_re6574881592172037608er_o_o @ code_pcr_integer
% 5.12/5.46 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.46 @ ord_less_int
% 5.12/5.46 @ ord_le6747313008572928689nteger ) ).
% 5.12/5.46
% 5.12/5.46 % less_integer.transfer
% 5.12/5.46 thf(fact_10092_divide__integer_Otransfer,axiom,
% 5.12/5.46 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ divide_divide_int @ divide6298287555418463151nteger ).
% 5.12/5.46
% 5.12/5.46 % divide_integer.transfer
% 5.12/5.46 thf(fact_10093_minus__integer_Otransfer,axiom,
% 5.12/5.46 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ minus_minus_int @ minus_8373710615458151222nteger ).
% 5.12/5.46
% 5.12/5.46 % minus_integer.transfer
% 5.12/5.46 thf(fact_10094_uminus__integer_Otransfer,axiom,
% 5.12/5.46 bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 5.12/5.46
% 5.12/5.46 % uminus_integer.transfer
% 5.12/5.46 thf(fact_10095_integer__of__nat_Otransfer,axiom,
% 5.12/5.46 ( bNF_re4153400068438556298nteger
% 5.12/5.46 @ ^ [Y4: nat,Z: nat] : ( Y4 = Z )
% 5.12/5.46 @ code_pcr_integer
% 5.12/5.46 @ semiri1314217659103216013at_int
% 5.12/5.46 @ code_integer_of_nat ) ).
% 5.12/5.46
% 5.12/5.46 % integer_of_nat.transfer
% 5.12/5.46 thf(fact_10096_zero__integer_Otransfer,axiom,
% 5.12/5.46 code_pcr_integer @ zero_zero_int @ zero_z3403309356797280102nteger ).
% 5.12/5.46
% 5.12/5.46 % zero_integer.transfer
% 5.12/5.46 thf(fact_10097_integer__of__natural_Otransfer,axiom,
% 5.12/5.46 bNF_re5252274238750452962nteger @ code_pcr_natural @ code_pcr_integer @ semiri1314217659103216013at_int @ code_i5400310926305786745atural ).
% 5.12/5.46
% 5.12/5.46 % integer_of_natural.transfer
% 5.12/5.46 thf(fact_10098_Suc_Otransfer,axiom,
% 5.12/5.46 bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural @ suc @ code_Suc ).
% 5.12/5.46
% 5.12/5.46 % Suc.transfer
% 5.12/5.46 thf(fact_10099_divide__natural_Otransfer,axiom,
% 5.12/5.46 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ divide_divide_nat @ divide5121882707175180666atural ).
% 5.12/5.46
% 5.12/5.46 % divide_natural.transfer
% 5.12/5.46 thf(fact_10100_less__natural_Otransfer,axiom,
% 5.12/5.46 ( bNF_re1639080489988575423ural_o @ code_pcr_natural
% 5.12/5.46 @ ( bNF_re2785088596696291543al_o_o @ code_pcr_natural
% 5.12/5.46 @ ^ [Y4: $o,Z: $o] : ( Y4 = Z ) )
% 5.12/5.46 @ ord_less_nat
% 5.12/5.46 @ ord_le5570908160329646204atural ) ).
% 5.12/5.46
% 5.12/5.46 % less_natural.transfer
% 5.12/5.46 thf(fact_10101_minus__natural_Otransfer,axiom,
% 5.12/5.46 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ minus_minus_nat @ minus_7197305767214868737atural ).
% 5.12/5.46
% 5.12/5.46 % minus_natural.transfer
% 5.12/5.46 thf(fact_10102_zero__natural_Otransfer,axiom,
% 5.12/5.46 code_pcr_natural @ zero_zero_nat @ zero_z2226904508553997617atural ).
% 5.12/5.46
% 5.12/5.46 % zero_natural.transfer
% 5.12/5.46 thf(fact_10103_one__natural_Otransfer,axiom,
% 5.12/5.46 code_pcr_natural @ one_one_nat @ one_one_Code_natural ).
% 5.12/5.46
% 5.12/5.46 % one_natural.transfer
% 5.12/5.46 thf(fact_10104_less__int__code_I3_J,axiom,
% 5.12/5.46 ! [L: num] :
% 5.12/5.46 ~ ( ord_less_int @ zero_zero_int @ ( neg @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(3)
% 5.12/5.46 thf(fact_10105_less__int__code_I7_J,axiom,
% 5.12/5.46 ! [K: num] : ( ord_less_int @ ( neg @ K ) @ zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(7)
% 5.12/5.46 thf(fact_10106_less__int__code_I9_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ( ( ord_less_int @ ( neg @ K ) @ ( neg @ L ) )
% 5.12/5.46 = ( ord_less_num @ L @ K ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(9)
% 5.12/5.46 thf(fact_10107_nat__code_I1_J,axiom,
% 5.12/5.46 ! [K: num] :
% 5.12/5.46 ( ( nat2 @ ( neg @ K ) )
% 5.12/5.46 = zero_zero_nat ) ).
% 5.12/5.46
% 5.12/5.46 % nat_code(1)
% 5.12/5.46 thf(fact_10108_less__eq__int__code_I7_J,axiom,
% 5.12/5.46 ! [K: num] : ( ord_less_eq_int @ ( neg @ K ) @ zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(7)
% 5.12/5.46 thf(fact_10109_less__eq__int__code_I3_J,axiom,
% 5.12/5.46 ! [L: num] :
% 5.12/5.46 ~ ( ord_less_eq_int @ zero_zero_int @ ( neg @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(3)
% 5.12/5.46 thf(fact_10110_less__eq__int__code_I9_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ( ( ord_less_eq_int @ ( neg @ K ) @ ( neg @ L ) )
% 5.12/5.46 = ( ord_less_eq_num @ L @ K ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(9)
% 5.12/5.46 thf(fact_10111_plus__int__code_I6_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( plus_plus_int @ ( neg @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( neg @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_int_code(6)
% 5.12/5.46 thf(fact_10112_Int_Osub__code_I4_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( sub @ one @ ( bit0 @ N ) )
% 5.12/5.46 = ( neg @ ( bitM @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(4)
% 5.12/5.46 thf(fact_10113_Int_Osub__code_I5_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( sub @ one @ ( bit1 @ N ) )
% 5.12/5.46 = ( neg @ ( bit0 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(5)
% 5.12/5.46 thf(fact_10114_minus__int__code_I6_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( minus_minus_int @ ( neg @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( sub @ N @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_int_code(6)
% 5.12/5.46 thf(fact_10115_Int_Osub__def,axiom,
% 5.12/5.46 ( sub
% 5.12/5.46 = ( ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_def
% 5.12/5.46 thf(fact_10116_Int_Osub__code_I1_J,axiom,
% 5.12/5.46 ( ( sub @ one @ one )
% 5.12/5.46 = zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(1)
% 5.12/5.46 thf(fact_10117_Int_Osub__code_I9_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( sub @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.46 = ( minus_minus_int @ ( dup @ ( sub @ M2 @ N ) ) @ one_one_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(9)
% 5.12/5.46 thf(fact_10118_Int_Osub__code_I8_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( sub @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 5.12/5.46 = ( plus_plus_int @ ( dup @ ( sub @ M2 @ N ) ) @ one_one_int ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(8)
% 5.12/5.46 thf(fact_10119_Int_Odup__code_I1_J,axiom,
% 5.12/5.46 ( ( dup @ zero_zero_int )
% 5.12/5.46 = zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % Int.dup_code(1)
% 5.12/5.46 thf(fact_10120_Int_Odup__def,axiom,
% 5.12/5.46 ( dup
% 5.12/5.46 = ( ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.dup_def
% 5.12/5.46 thf(fact_10121_Int_Odup__code_I3_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( dup @ ( neg @ N ) )
% 5.12/5.46 = ( neg @ ( bit0 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.dup_code(3)
% 5.12/5.46 thf(fact_10122_Int_Osub__code_I6_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( sub @ ( bit0 @ M2 ) @ ( bit0 @ N ) )
% 5.12/5.46 = ( dup @ ( sub @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(6)
% 5.12/5.46 thf(fact_10123_Int_Osub__code_I7_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( sub @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 5.12/5.46 = ( dup @ ( sub @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(7)
% 5.12/5.46 thf(fact_10124_Int_Osub__code_I2_J,axiom,
% 5.12/5.46 ! [M2: num] :
% 5.12/5.46 ( ( sub @ ( bit0 @ M2 ) @ one )
% 5.12/5.46 = ( pos @ ( bitM @ M2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(2)
% 5.12/5.46 thf(fact_10125_Int_Osub__code_I3_J,axiom,
% 5.12/5.46 ! [M2: num] :
% 5.12/5.46 ( ( sub @ ( bit1 @ M2 ) @ one )
% 5.12/5.46 = ( pos @ ( bit0 @ M2 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.sub_code(3)
% 5.12/5.46 thf(fact_10126_Int_Odup__code_I2_J,axiom,
% 5.12/5.46 ! [N: num] :
% 5.12/5.46 ( ( dup @ ( pos @ N ) )
% 5.12/5.46 = ( pos @ ( bit0 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.dup_code(2)
% 5.12/5.46 thf(fact_10127_less__int__code_I6_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ~ ( ord_less_int @ ( pos @ K ) @ ( neg @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(6)
% 5.12/5.46 thf(fact_10128_less__int__code_I8_J,axiom,
% 5.12/5.46 ! [K: num,L: num] : ( ord_less_int @ ( neg @ K ) @ ( pos @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(8)
% 5.12/5.46 thf(fact_10129_uminus__int__code_I3_J,axiom,
% 5.12/5.46 ! [M2: num] :
% 5.12/5.46 ( ( uminus_uminus_int @ ( neg @ M2 ) )
% 5.12/5.46 = ( pos @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % uminus_int_code(3)
% 5.12/5.46 thf(fact_10130_uminus__int__code_I2_J,axiom,
% 5.12/5.46 ! [M2: num] :
% 5.12/5.46 ( ( uminus_uminus_int @ ( pos @ M2 ) )
% 5.12/5.46 = ( neg @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % uminus_int_code(2)
% 5.12/5.46 thf(fact_10131_Int_ONeg__def,axiom,
% 5.12/5.46 ( neg
% 5.12/5.46 = ( ^ [N4: num] : ( uminus_uminus_int @ ( pos @ N4 ) ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % Int.Neg_def
% 5.12/5.46 thf(fact_10132_less__eq__int__code_I6_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ~ ( ord_less_eq_int @ ( pos @ K ) @ ( neg @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(6)
% 5.12/5.46 thf(fact_10133_less__eq__int__code_I8_J,axiom,
% 5.12/5.46 ! [K: num,L: num] : ( ord_less_eq_int @ ( neg @ K ) @ ( pos @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(8)
% 5.12/5.46 thf(fact_10134_times__int__code_I3_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( times_times_int @ ( pos @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( pos @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_int_code(3)
% 5.12/5.46 thf(fact_10135_Int_OPos__def,axiom,
% 5.12/5.46 pos = numeral_numeral_int ).
% 5.12/5.46
% 5.12/5.46 % Int.Pos_def
% 5.12/5.46 thf(fact_10136_plus__int__code_I3_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( plus_plus_int @ ( pos @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( pos @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_int_code(3)
% 5.12/5.46 thf(fact_10137_less__eq__int__code_I5_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ( ( ord_less_eq_int @ ( pos @ K ) @ ( pos @ L ) )
% 5.12/5.46 = ( ord_less_eq_num @ K @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(5)
% 5.12/5.46 thf(fact_10138_less__eq__int__code_I2_J,axiom,
% 5.12/5.46 ! [L: num] : ( ord_less_eq_int @ zero_zero_int @ ( pos @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(2)
% 5.12/5.46 thf(fact_10139_less__eq__int__code_I4_J,axiom,
% 5.12/5.46 ! [K: num] :
% 5.12/5.46 ~ ( ord_less_eq_int @ ( pos @ K ) @ zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % less_eq_int_code(4)
% 5.12/5.46 thf(fact_10140_nat__code_I3_J,axiom,
% 5.12/5.46 ! [K: num] :
% 5.12/5.46 ( ( nat2 @ ( pos @ K ) )
% 5.12/5.46 = ( nat_of_num @ K ) ) ).
% 5.12/5.46
% 5.12/5.46 % nat_code(3)
% 5.12/5.46 thf(fact_10141_less__int__code_I5_J,axiom,
% 5.12/5.46 ! [K: num,L: num] :
% 5.12/5.46 ( ( ord_less_int @ ( pos @ K ) @ ( pos @ L ) )
% 5.12/5.46 = ( ord_less_num @ K @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(5)
% 5.12/5.46 thf(fact_10142_one__int__code,axiom,
% 5.12/5.46 ( one_one_int
% 5.12/5.46 = ( pos @ one ) ) ).
% 5.12/5.46
% 5.12/5.46 % one_int_code
% 5.12/5.46 thf(fact_10143_less__int__code_I4_J,axiom,
% 5.12/5.46 ! [K: num] :
% 5.12/5.46 ~ ( ord_less_int @ ( pos @ K ) @ zero_zero_int ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(4)
% 5.12/5.46 thf(fact_10144_less__int__code_I2_J,axiom,
% 5.12/5.46 ! [L: num] : ( ord_less_int @ zero_zero_int @ ( pos @ L ) ) ).
% 5.12/5.46
% 5.12/5.46 % less_int_code(2)
% 5.12/5.46 thf(fact_10145_minus__int__code_I3_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( minus_minus_int @ ( pos @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( sub @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_int_code(3)
% 5.12/5.46 thf(fact_10146_minus__int__code_I4_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( minus_minus_int @ ( pos @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( pos @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_int_code(4)
% 5.12/5.46 thf(fact_10147_minus__int__code_I5_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( minus_minus_int @ ( neg @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( neg @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % minus_int_code(5)
% 5.12/5.46 thf(fact_10148_times__int__code_I4_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( times_times_int @ ( pos @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( neg @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_int_code(4)
% 5.12/5.46 thf(fact_10149_times__int__code_I5_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( times_times_int @ ( neg @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( neg @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_int_code(5)
% 5.12/5.46 thf(fact_10150_times__int__code_I6_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( times_times_int @ ( neg @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( pos @ ( times_times_num @ M2 @ N ) ) ) ).
% 5.12/5.46
% 5.12/5.46 % times_int_code(6)
% 5.12/5.46 thf(fact_10151_plus__int__code_I5_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( plus_plus_int @ ( neg @ M2 ) @ ( pos @ N ) )
% 5.12/5.46 = ( sub @ N @ M2 ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_int_code(5)
% 5.12/5.46 thf(fact_10152_plus__int__code_I4_J,axiom,
% 5.12/5.46 ! [M2: num,N: num] :
% 5.12/5.46 ( ( plus_plus_int @ ( pos @ M2 ) @ ( neg @ N ) )
% 5.12/5.46 = ( sub @ M2 @ N ) ) ).
% 5.12/5.46
% 5.12/5.46 % plus_int_code(4)
% 5.12/5.46 thf(fact_10153_Quotient3__real,axiom,
% 5.12/5.46 quotie8700032322157300518t_real @ realrel @ real2 @ rep_real ).
% 5.12/5.46
% 5.12/5.46 % Quotient3_real
% 5.12/5.46
% 5.12/5.46 % Helper facts (38)
% 5.12/5.46 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.12/5.46 ! [X: int,Y: int] :
% 5.12/5.46 ( ( if_int @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.12/5.46 ! [X: int,Y: int] :
% 5.12/5.46 ( ( if_int @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.12/5.46 ! [X: nat,Y: nat] :
% 5.12/5.46 ( ( if_nat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.12/5.46 ! [X: nat,Y: nat] :
% 5.12/5.46 ( ( if_nat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.12/5.46 ! [X: num,Y: num] :
% 5.12/5.46 ( ( if_num @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.12/5.46 ! [X: num,Y: num] :
% 5.12/5.46 ( ( if_num @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( if_rat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.12/5.46 ! [X: rat,Y: rat] :
% 5.12/5.46 ( ( if_rat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.12/5.46 ! [X: real,Y: real] :
% 5.12/5.46 ( ( if_real @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.12/5.46 ! [X: real,Y: real] :
% 5.12/5.46 ( ( if_real @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.12/5.46 ! [P: real > $o] :
% 5.12/5.46 ( ( P @ ( fChoice_real @ P ) )
% 5.12/5.46 = ( ? [X7: real] : ( P @ X7 ) ) ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.12/5.46 ! [X: complex,Y: complex] :
% 5.12/5.46 ( ( if_complex @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.12/5.46 ! [X: complex,Y: complex] :
% 5.12/5.46 ( ( if_complex @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.12/5.46 ! [X: extended_enat,Y: extended_enat] :
% 5.12/5.46 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.12/5.46 ! [X: extended_enat,Y: extended_enat] :
% 5.12/5.46 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.12/5.46 ! [X: code_integer,Y: code_integer] :
% 5.12/5.46 ( ( if_Code_integer @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.12/5.46 ! [X: code_integer,Y: code_integer] :
% 5.12/5.46 ( ( if_Code_integer @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 5.12/5.46 ! [X: code_natural,Y: code_natural] :
% 5.12/5.46 ( ( if_Code_natural @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 5.12/5.46 ! [X: code_natural,Y: code_natural] :
% 5.12/5.46 ( ( if_Code_natural @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: set_int,Y: set_int] :
% 5.12/5.46 ( ( if_set_int @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: set_int,Y: set_int] :
% 5.12/5.46 ( ( if_set_int @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: list_int,Y: list_int] :
% 5.12/5.46 ( ( if_list_int @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: list_int,Y: list_int] :
% 5.12/5.46 ( ( if_list_int @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.12/5.46 ! [X: list_nat,Y: list_nat] :
% 5.12/5.46 ( ( if_list_nat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.12/5.46 ! [X: list_nat,Y: list_nat] :
% 5.12/5.46 ( ( if_list_nat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.12/5.46 ! [X: nat > rat,Y: nat > rat] :
% 5.12/5.46 ( ( if_nat_rat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.12/5.46 ! [X: nat > rat,Y: nat > rat] :
% 5.12/5.46 ( ( if_nat_rat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.12/5.46 ! [X: option_num,Y: option_num] :
% 5.12/5.46 ( ( if_option_num @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.12/5.46 ! [X: option_num,Y: option_num] :
% 5.12/5.46 ( ( if_option_num @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.12/5.46 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.12/5.46 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.12/5.46 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.12/5.46 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.12/5.46 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.12/5.46 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.12/5.46 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.12/5.46 = X ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.12/5.46 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.12/5.46 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 5.12/5.46 = Y ) ).
% 5.12/5.46
% 5.12/5.46 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.12/5.46 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.19/6.56 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 6.19/6.56 = X ) ).
% 6.19/6.56
% 6.19/6.56 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.19/6.56 ! [P: $o] :
% 6.19/6.56 ( ( P = $true )
% 6.19/6.56 | ( P = $false ) ) ).
% 6.19/6.56
% 6.19/6.56 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.19/6.56 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.19/6.56 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 6.19/6.56 = Y ) ).
% 6.19/6.56
% 6.19/6.56 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.19/6.56 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.19/6.56 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 6.19/6.56 = X ) ).
% 6.19/6.56
% 6.19/6.56 % Conjectures (2)
% 6.19/6.56 thf(conj_0,hypothesis,
% 6.19/6.56 vEBT_invar_vebt @ t @ n ).
% 6.19/6.56
% 6.19/6.56 thf(conj_1,conjecture,
% 6.19/6.56 ( ( vEBT_vebt_member @ t @ x )
% 6.19/6.56 = ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ) ).
% 6.19/6.56
% 6.19/6.56 %------------------------------------------------------------------------------
% 6.19/6.56 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.vjHYePTLts/cvc5---1.0.5_32386.p...
% 6.19/6.56 (declare-sort $$unsorted 0)
% 6.19/6.56 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.19/6.56 (declare-sort tptp.produc5835291356934675326atural 0)
% 6.19/6.56 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.19/6.56 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.19/6.56 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.19/6.56 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.19/6.56 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.19/6.56 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.19/6.56 (declare-sort tptp.produc7822875418678951345atural 0)
% 6.19/6.56 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.19/6.56 (declare-sort tptp.produc7272778201969148633d_enat 0)
% 6.19/6.56 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.19/6.56 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.19/6.56 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.19/6.56 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.19/6.56 (declare-sort tptp.list_P1726324292696863441at_num 0)
% 6.19/6.56 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.19/6.56 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.19/6.56 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.19/6.56 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.19/6.56 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.19/6.56 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.19/6.56 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.19/6.56 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.19/6.56 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.19/6.56 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.19/6.56 (declare-sort tptp.product_prod_num_num 0)
% 6.19/6.56 (declare-sort tptp.product_prod_nat_num 0)
% 6.19/6.56 (declare-sort tptp.product_prod_nat_nat 0)
% 6.19/6.56 (declare-sort tptp.product_prod_int_int 0)
% 6.19/6.56 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.19/6.56 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.19/6.56 (declare-sort tptp.set_list_nat 0)
% 6.19/6.56 (declare-sort tptp.product_prod_o_nat 0)
% 6.19/6.56 (declare-sort tptp.product_prod_o_int 0)
% 6.19/6.56 (declare-sort tptp.list_set_nat 0)
% 6.19/6.56 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.19/6.56 (declare-sort tptp.set_set_nat 0)
% 6.19/6.56 (declare-sort tptp.set_Code_integer 0)
% 6.19/6.56 (declare-sort tptp.set_Product_unit 0)
% 6.19/6.56 (declare-sort tptp.list_complex 0)
% 6.19/6.56 (declare-sort tptp.product_prod_o_o 0)
% 6.19/6.56 (declare-sort tptp.set_complex 0)
% 6.19/6.56 (declare-sort tptp.filter_real 0)
% 6.19/6.56 (declare-sort tptp.option_num 0)
% 6.19/6.56 (declare-sort tptp.filter_nat 0)
% 6.19/6.56 (declare-sort tptp.filter_int 0)
% 6.19/6.56 (declare-sort tptp.set_char 0)
% 6.19/6.56 (declare-sort tptp.list_real 0)
% 6.19/6.56 (declare-sort tptp.set_real 0)
% 6.19/6.56 (declare-sort tptp.list_num 0)
% 6.19/6.56 (declare-sort tptp.list_nat 0)
% 6.19/6.56 (declare-sort tptp.list_int 0)
% 6.19/6.56 (declare-sort tptp.vEBT_VEBT 0)
% 6.19/6.56 (declare-sort tptp.set_rat 0)
% 6.19/6.56 (declare-sort tptp.set_num 0)
% 6.19/6.56 (declare-sort tptp.set_nat 0)
% 6.19/6.56 (declare-sort tptp.set_int 0)
% 6.19/6.56 (declare-sort tptp.code_natural 0)
% 6.19/6.56 (declare-sort tptp.code_integer 0)
% 6.19/6.56 (declare-sort tptp.product_unit 0)
% 6.19/6.56 (declare-sort tptp.extended_enat 0)
% 6.19/6.56 (declare-sort tptp.list_o 0)
% 6.19/6.56 (declare-sort tptp.complex 0)
% 6.19/6.56 (declare-sort tptp.literal 0)
% 6.19/6.56 (declare-sort tptp.set_o 0)
% 6.19/6.56 (declare-sort tptp.char 0)
% 6.19/6.56 (declare-sort tptp.real 0)
% 6.19/6.56 (declare-sort tptp.rat 0)
% 6.19/6.56 (declare-sort tptp.num 0)
% 6.19/6.56 (declare-sort tptp.nat 0)
% 6.19/6.56 (declare-sort tptp.int 0)
% 6.19/6.56 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.19/6.56 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.19/6.56 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.19/6.56 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.19/6.56 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.19/6.56 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.19/6.56 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re6321650412969554871eger_o ((-> tptp.int tptp.code_integer Bool) (-> (-> tptp.int Bool) (-> tptp.code_integer Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.code_integer tptp.code_integer Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re398004352372739002nteger ((-> tptp.int tptp.code_integer Bool) (-> (-> tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re6574881592172037608er_o_o ((-> tptp.int tptp.code_integer Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.code_integer Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re3379532845092657523nteger ((-> tptp.int tptp.code_integer Bool) (-> tptp.int tptp.code_integer Bool) (-> tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re157797125943740599nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.product_prod_int_int)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re3461391660133120880nt_rat ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re6250860962936578807nt_int ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re2214769303045360666nt_rat ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re1639080489988575423ural_o ((-> tptp.nat tptp.code_natural Bool) (-> (-> tptp.nat Bool) (-> tptp.code_natural Bool) Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.code_natural tptp.code_natural Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re88643428490162567atural ((-> tptp.nat tptp.code_natural Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural tptp.code_natural)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re2785088596696291543al_o_o ((-> tptp.nat tptp.code_natural Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.code_natural Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re5252274238750452962nteger ((-> tptp.nat tptp.code_natural Bool) (-> tptp.int tptp.code_integer Bool) (-> tptp.nat tptp.int) (-> tptp.code_natural tptp.code_integer)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re3704215830270325841atural ((-> tptp.nat tptp.code_natural Bool) (-> tptp.nat tptp.code_natural Bool) (-> tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re4153400068438556298nteger ((-> tptp.nat tptp.nat Bool) (-> tptp.int tptp.code_integer Bool) (-> tptp.nat tptp.int) (-> tptp.nat tptp.code_integer)) Bool)
% 6.19/6.56 (declare-fun tptp.bNF_re6650684261131312217nt_int ((-> tptp.nat tptp.nat Bool) (-> tptp.int tptp.int Bool) (-> tptp.nat tptp.int) (-> tptp.nat tptp.int)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re7876454716742015248nteger ((-> tptp.num tptp.num Bool) (-> (-> tptp.num tptp.int) (-> tptp.num tptp.code_integer) Bool) (-> tptp.num tptp.num tptp.int) (-> tptp.num tptp.num tptp.code_integer)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re6501075790457514782nteger ((-> tptp.num tptp.num Bool) (-> tptp.int tptp.code_integer Bool) (-> tptp.num tptp.int) (-> tptp.num tptp.code_integer)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re7145576690424134365nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re8279943556446156061nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re4555766996558763186at_nat ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.int tptp.nat)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_re8246922863344978751at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat)) Bool)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.19/6.56 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se2773287842338716102atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se168947363167071951atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se1617098188084679374atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se569199155075624693atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se7083795435491715335atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.bit_se8040316288895769887atural (tptp.code_natural tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.19/6.56 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.19/6.56 (declare-fun tptp.code_Suc (tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.19/6.56 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.19/6.56 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_i5400310926305786745atural (tptp.code_natural) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.19/6.56 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 6.19/6.56 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.19/6.56 (declare-fun tptp.code_pcr_integer (tptp.int tptp.code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.code_pcr_natural (tptp.nat tptp.code_natural) Bool)
% 6.19/6.56 (declare-fun tptp.code_sub (tptp.num tptp.num) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.code_T6385005292777649522of_nat (tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.complete_Inf_Inf_int (tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.19/6.56 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.19/6.56 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.19/6.56 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.19/6.56 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.19/6.56 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.19/6.56 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.euclid3398187327856392827nt_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 6.19/6.56 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.semiri2447717529341329178atural (tptp.nat) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.19/6.56 (declare-fun tptp.at_top_int () tptp.filter_int)
% 6.19/6.56 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.19/6.56 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.19/6.56 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.19/6.56 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.19/6.56 (declare-fun tptp.filterlim_nat_int ((-> tptp.nat tptp.int) tptp.filter_int tptp.filter_nat) Bool)
% 6.19/6.56 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.19/6.56 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.19/6.56 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.19/6.56 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.19/6.56 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.bij_betw_int_nat ((-> tptp.int tptp.nat) tptp.set_int tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_be8532844293280997160at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.bij_betw_nat_int ((-> tptp.nat tptp.int) tptp.set_nat tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.bij_be6293887246118711976st_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat tptp.set_list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_be8693218025023041337at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bij_be5333170631980326235at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.id_o (Bool) Bool)
% 6.19/6.56 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.inj_on_int_nat ((-> tptp.int tptp.nat) tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_nat_list_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on5538052773655684606at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on2178005380612969504at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.19/6.56 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.map_fu8272188784021352819nteger ((-> tptp.code_integer tptp.int) (-> (-> tptp.int tptp.int) tptp.code_integer tptp.code_integer) (-> tptp.int tptp.int tptp.int) tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.map_fu2599414010547811884nteger ((-> tptp.code_integer tptp.int) (-> tptp.int tptp.code_integer) (-> tptp.int tptp.int) tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.map_fu6549440983881763648atural ((-> tptp.code_natural tptp.nat) (-> (-> tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) (-> tptp.nat tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.map_fu2787874002554666395nteger ((-> tptp.code_natural tptp.nat) (-> tptp.int tptp.code_integer) (-> tptp.nat tptp.int) tptp.code_natural) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.map_fu1239815594074539274atural ((-> tptp.code_natural tptp.nat) (-> tptp.nat tptp.code_natural) (-> tptp.nat tptp.nat) tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.map_fu6290471996055670595nteger ((-> tptp.nat tptp.nat) (-> tptp.int tptp.code_integer) (-> tptp.nat tptp.int) tptp.nat) tptp.code_integer)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.map_fu5673905371560938248nt_rat ((-> tptp.rat tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat) tptp.rat)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.fun_is_measure_int ((-> tptp.int tptp.nat)) Bool)
% 6.19/6.56 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.19/6.56 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.19/6.56 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.gcd_Lcm_int (tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.gcd_lcm_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.comm_monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 6.19/6.56 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.minus_2270307095948843157_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.minus_7197305767214868737atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.19/6.56 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.19/6.56 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.one_one_int () tptp.int)
% 6.19/6.56 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.19/6.56 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.19/6.56 (declare-fun tptp.one_one_real () tptp.real)
% 6.19/6.56 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.plus_plus_literal (tptp.literal tptp.literal) tptp.literal)
% 6.19/6.56 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.uminus1680532995456772888plex_o ((-> tptp.complex Bool) tptp.complex) Bool)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.uminus5770388063884162150_nat_o ((-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_real_o ((-> tptp.real Bool) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.uminus3195874150345416415st_nat (tptp.set_list_nat) tptp.set_list_nat)
% 6.19/6.56 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.19/6.56 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.19/6.56 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.19/6.56 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.19/6.56 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.19/6.56 (declare-fun tptp.zero_zero_literal () tptp.literal)
% 6.19/6.56 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.19/6.56 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.19/6.56 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.19/6.56 (declare-fun tptp.groups9119017779487936845_o_nat ((-> Bool tptp.nat) tptp.nat tptp.list_o) tptp.nat)
% 6.19/6.56 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.19/6.56 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.19/6.56 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.if_Code_natural (Bool tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.19/6.56 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.neg (tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.pos (tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.cr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.dup (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.19/6.56 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.19/6.56 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.19/6.56 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 6.19/6.56 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 6.19/6.56 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 6.19/6.56 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.19/6.56 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.19/6.56 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.19/6.56 (declare-fun tptp.sub (tptp.num tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.semila9081495762789891438tr_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.lattic7826324295020591184_F_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.set_nat) tptp.nat)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.quotie1194848508323700631at_int ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.19/6.56 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.nil_int () tptp.list_int)
% 6.19/6.56 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.19/6.56 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.19/6.56 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.19/6.56 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.19/6.56 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.19/6.56 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.19/6.56 (declare-fun tptp.nth_Pr8326237132889035090at_num (tptp.list_P1726324292696863441at_num tptp.nat) tptp.product_prod_nat_num)
% 6.19/6.56 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.19/6.56 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.19/6.56 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.19/6.56 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.19/6.56 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.19/6.56 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.19/6.56 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.19/6.56 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.19/6.56 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.19/6.56 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.19/6.56 (declare-fun tptp.product_nat_num (tptp.list_nat tptp.list_num) tptp.list_P1726324292696863441at_num)
% 6.19/6.56 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.19/6.56 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.19/6.56 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.19/6.56 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.19/6.56 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.19/6.56 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.19/6.56 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.19/6.56 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.19/6.56 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.19/6.56 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.19/6.56 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.rotate1_o (tptp.list_o) tptp.list_o)
% 6.19/6.56 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.rotate1_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.19/6.56 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.19/6.56 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.semiring_1_Nats_int () tptp.set_int)
% 6.19/6.56 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.semiri3763490453095760265atural (tptp.nat) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nat_int_decode (tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.nat_int_encode (tptp.int) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.one () tptp.num)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.19/6.56 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.19/6.56 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.19/6.56 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.19/6.56 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.19/6.56 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.19/6.56 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.19/6.56 (declare-fun tptp.none_num () tptp.option_num)
% 6.19/6.56 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.19/6.56 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.19/6.56 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.19/6.56 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.19/6.56 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.19/6.56 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.19/6.56 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.19/6.56 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.19/6.56 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 6.19/6.56 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.19/6.56 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.ord_min_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.19/6.56 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.19/6.56 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 6.19/6.56 (declare-fun tptp.top_top_set_list_nat () tptp.set_list_nat)
% 6.19/6.56 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.top_to4669805908274784177at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.19/6.56 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.19/6.56 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.19/6.56 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.19/6.56 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.19/6.56 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.19/6.56 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.19/6.56 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.19/6.56 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.19/6.56 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.19/6.56 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 6.19/6.56 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.19/6.56 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.19/6.56 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.19/6.56 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.19/6.56 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.19/6.56 (declare-fun tptp.produc581526299967858633d_enat (tptp.vEBT_VEBT tptp.extended_enat) tptp.produc7272778201969148633d_enat)
% 6.19/6.56 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.19/6.56 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.19/6.56 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.19/6.56 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.19/6.56 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.19/6.56 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.19/6.56 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.19/6.56 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.19/6.56 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.19/6.56 (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)
% 6.19/6.56 (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)
% 6.19/6.56 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 6.19/6.56 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.19/6.56 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.19/6.56 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.19/6.56 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.19/6.56 (declare-fun tptp.quotie8700032322157300518t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real) (-> tptp.real tptp.nat tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.quotie6776551016481293500at_int ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.int tptp.product_prod_nat_nat)) Bool)
% 6.19/6.56 (declare-fun tptp.inc_shift (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.19/6.56 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.log_rel (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) Bool)
% 6.19/6.56 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.19/6.56 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.19/6.56 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.19/6.56 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.19/6.56 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.19/6.56 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.19/6.56 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.19/6.56 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.19/6.56 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.ratreal (tptp.rat) tptp.real)
% 6.19/6.56 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.19/6.56 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.19/6.56 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.19/6.56 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.19/6.56 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.id_nat2 () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.transp_nat_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.19/6.56 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.19/6.56 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.unit_f2748546683901255202or_nat (tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.19/6.56 (declare-fun tptp.zero_n8403883297036319079atural (Bool) tptp.code_natural)
% 6.19/6.56 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.19/6.56 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.19/6.56 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.19/6.56 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.19/6.56 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.19/6.56 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.19/6.56 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.19/6.56 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.19/6.56 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.19/6.56 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.19/6.56 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.19/6.56 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.19/6.56 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.19/6.56 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.19/6.56 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.19/6.56 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.19/6.56 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.19/6.56 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.19/6.56 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.image_nat_list_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat) tptp.set_list_nat)
% 6.19/6.56 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.image_5846123807819985514at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.19/6.56 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.19/6.56 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.19/6.56 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.19/6.56 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.19/6.56 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.19/6.56 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.19/6.56 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.19/6.56 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.19/6.56 (declare-fun tptp.abort_real (tptp.literal (-> tptp.product_unit tptp.real)) tptp.real)
% 6.19/6.56 (declare-fun tptp.literal2 (Bool Bool Bool Bool Bool Bool Bool tptp.literal) tptp.literal)
% 6.19/6.56 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.19/6.56 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 6.19/6.56 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.19/6.56 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.19/6.56 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.19/6.56 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.19/6.56 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.19/6.56 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.19/6.56 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.log2 (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.pi () tptp.real)
% 6.19/6.56 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.powr_real2 (tptp.real tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.19/6.56 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.19/6.56 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.19/6.56 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.19/6.56 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.vEBT_V312737461966249ad_rel (tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.19/6.56 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P8126237942716283194atural ((-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool) tptp.produc7822875418678951345atural) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P6183159247885693666d_enat ((-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool) tptp.produc7272778201969148633d_enat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.19/6.56 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.19/6.56 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.19/6.56 (declare-fun tptp.wf_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 6.19/6.56 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.19/6.56 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.19/6.56 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.19/6.56 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.19/6.56 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.19/6.56 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.19/6.56 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.19/6.56 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.19/6.56 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.19/6.56 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.19/6.56 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.19/6.56 (declare-fun tptp.n () tptp.nat)
% 6.19/6.56 (declare-fun tptp.t () tptp.vEBT_VEBT)
% 6.19/6.56 (declare-fun tptp.x () tptp.nat)
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.19/6.56 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.19/6.56 (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))))
% 6.19/6.56 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.19/6.56 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.19/6.56 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.19/6.56 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.19/6.56 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.19/6.56 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.19/6.56 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.19/6.56 (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))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.19/6.56 (assert (forall ((X21 Bool) (X22 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X22) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 6.19/6.56 (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)))))
% 6.19/6.56 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.19/6.56 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.19/6.56 (assert (forall ((X tptp.literal)) (= (= tptp.zero_zero_literal X) (= X tptp.zero_zero_literal))))
% 6.19/6.56 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.19/6.56 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.19/6.56 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.19/6.56 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (not (@ P M)))))) (@ P N))))
% 6.19/6.56 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (@ P N2))) (@ P N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.19/6.56 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N)))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 6.19/6.56 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.19/6.56 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.19/6.56 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.19/6.56 (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 ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (not (@ P M))))))) (@ P N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.19/6.56 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X222))))))))
% 6.19/6.56 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X22 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X22)))))
% 6.19/6.56 (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))))))
% 6.19/6.56 (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))))))
% 6.19/6.56 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A4 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B3)))))))
% 6.19/6.56 (assert (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 6.19/6.56 (assert (forall ((D1 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.56 (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))))))
% 6.19/6.56 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 6.19/6.56 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 6.19/6.56 (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))))
% 6.19/6.56 (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))))
% 6.19/6.56 (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)))))
% 6.19/6.56 (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))))
% 6.19/6.56 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.19/6.56 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.19/6.56 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy)))))))))
% 6.19/6.56 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.19/6.56 (assert (forall ((X23 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y2)) (= X23 Y2))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) (@ tptp.semiri8010041392384452111omplex N)) (= M2 N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N)) (= M2 N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) (@ tptp.semiri681578069525770553at_rat N)) (= M2 N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) (@ tptp.semiri1316708129612266289at_nat N)) (= M2 N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N)) (= M2 N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.19/6.56 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.19/6.56 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.19/6.56 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.19/6.56 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M2) tptp.zero_zero_complex) (= M2 tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.19/6.56 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.19/6.56 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.19/6.56 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.19/6.56 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.19/6.56 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.19/6.56 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.19/6.56 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.19/6.56 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.19/6.56 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.19/6.56 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.19/6.56 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.56 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.56 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 6.19/6.56 (assert (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))))
% 6.19/6.56 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 6.19/6.56 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 6.19/6.56 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.19/6.56 (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))))))
% 6.19/6.56 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 6.19/6.56 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.19/6.56 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 6.19/6.56 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.19/6.56 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.19/6.56 (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)))))
% 6.19/6.56 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M2) N))))))
% 6.19/6.56 (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)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 6.19/6.56 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J))))))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J)))))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M4 tptp.nat)) (and (= M2 (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N) M4))))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 6.19/6.56 (assert (forall ((I tptp.nat) (J2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ (@ tptp.ord_less_nat J) K2) (=> (@ _let_1 J) (=> (@ (@ P J) K2) (@ _let_1 K2))))))) (@ (@ P I) J2))))))
% 6.19/6.56 (assert (forall ((I tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (forall ((I3 tptp.nat)) (=> (= J2 (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I))))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))))
% 6.19/6.56 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.56 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.19/6.56 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.19/6.56 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_real (@ F N)) (@ F N3))))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N3))))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_num (@ F N)) (@ F N3))))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N3))))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_int (@ F N)) (@ F N3))))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P tptp.zero_zero_nat) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.19/6.56 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.19/6.56 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 6.19/6.56 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M2 (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 6.19/6.57 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.19/6.57 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))))
% 6.19/6.57 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.19/6.57 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)) Uz))))
% 6.19/6.57 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.57 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (@ tptp.suc N2))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N2 tptp.nat)) (and (not (@ P N2)) (@ P (@ tptp.suc N2))))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.19/6.57 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.19/6.57 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.19/6.57 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.19/6.57 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.19/6.57 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.19/6.57 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.57 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.19/6.57 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N)) (= M2 N))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J2)))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (= (lambda ((Y4 tptp.real) (Z tptp.real)) (= Y4 Z)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.19/6.57 (assert (= (lambda ((Y4 tptp.rat) (Z tptp.rat)) (= Y4 Z)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.19/6.57 (assert (= (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M2) tptp.zero_zero_nat) (= M2 N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)))
% 6.19/6.57 (assert (forall ((J2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.19/6.57 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.57 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.57 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) E2)))))))
% 6.19/6.57 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) E2)))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.19/6.57 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 6.19/6.57 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 6.19/6.57 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 6.19/6.57 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 6.19/6.57 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.19/6.57 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.19/6.57 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.19/6.57 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.19/6.57 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.19/6.57 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M2))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.19/6.57 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.19/6.57 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.19/6.57 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (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 ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (not (forall ((M3 tptp.nat) (N2 tptp.nat)) (not (= Z2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z2 (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 6.19/6.57 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.19/6.57 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z2 (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (Z2 tptp.int)) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N2))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))) (@ P Z2)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))))))
% 6.19/6.57 (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))))))))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.19/6.57 (assert (forall ((M2 tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))))))))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.19/6.57 (assert (forall ((P Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 6.19/6.57 (assert (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A3) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.19/6.57 (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)))))))))
% 6.19/6.57 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N2 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.19/6.57 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X4) X_1))))
% 6.19/6.57 (assert (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_1))))
% 6.19/6.57 (assert (forall ((X4 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.19/6.57 (assert (forall ((X4 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M5) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M5) N4)) N4))))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.19/6.57 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.19/6.57 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.57 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.57 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.19/6.57 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R tptp.int)) (@ (@ (@ tptp.if_int (= R tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 6.19/6.57 (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))))))))))
% 6.19/6.57 (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)))))))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (= tptp.case_nat_o (lambda ((X2 Bool) (F2 (-> tptp.nat Bool)) (N4 tptp.nat)) (let ((_let_1 (= N4 tptp.zero_zero_nat))) (and (=> _let_1 X2) (=> (not _let_1) (@ F2 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat))))))))
% 6.19/6.57 (assert (= tptp.case_nat_nat (lambda ((X2 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) X2) (@ F2 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat))))))
% 6.19/6.57 (assert (= tptp.case_nat_option_num (lambda ((X2 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (N4 tptp.nat)) (@ (@ (@ tptp.if_option_num (= N4 tptp.zero_zero_nat)) X2) (@ F2 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) A) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.zero_z2226904508553997617atural) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M2))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N)) N)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int) (= (@ tptp.nat2 Z2) tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))) (and (=> _let_2 (= _let_1 Z2)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z2) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z2))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int W) Z2)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.19/6.57 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M2) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M2)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri3763490453095760265atural (@ (@ tptp.modulo_modulo_nat M2) N)) (@ (@ tptp.modulo8411746178871703098atural (@ tptp.semiri3763490453095760265atural M2)) (@ tptp.semiri3763490453095760265atural N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M2) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (=> (@ _let_1 Z3) (= (= (@ tptp.nat2 Z2) (@ tptp.nat2 Z3)) (= Z2 Z3)))))))
% 6.19/6.57 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X5 tptp.nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.19/6.57 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.19/6.57 (assert (forall ((M2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M2) K)) M2))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N3))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N3))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N3))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N3))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N3))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F N))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F N))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F N))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F N))))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F N))))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J2)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J2)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J2)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.19/6.57 (assert (forall ((W tptp.int) (Z2 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_eq_int W) Z2)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z2)) Z2))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (Z2 tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M2) Z2) (and (= M2 (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.19/6.57 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A5) B4)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B4)) C))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (forall ((B4 tptp.real) (A5 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A5)) (@ (@ tptp.ord_less_real A5) B4))))
% 6.19/6.57 (assert (forall ((B4 tptp.rat) (A5 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A5)) (@ (@ tptp.ord_less_rat A5) B4))))
% 6.19/6.57 (assert (forall ((B4 tptp.num) (A5 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A5)) (@ (@ tptp.ord_less_num A5) B4))))
% 6.19/6.57 (assert (forall ((B4 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A5)) (@ (@ tptp.ord_less_nat A5) B4))))
% 6.19/6.57 (assert (forall ((B4 tptp.int) (A5 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A5)) (@ (@ tptp.ord_less_int A5) B4))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y))))
% 6.19/6.57 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1)))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M3 tptp.nat)) (= M6 (@ tptp.suc M3))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M2 _let_1)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ P M))) (@ P N2))) (@ P N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ P M2) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (forall ((X3 tptp.nat)) (@ (@ R2 X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R2 X3))) (=> (@ _let_1 Y3) (=> (@ (@ R2 Y3) Z4) (@ _let_1 Z4))))) (=> (forall ((N2 tptp.nat)) (@ (@ R2 N2) (@ tptp.suc N2))) (@ (@ R2 M2) N)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.19/6.57 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.19/6.57 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J2 tptp.nat)) (=> (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J)))) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J2))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M5) N4) (= M5 N4)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N4) (not (= M5 N4))))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N) K)) (= M2 N)))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M2) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) M2)))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 6.19/6.57 (assert (forall ((W tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W) Z2)))))
% 6.19/6.57 (assert (forall ((W tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M2) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M2 (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.19/6.57 (assert (forall ((Z3 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (=> (@ (@ tptp.ord_less_eq_int Z3) Z2) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z2) Z3)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z2)) (@ tptp.nat2 Z3)))))))
% 6.19/6.57 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((F1 Bool) (F22 (-> tptp.nat Bool)) (X23 tptp.nat)) (= (@ (@ (@ tptp.case_nat_o F1) F22) (@ tptp.suc X23)) (@ F22 X23))))
% 6.19/6.57 (assert (forall ((F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (X23 tptp.nat)) (= (@ (@ (@ tptp.case_nat_nat F1) F22) (@ tptp.suc X23)) (@ F22 X23))))
% 6.19/6.57 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (X23 tptp.nat)) (= (@ (@ (@ tptp.case_nat_option_num F1) F22) (@ tptp.suc X23)) (@ F22 X23))))
% 6.19/6.57 (assert (forall ((F1 Bool) (F22 (-> tptp.nat Bool))) (= (@ (@ (@ tptp.case_nat_o F1) F22) tptp.zero_zero_nat) F1)))
% 6.19/6.57 (assert (forall ((F1 tptp.nat) (F22 (-> tptp.nat tptp.nat))) (= (@ (@ (@ tptp.case_nat_nat F1) F22) tptp.zero_zero_nat) F1)))
% 6.19/6.57 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num))) (= (@ (@ (@ tptp.case_nat_option_num F1) F22) tptp.zero_zero_nat) F1)))
% 6.19/6.57 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.19/6.57 (assert (forall ((W tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M2) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M2))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) A) (= (@ (@ tptp.divide5121882707175180666atural A) B) tptp.zero_z2226904508553997617atural))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M2))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.19/6.57 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.19/6.57 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J2) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J2))))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (=> (@ P J2) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J2) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K2) (not (@ P I4)))) (@ P K2)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M2) N)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N))))
% 6.19/6.57 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.19/6.57 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.19/6.57 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W) Z2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z2))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M2)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z2)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z2)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.19/6.57 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.19/6.57 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.57 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.57 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B5) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B5) N))))))))
% 6.19/6.57 (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)))))))))
% 6.19/6.57 (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))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K2) (not (@ P I4)))) (@ P (@ tptp.suc K2))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N4 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N4)) (@ P N4))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 6.19/6.57 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B5) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y)) (= X Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat M2) N) M2))))
% 6.19/6.57 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M2) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M2) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M2) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M2) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M2) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M2)) N))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N2))))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N2)) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.19/6.57 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 6.19/6.57 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) S3)) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z5)))) (exists ((Y3 tptp.real)) (and (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (@ (@ tptp.ord_less_eq_real X4) Y3))) (forall ((Z5 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z5))) (@ (@ tptp.ord_less_eq_real Y3) Z5)))))))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) N))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P4 tptp.nat) (M2 tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P4) (=> (@ (@ tptp.ord_less_nat M2) P4) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) P4) (=> (@ P N2) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) P4))))) (@ P M2)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N))) N)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 6.19/6.57 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M5) N4)) M5) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M5) N4)) N4)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 6.19/6.57 (assert (forall ((A2 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B5) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B5) N))))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z2)) N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M2) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M2) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M2) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N))))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A4 tptp.real) (B3 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B3) (=> (@ (@ P B3) C2) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (=> (@ (@ tptp.ord_less_eq_real B3) C2) (@ _let_1 C2))))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((A4 tptp.real) (B3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A4) X3) (@ (@ tptp.ord_less_eq_real X3) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B3) A4)) D3)) (@ (@ P A4) B3)))))))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M3 tptp.nat)) (@ (@ P M3) tptp.zero_zero_nat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ P N2) (@ (@ tptp.modulo_modulo_nat M3) N2)) (@ (@ P M3) N2)))) (@ (@ P M2) N)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N) A)) (= Y5 X3)))))))))
% 6.19/6.57 (assert (forall ((P (-> Bool Bool)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P (@ F22 _let_1))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P (@ F22 _let_1))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.option_num Bool)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P (@ F22 _let_1))))))))
% 6.19/6.57 (assert (forall ((P (-> Bool Bool)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P (@ F22 _let_1))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P (@ F22 _let_1))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.option_num Bool)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P (@ F22 _let_1))))))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P5 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P5)) (= (=> (@ _let_1 X) P) (=> _let_2 P5))))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P5 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P5)) (= (and (@ _let_1 X) P) (and _let_2 P5))))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ tptp.arsinh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arsinh_real X)))))
% 6.19/6.57 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (@ (@ tptp.ord_less_real X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (@ (@ tptp.ord_less_rat X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (@ (@ tptp.ord_less_num X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (@ (@ tptp.ord_less_nat X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (@ (@ tptp.ord_less_int X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (@ (@ tptp.ord_less_real T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (@ (@ tptp.ord_less_rat T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (@ (@ tptp.ord_less_num T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_nat T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (@ (@ tptp.ord_less_int T) X4))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (= (and (@ P X4) (@ Q X4)) (and (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q2 X3))))) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (= (or (@ P X4) (@ Q X4)) (or (@ P5 X4) (@ Q2 X4))))))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (= X4 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (@ (@ tptp.ord_less_real T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (@ (@ tptp.ord_less_rat T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (@ (@ tptp.ord_less_num T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (@ (@ tptp.ord_less_nat T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (@ (@ tptp.ord_less_int T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (not (@ (@ tptp.ord_less_eq_real X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (not (@ (@ tptp.ord_less_eq_rat X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (not (@ (@ tptp.ord_less_eq_num X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (not (@ (@ tptp.ord_less_eq_nat X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (not (@ (@ tptp.ord_less_eq_int X4) T)))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X4) (@ (@ tptp.ord_less_eq_real T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X4) (@ (@ tptp.ord_less_eq_rat T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X4) (@ (@ tptp.ord_less_eq_num T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (@ (@ tptp.ord_less_eq_nat T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X4) (@ (@ tptp.ord_less_eq_int T) X4))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (@ (@ tptp.ord_less_eq_real X4) T))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (@ (@ tptp.ord_less_eq_rat X4) T))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (@ (@ tptp.ord_less_eq_num X4) T))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (@ (@ tptp.ord_less_eq_nat X4) T))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (@ (@ tptp.ord_less_eq_int X4) T))))))
% 6.19/6.57 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z4) (not (@ (@ tptp.ord_less_eq_real T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z4) (not (@ (@ tptp.ord_less_eq_rat T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z4) (not (@ (@ tptp.ord_less_eq_num T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X4)))))))
% 6.19/6.57 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z4) (not (@ (@ tptp.ord_less_eq_int T) X4)))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M2)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.exp_real X) (@ tptp.exp_real Y)) (= X Y))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ tptp.ln_ln_real (@ tptp.exp_real X)) X)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.19/6.57 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.19/6.57 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z2)) tptp.one_one_int) (= Z2 tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (Y 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) Y)) (@ _let_1 Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (Y 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) Y)) (@ _let_1 Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.57 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))))
% 6.19/6.57 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X) (@ tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.19/6.57 (assert (forall ((X tptp.complex)) (not (= (@ tptp.exp_complex X) tptp.zero_zero_complex))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (not (= (@ tptp.exp_real X) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ tptp.exp_real Y) X) (= (@ tptp.ln_ln_real X) Y))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.19/6.57 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (= (@ tptp.exp_real X3) Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E))) (= X tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E))) (= X tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.57 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.19/6.57 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.19/6.57 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.19/6.57 (assert (= tptp.abs_abs_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I2)) I2))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.19/6.57 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.19/6.57 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.19/6.57 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z4) (@ (@ tptp.ord_less_real Z4) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z4 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z4) (@ (@ tptp.ord_less_rat Z4) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X3) (@ P Y5))) (@ P X3))) (@ P A))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.19/6.57 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P3 N4) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (not (@ P3 M5)))))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.real)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.rat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.num)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.19/6.57 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.19/6.57 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 6.19/6.57 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X)))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X)))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M2)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K)))))))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.19/6.57 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.19/6.57 (assert (forall ((Z2 tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (@ (@ tptp.ord_less_eq_real Y) X3))) (@ (@ tptp.ord_less_eq_real Y) Z2))))
% 6.19/6.57 (assert (forall ((Z2 tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z2))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (Z2 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Z2))) (@ (@ tptp.ord_less_eq_real Y) Z2))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (Z2 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z2))) (@ (@ tptp.ord_less_eq_rat Y) Z2))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (@ (@ tptp.ord_less_eq_real Y6) X2))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y6) (not (@ (@ tptp.ord_less_eq_set_nat Y6) X2))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (@ (@ tptp.ord_less_eq_rat Y6) X2))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (@ (@ tptp.ord_less_eq_num Y6) X2))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X2))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (@ (@ tptp.ord_less_eq_int Y6) X2))))))
% 6.19/6.57 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.57 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.19/6.57 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.19/6.57 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.19/6.57 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B2 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B2 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (@ (@ tptp.ord_less_eq_real B2) A3))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B2 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B2) (not (@ (@ tptp.ord_less_eq_set_nat B2) A3))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (@ (@ tptp.ord_less_eq_rat B2) A3))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (@ (@ tptp.ord_less_eq_num B2) A3))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (@ (@ tptp.ord_less_eq_nat B2) A3))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (@ (@ tptp.ord_less_eq_int B2) A3))))))
% 6.19/6.57 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z2)))))
% 6.19/6.57 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) W2) (=> (@ (@ tptp.ord_less_rat W2) X) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z2)))) (@ (@ tptp.ord_less_eq_real Y) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z2)))) (@ (@ tptp.ord_less_eq_rat Y) Z2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_set_nat (lambda ((B2 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((B2 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 6.19/6.57 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B) (@ (@ tptp.ord_less_set_nat C) A)))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (@ (@ tptp.ord_less_eq_real A3) B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((B2 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B2) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (@ (@ tptp.ord_less_eq_num A3) B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B2))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (@ (@ tptp.ord_less_eq_int A3) B2))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.19/6.57 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.19/6.57 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y6) (= X2 Y6)))))
% 6.19/6.57 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y6) (not (= X2 Y6))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_set_nat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z2) (@ (@ tptp.ord_less_real X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z2) (@ (@ tptp.ord_less_set_nat X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z2) (@ (@ tptp.ord_less_rat X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num) (Z2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z2) (@ (@ tptp.ord_less_num X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z2) (@ (@ tptp.ord_less_nat X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z2) (@ (@ tptp.ord_less_int X) Z2)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.num) (Y tptp.num) (Z2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((X tptp.int) (Y tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z2) (@ _let_1 Z2))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log2 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))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C2) (@ (@ tptp.ord_less_eq_real C2) B) (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_real X4) C2)) (@ P X4))) (forall ((D3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_real X3) D3)) (@ P X3))) (@ (@ tptp.ord_less_eq_real D3) C2))))))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat C2) B) (forall ((X4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X4) (@ (@ tptp.ord_less_nat X4) C2)) (@ P X4))) (forall ((D3 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) D3)) (@ P X3))) (@ (@ tptp.ord_less_eq_nat D3) C2))))))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int C2) B) (forall ((X4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X4) (@ (@ tptp.ord_less_int X4) C2)) (@ P X4))) (forall ((D3 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) D3)) (@ P X3))) (@ (@ tptp.ord_less_eq_int D3) C2))))))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ 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) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.19/6.57 (assert (forall ((A2 tptp.int) (B5 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B5) (=> (@ (@ 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 B5) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B5) N))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A2 tptp.nat) (B5 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B5) (=> (@ (@ 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 B5) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B5) N))))))
% 6.19/6.57 (assert (forall ((X tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) (@ tptp.suc N2)))))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal tptp.zero_zero_literal) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.19/6.57 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.19/6.57 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal A) tptp.zero_zero_literal) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K))))))
% 6.19/6.57 (assert (forall ((W tptp.real) (Z2 tptp.real)) (= (= (@ (@ tptp.powr_real W) Z2) tptp.zero_zero_real) (= W tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z2) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.19/6.57 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.19/6.57 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.19/6.57 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.19/6.57 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I)) K)))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J2)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 6.19/6.57 (assert (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.57 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log2 A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.19/6.57 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K) I))))))
% 6.19/6.57 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J2))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.19/6.57 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.19/6.57 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log2 A) A) tptp.one_one_real)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y)))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log2 A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log2 A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log2 A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log2 A) X)) (@ _let_1 X))))))))
% 6.19/6.57 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z2))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log2 A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log2 A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log2 A) (@ (@ tptp.powr_real A) Y)) Y)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log2 A) X)) X)))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log2 A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J2) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J2) (= K L)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J2) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J2) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.19/6.57 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.19/6.57 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.19/6.57 (assert (forall ((B5 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))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.19/6.57 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.19/6.57 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.19/6.57 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ (@ tptp.powr_real (@ _let_1 B)) A)))))
% 6.19/6.57 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N))) Z2))))
% 6.19/6.57 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log2 (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log2 A) X)) B)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J2) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J2) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J2) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J2) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J2) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J2) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J2) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J2) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J2) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J2) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J2) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C3))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.19/6.57 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.19/6.57 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.19/6.57 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.57 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.19/6.57 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J2) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J2) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J2) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J2) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J2) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J2) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J2) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J2) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J2) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J2) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J2) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.57 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J2) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.57 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 6.19/6.57 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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))))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))
% 6.19/6.57 (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)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N)))))
% 6.19/6.58 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A4) B3) (@ (@ P B3) A4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) tptp.zero_zero_nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A4) B3))))) (@ (@ P A) B))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N) M2) (= N tptp.zero_zero_nat))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.19/6.58 (assert (forall ((K tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) K)))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I)) I))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J2)) I))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J2)) K) (@ (@ tptp.ord_less_nat I) K))))
% 6.19/6.58 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.19/6.58 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M2))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M2) N))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) K)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M2))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J2))))))
% 6.19/6.58 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M5) K3))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M2)) N) M2)))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) N) M2)))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log2 B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log2 B) X)) Y) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log2 B) X)) Y))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log2 B) X)))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (=> (@ _let_1 Z3) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z2) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z2)) (@ tptp.nat2 Z3))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log2 B) X)))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 B) X)) Y))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log2 B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.19/6.58 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J2) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J2) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J2) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.real) (J2 tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J2) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.rat) (J2 tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J2) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J2) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 6.19/6.58 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J2) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J2) L)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (= tptp.log2 (lambda ((A3 tptp.real) (X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real A3)))))
% 6.19/6.58 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J2 tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J2) 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)) J2)))))))))
% 6.19/6.58 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J2) 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)) J2)))))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J2) 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)) J2)))))))))
% 6.19/6.58 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J2) 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)) J2)))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((B5 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B5 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (forall ((B5 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B5 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (forall ((B5 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B5 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (forall ((B5 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B5 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (forall ((B5 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B5 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.19/6.58 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.19/6.58 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.19/6.58 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.19/6.58 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) C)) (@ (@ tptp.divide5121882707175180666atural B) C))) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) C)) (@ (@ tptp.modulo8411746178871703098atural B) C))) C)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N) _let_1) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q3)))))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))))
% 6.19/6.58 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M5) K3)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K2)))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I) K2) J2))))))
% 6.19/6.58 (assert (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_nat (@ F M3)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M2)) K)) (@ F (@ (@ tptp.plus_plus_nat M2) K))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M2)) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J2))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))))
% 6.19/6.58 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 6.19/6.58 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.19/6.58 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)) Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K)) I) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I) K)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J2) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J2)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K)))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K)) I)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I) K) (= J2 (@ (@ tptp.plus_plus_nat K) I))))))
% 6.19/6.58 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.19/6.58 (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 ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)) (or (@ _let_1 Z2) (= W Z2))))))
% 6.19/6.58 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N4 tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N4)))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.19/6.58 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y6)))))
% 6.19/6.58 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.19/6.58 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.19/6.58 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.19/6.58 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X) Y)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.19/6.58 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.19/6.58 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.19/6.58 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.19/6.58 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.58 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.58 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R4 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R4) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R4)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (R4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R4) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R4)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.rat) (R4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R4) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R4)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (A tptp.int) (R4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R4) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R4)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R4))))))
% 6.19/6.58 (assert (= tptp.ln_ln_real (@ tptp.log2 (@ tptp.exp_real tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R4 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R4) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R4)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (R4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R4) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R4)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.rat) (R4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R4) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R4)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R4))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (A tptp.int) (R4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R4) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R4)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R4))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (exists ((B3 tptp.real)) (or (@ (@ tptp.ord_less_real A) B3) (@ (@ tptp.ord_less_real B3) A)))))
% 6.19/6.58 (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 ((D4 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D4)) (not (@ P D4)))))))))
% 6.19/6.58 (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 ((D4 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D4)) (@ P D4)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K)) I) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I) K))))))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.19/6.58 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N4 tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)) Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z2) (@ (@ tptp.ord_less_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z2))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.19/6.58 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.19/6.58 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.19/6.58 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.19/6.58 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log2 B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) N)))))
% 6.19/6.58 (assert (forall ((B tptp.real) (N tptp.nat) (M2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 B) M2))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log2 B) _let_1)))))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 6.19/6.58 (assert (= tptp.plus_plus_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N4))))))
% 6.19/6.58 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N4)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M5)))))
% 6.19/6.58 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M5)) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.19/6.58 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (N tptp.nat) (M2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 B) M2))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log2 (@ (@ tptp.power_power_real A) N)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log2 A) X)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.suc (@ tptp.nat2 Z2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z2))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ 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) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log2 B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D5) (and (@ (@ tptp.ord_less_eq_real A) Y5) (@ (@ tptp.ord_less_eq_real Y5) B))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log2 B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D5) (and (@ (@ tptp.ord_less_real A) Y5) (@ (@ tptp.ord_less_real Y5) B))))))))))
% 6.19/6.58 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.19/6.58 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_eq_real R4) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R4))))))
% 6.19/6.58 (assert (forall ((R4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R4) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R4))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.19/6.58 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys)) (@ tptp.size_size_list_o Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.19/6.58 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.19/6.58 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys)) (@ tptp.size_size_list_int Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z2)) (= Y (@ (@ tptp.plus_plus_real X) Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ 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) X) (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)))))))))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log2 (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 B) X)))))))
% 6.19/6.58 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.19/6.58 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.19/6.58 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.19/6.58 (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 ((I2 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) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.tanh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_real W) (@ tptp.ring_1_of_int_real Z2)) (= W Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_rat W) (@ tptp.ring_1_of_int_rat Z2)) (= W Z2))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.tanh_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ tptp.tanh_real X)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.19/6.58 (assert (forall ((R4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R4))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R4)) (@ (@ tptp.divide_divide_real A) R4)))))
% 6.19/6.58 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.ring_1_of_int_rat Z2)) Z2)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.ring_1_of_int_real Z2)) Z2)))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.tanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.tanh_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ tptp.tanh_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.tanh_complex X)))))
% 6.19/6.58 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int Z2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real Z2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex Z2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat Z2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z2) (@ tptp.uminus_uminus_int Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z2) (@ tptp.uminus_uminus_real Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z2) (@ tptp.uminus1482373934393186551omplex Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z2) (@ tptp.uminus1351360451143612070nteger Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z2) (@ tptp.uminus_uminus_rat Z2))))
% 6.19/6.58 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.58 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural B) A)) B) tptp.zero_z2226904508553997617atural)))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z2) tptp.zero_zero_int) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z2) tptp.zero_zero_real) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z2) tptp.zero_zero_rat) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z2)) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z2)) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z2)) (= Z2 tptp.zero_zero_int))))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_eq_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int W) Z2))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_int W) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z2) tptp.one_one_complex) (= Z2 tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z2) tptp.one_one_int) (= Z2 tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z2) tptp.one_one_real) (= Z2 tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z2) tptp.one_one_rat) (= Z2 tptp.one_one_int))))
% 6.19/6.58 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.19/6.58 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z2)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z2)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z2)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z2)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int Z2)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int Z2)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int Z2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int Z2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int Z2)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z2)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z2)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z2)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri8010041392384452111omplex N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri5074537144036343181t_real N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri681578069525770553at_rat N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int X)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger X)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat X)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z2)) N))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z2)) N))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z2)) N))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z2) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z2)) N))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z2))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) Z2))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) Z2))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z2))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) Z2))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z2))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 Z2)) (@ tptp.ring_17405671764205052669omplex Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z2)) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z2)) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z2)) (@ tptp.ring_1_of_int_int Z2)))))
% 6.19/6.58 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (not (= Xs Ys2)))))
% 6.19/6.58 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2))) (not (= Xs Ys2)))))
% 6.19/6.58 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2))) (not (= Xs Ys2)))))
% 6.19/6.58 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2))) (not (= Xs Ys2)))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.19/6.58 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.19/6.58 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.19/6.58 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z4)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z4)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z4)) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z4)) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z4)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z4)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E2)) C))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) C))))
% 6.19/6.58 (assert (forall ((P (-> tptp.real Bool)) (D6 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D6))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D6))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D6)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.rat Bool)) (D6 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D6))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D6))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D6)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (D6 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D6)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.real Bool)) (D6 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D6))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D6))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D6)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.rat Bool)) (D6 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D6))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D6))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D6)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (D6 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D6)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z2 tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z2) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z2) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z2) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y) Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z2 tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z2) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (Z2 tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z2) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y) W)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z2) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.19/6.58 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.19/6.58 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.19/6.58 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.19/6.58 (assert (forall ((R4 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R4))) (=> (not (= R4 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.19/6.58 (assert (forall ((R4 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R4))) (=> (not (= R4 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.19/6.58 (assert (forall ((R4 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R4))) (=> (not (= R4 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.19/6.58 (assert (forall ((R4 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R4))) (=> (not (= R4 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.artanh_real (@ tptp.tanh_real X)) X)))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((M2 tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M2) N)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))))
% 6.19/6.58 (assert (forall ((Y tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z2)) (= (@ (@ tptp.times_times_complex X) Z2) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z2)) (= (@ (@ tptp.times_times_real X) Z2) (@ (@ tptp.times_times_real W) Y)))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W) Z2)) (= (@ (@ tptp.times_times_rat X) Z2) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C) D))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M2))) (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)))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M2))) (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)))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))))
% 6.19/6.58 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J2)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.19/6.58 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N tptp.one_one_int)) (and (= M2 _let_1) (= N _let_1)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M2) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M2) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q3))))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M2) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M2 (@ (@ tptp.times_times_int D) Q4))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q5) (@ (@ tptp.ord_less_eq_real P4) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P4) Q5)))) Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q5) (@ (@ tptp.ord_less_eq_rat P4) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P4) Q5)))) Q5)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 6.19/6.58 (assert (forall ((Q5 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q5) (@ (@ 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 P4) Q5)))) tptp.one_one_real)) Q5)) P4))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q5) (@ (@ 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 P4) Q5)))) tptp.one_one_rat)) Q5)) P4))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z2) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z2) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) A))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z2) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z2) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (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)))))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z2) Y)) X) (@ (@ tptp.ord_less_real Z2) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z2) Y)) X) (@ (@ tptp.ord_less_rat Z2) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z2) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z2) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z2)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((Y tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z2) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Y tptp.complex) (Z2 tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z2) Y))) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z2)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z2)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z2)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z2)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z2)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z2)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Y tptp.complex) (Z2 tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z2)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z2)))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z2)))) (let ((_let_2 (= Z2 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) Z2)) B)) Z2))))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) X))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C))) C))))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.19/6.58 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)))))
% 6.19/6.58 (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)))
% 6.19/6.58 (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)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 6.19/6.58 (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)))
% 6.19/6.58 (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)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) A)))
% 6.19/6.58 (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)))
% 6.19/6.58 (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)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) A)))
% 6.19/6.58 (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)))
% 6.19/6.58 (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)))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.19/6.58 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B)))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.19/6.58 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y5 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)))))))
% 6.19/6.58 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (P5 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P5 X3) (@ P5 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (exists ((X_12 tptp.int)) (@ P5 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (exists ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (exists ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R4))) (@ (@ tptp.plus_plus_real R4) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((R4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R4))) (@ (@ tptp.plus_plus_rat R4) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R4))) tptp.one_one_real)) R4)))
% 6.19/6.58 (assert (forall ((R4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R4))) tptp.one_one_rat)) R4)))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z4) (=> (@ (@ tptp.ord_less_real Z4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z4) (=> (@ (@ tptp.ord_less_rat Z4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))))))
% 6.19/6.58 (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)))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (X tptp.real) (Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z2) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z2) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z2)))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) Y)) X) (@ (@ tptp.ord_less_eq_real Z2) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) Y)) X) (@ (@ tptp.ord_less_eq_rat Z2) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.19/6.58 (assert (= tptp.ord_less_eq_int (lambda ((N4 tptp.int) (M5 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M5)) tptp.one_one_real)))))
% 6.19/6.58 (assert (= tptp.ord_less_int (lambda ((N4 tptp.int) (M5 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N4)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M5)))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z2))) tptp.zero_zero_real))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z2))) tptp.zero_zero_rat))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (Z2 tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z2)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z2))) tptp.zero_zero_real))))))
% 6.19/6.58 (assert (forall ((Y tptp.rat) (Z2 tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z2))) tptp.zero_zero_rat))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z2))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z2))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z2))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z2))) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z2)) B))) (let ((_let_2 (= Z2 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) Z2))) Z2))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z2))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z2))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z2))) Z2)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z2))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z2))) Z2)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M2))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.19/6.58 (assert (forall ((A tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural M2))) (let ((_let_2 (@ tptp.modulo8411746178871703098atural A))) (let ((_let_3 (@ tptp.semiri3763490453095760265atural N))) (let ((_let_4 (@ tptp.times_2397367101498566445atural _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_4 (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.divide5121882707175180666atural A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.19/6.58 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M2))) (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)))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M2))) (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)))))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.19/6.58 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J2)))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (Q6 tptp.int) (R5 tptp.int) (Q5 tptp.int) (R4 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 Q6)) R5)) (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int R4) tptp.zero_zero_int) (=> (@ _let_1 R4) (=> (@ _let_1 R5) (@ (@ tptp.ord_less_eq_int Q5) Q6)))))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (Q6 tptp.int) (R5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q6)) R5)) (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int R5) B) (=> (@ (@ tptp.ord_less_int R4) B) (@ (@ tptp.ord_less_eq_int Q6) Q5))))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (B4 tptp.int) (Q6 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q6) Q5))))))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (B4 tptp.int) (Q6 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R5))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R5) B4) (=> (@ _let_1 R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q5) Q6)))))))))))
% 6.19/6.58 (assert (forall ((B4 tptp.int) (Q6 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q6)) R5)) (=> (@ (@ tptp.ord_less_int R5) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q6)))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.19/6.58 (assert (= tptp.powr_real (lambda ((X2 tptp.real) (A3 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A3) (@ tptp.ln_ln_real X2)))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (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 I2)))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (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 I2)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z2))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z2))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z2))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X) Z2))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat)) X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real)) X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (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)))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((U tptp.real) (V tptp.real) (R4 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R4) (=> (@ (@ tptp.ord_less_eq_real R4) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R4) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.19/6.58 (assert (forall ((U tptp.rat) (V tptp.rat) (R4 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R4) (=> (@ (@ tptp.ord_less_eq_rat R4) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R4) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 6.19/6.58 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 6.19/6.58 (assert (= tptp.power_power_complex (lambda ((P6 tptp.complex) (M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P6) (@ (@ tptp.power_power_complex P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.58 (assert (= tptp.power_power_real (lambda ((P6 tptp.real) (M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P6) (@ (@ tptp.power_power_real P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.58 (assert (= tptp.power_power_rat (lambda ((P6 tptp.rat) (M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P6) (@ (@ tptp.power_power_rat P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.58 (assert (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.58 (assert (= tptp.power_power_int (lambda ((P6 tptp.int) (M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.19/6.58 (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 ((I2 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) I2)) J3))) (@ P I2)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 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) I2)) J3))) (@ P I2))))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int R4) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R4) (= (@ (@ tptp.divide_divide_int A) B) Q5))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (= (@ (@ tptp.divide_divide_int A) B) Q5))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log2 B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X)))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (= (@ (@ tptp.modulo_modulo_int A) B) R4))))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4)) (=> (@ (@ tptp.ord_less_eq_int R4) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R4) (= (@ (@ tptp.modulo_modulo_int A) B) R4))))))
% 6.19/6.58 (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 ((I2 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) I2)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 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) I2)) J3))) (@ P J3))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 6.19/6.58 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))
% 6.19/6.58 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))
% 6.19/6.58 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 6.19/6.58 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.log2 A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log2 B) X)))))))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (Z2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z2) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z2))) tptp.one_one_int)) D))))))
% 6.19/6.58 (assert (forall ((D tptp.int) (X tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z2))) tptp.one_one_int)) D))) Z2)))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log2 B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.19/6.58 (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 ((I2 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) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y) Z2)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y) Z2)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z2)) (@ (@ tptp.times_times_int Y) Z2)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z2)) (@ (@ tptp.times_times_real Y) Z2)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z2)) (@ (@ tptp.times_times_rat Y) Z2)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z2)) (@ (@ tptp.times_times_int Y) Z2)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log2 B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)) X) (@ P Y6))))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y))) (let ((_let_2 (@ tptp.tanh_complex X))) (=> (not (= (@ tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y))) (let ((_let_2 (@ tptp.tanh_real X))) (=> (not (= (@ tptp.cosh_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.cosh_real X) (@ tptp.cosh_real Y)) (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.cosh_real (@ tptp.abs_abs_real X)) (@ tptp.cosh_real X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.tanh_real X) (@ tptp.tanh_real Y)) (= X Y))))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.58 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= M2 N) (= K tptp.zero_zero_nat))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K) (@ (@ tptp.times_times_nat N) K)) (or (= M2 N) (= K tptp.zero_zero_nat)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N)) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.cosh_real (@ tptp.uminus_uminus_real X)) (@ tptp.cosh_real X))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ tptp.cosh_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.cosh_complex X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.ring_1_of_int_real Z2)) Z2)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.ring_1_of_int_rat Z2)) Z2)))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.arctan X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.58 (assert (= (@ tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.19/6.58 (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) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_real B) A)))))))
% 6.19/6.58 (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) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ _let_1 A)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (= M2 _let_1) (= N _let_1))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N))))))
% 6.19/6.58 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.19/6.58 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.19/6.58 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.58 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.19/6.58 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.19/6.58 (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) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.19/6.58 (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) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.19/6.58 (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_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.19/6.58 (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_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((M2 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 M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (K tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M2))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z2))) (@ tptp.uminus_uminus_int Z2))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat Z2))) (@ tptp.uminus_uminus_int Z2))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z2))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) Z2))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z2))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) Z2))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.arctan X) (@ tptp.arctan Y)) (= X Y))))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.19/6.58 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= A B))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))))
% 6.19/6.58 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))))
% 6.19/6.58 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 6.19/6.58 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (not (= (@ tptp.cosh_real X) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N)))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J2))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J2) K)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J2) L))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q5)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q5)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.arctan (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arctan X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.inverse_inverse_real A)) (=> (not (= A tptp.zero_zero_real)) (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A)))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B)) (@ tptp.invers8013647133539491842omplex A)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.19/6.58 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.19/6.58 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.19/6.58 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.19/6.58 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.19/6.58 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.19/6.58 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.19/6.58 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))))
% 6.19/6.58 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))))
% 6.19/6.58 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B2)) A3))))
% 6.19/6.58 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.19/6.58 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.19/6.58 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.19/6.58 (assert (forall ((X tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M2))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M2))) (let ((_let_2 (@ tptp.inverse_inverse_real X))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M2))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M2))) (let ((_let_2 (@ tptp.inverse_inverse_rat X))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.19/6.58 (assert (forall ((Xa tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.19/6.58 (assert (forall ((Xa tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.19/6.58 (assert (forall ((Xa tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.19/6.58 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.19/6.58 (assert (forall ((Xa tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.19/6.58 (assert (forall ((Xa tptp.int) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.19/6.58 (assert (forall ((Xa tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.19/6.58 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 6.19/6.58 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 6.19/6.58 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 6.19/6.58 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 6.19/6.58 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 6.19/6.58 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 6.19/6.58 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 6.19/6.58 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 6.19/6.58 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 6.19/6.58 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X)) (@ tptp.abs_abs_Code_integer X)) X)))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 6.19/6.58 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ 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))))))
% 6.19/6.58 (assert (forall ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.19/6.58 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.19/6.58 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim2889992004027027881ng_rat X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.exp_real (@ tptp.uminus_uminus_real X)) (@ tptp.inverse_inverse_real (@ tptp.exp_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.invers8013647133539491842omplex (@ tptp.exp_complex X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ tptp.inverse_inverse_real (@ _let_1 A))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 6.19/6.58 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y6)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J2) K))))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J2)))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N)) (or (= N tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N)) M2)))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N))) M2)))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q3))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.plus_plus_real A) B))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.plus_plus_complex A) B))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_2)) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_2)) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real B) A))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex B) A))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z2) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z2)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) Z2) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (= (@ (@ tptp.plus_plus_int Z2) (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z2)) X)))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (= (@ (@ tptp.plus_plus_int Z2) (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z2)) X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) Z2) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ tptp.ring_1_of_int_real Z2))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) Z2) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z2))))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.19/6.58 (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))))
% 6.19/6.58 (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))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_int (@ tptp.archim6058952711729229775r_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat X)) (@ tptp.uminus_uminus_int (@ tptp.archim3151403230148437115or_rat X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_int (@ tptp.archim7802044766580827645g_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat X)) (@ tptp.uminus_uminus_int (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.19/6.58 (assert (= tptp.archim7802044766580827645g_real (lambda ((X2 tptp.real)) (@ tptp.uminus_uminus_int (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real X2))))))
% 6.19/6.58 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X2 tptp.rat)) (@ tptp.uminus_uminus_int (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat X2))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (=> (= X (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real 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)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat 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)))))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.19/6.58 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q5) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q5)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q5))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q5)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M2) N)) Q5))) (@ _let_1 N)))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M5) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M5) N4)) N4)))))
% 6.19/6.58 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z2))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z2))))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R4) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R4)))) R4))))
% 6.19/6.58 (assert (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R4) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R4)))) R4))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) X)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) X)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M2) N)))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M2) N)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_int (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_int (= X2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X2)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_rat (lambda ((X2 tptp.rat)) (@ (@ (@ tptp.if_rat (= X2 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.19/6.58 (assert (= tptp.archim7802044766580827645g_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (@ (@ (@ tptp.if_int (= X2 (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.19/6.58 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (@ (@ (@ tptp.if_int (= X2 (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X))) tptp.one_one_int)))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X))) tptp.one_one_int)))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_real R4) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R4))) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_eq_real R4) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R4))) tptp.one_one_real))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R4) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R4)))))
% 6.19/6.58 (assert (forall ((R4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R4) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R4)))))
% 6.19/6.58 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ P E)))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D5 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D5) E) (=> (@ P D5) (@ P E)))) (=> (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) E2) (@ P E2))))))
% 6.19/6.58 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4)))) (and (not (= N4 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (Q5 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q5)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q5))) (= (@ (@ tptp.divide_divide_nat M2) N) Q5))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q5) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q5)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q5)) N)))))
% 6.19/6.58 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P I2))))))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))))
% 6.19/6.58 (assert (= tptp.times_times_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N4))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P J3))))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z2) Z3)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z2)) (@ tptp.nat2 Z3))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z2))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z2))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X) Z2))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (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 I2)))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (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 I2)))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z2) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real)) X))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z2) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat)) X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z2) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z2)) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z2) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.one_one_rat)))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))) X))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N2))) X))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) M2))))))))
% 6.19/6.58 (assert (forall ((X tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) M2))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) M2))))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 6.19/6.58 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log2 A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.19/6.58 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) 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)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.19/6.58 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))))
% 6.19/6.58 (assert (forall ((Q5 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P4) Q5)))) Q5)) P4))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P4) Q5)))) Q5)) P4))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z2) Z3)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z2))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z3)))))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X)))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 6.19/6.58 (assert (forall ((Q5 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q5) (@ (@ tptp.ord_less_real P4) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P4) Q5)))) tptp.one_one_real)) Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q5) (@ (@ tptp.ord_less_rat P4) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P4) Q5)))) tptp.one_one_rat)) Q5)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _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 M2) N)))))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I)) U)) N))))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J2)) U)) M2)) N)))))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.19/6.58 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I)) U)) N))))))
% 6.19/6.58 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat) (L3 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L3)) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.19/6.58 (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))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (= I2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.19/6.58 (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))))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M2 N))))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real X)))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex X)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 6.19/6.58 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real X2) (@ tptp.abs_abs_real X2)))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J2)) U)) M2) N)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I)) U)) N))))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J2)) U)) M2)) N)))))
% 6.19/6.58 (assert (forall ((I tptp.nat) (J2 tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I)) U)) N))))))
% 6.19/6.58 (assert (forall ((J2 tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J2)) U)) M2)) N)))))
% 6.19/6.58 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M5)) (@ X7 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.archim2898591450579166408c_real X)) tptp.ring_1_Ints_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.19/6.58 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.19/6.58 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.19/6.58 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.19/6.58 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.19/6.58 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z2)) tptp.zero_zero_real)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.zero_zero_rat)))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) tptp.zero_zero_rat) (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))))
% 6.19/6.58 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (or (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (or (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X)) (not (@ (@ tptp.member_real X) tptp.ring_1_Ints_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X)) (not (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat)))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 6.19/6.58 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)) K))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.semiri8010041392384452111omplex X)) N) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.semiri5074537144036343181t_real X)) N) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.semiri681578069525770553at_rat X)) N) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat (@ tptp.semiri1316708129612266289at_nat X)) N) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.semiri1314217659103216013at_int X)) N) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.58 (assert (@ (@ tptp.member_complex tptp.zero_zero_complex) tptp.ring_1_Ints_complex))
% 6.19/6.58 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 6.19/6.58 (assert (@ (@ tptp.member_rat tptp.zero_zero_rat) tptp.ring_1_Ints_rat))
% 6.19/6.58 (assert (@ (@ tptp.member_int tptp.zero_zero_int) tptp.ring_1_Ints_int))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.times_times_complex A) B)) tptp.ring_1_Ints_complex)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.times_times_real A) B)) tptp.ring_1_Ints_real)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.times_times_rat A) B)) tptp.ring_1_Ints_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.times_times_int A) B)) tptp.ring_1_Ints_int)))))
% 6.19/6.58 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 6.19/6.58 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 6.19/6.58 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 6.19/6.58 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.ring_1_Ints_complex)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.ring_1_Ints_real)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B)) tptp.ring_1_Ints_int)))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.minus_minus_complex A) B)) tptp.ring_1_Ints_complex)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real A) B)) tptp.ring_1_Ints_real)))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int A) B)) tptp.ring_1_Ints_int)))))
% 6.19/6.58 (assert (forall ((X tptp.int)) (= (@ (@ tptp.member_int (@ tptp.uminus_uminus_int X)) tptp.ring_1_Ints_int) (@ (@ tptp.member_int X) tptp.ring_1_Ints_int))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.uminus_uminus_real X)) tptp.ring_1_Ints_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.member_complex (@ tptp.uminus1482373934393186551omplex X)) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex X) tptp.ring_1_Ints_complex))))
% 6.19/6.58 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger X)) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.member_rat (@ tptp.uminus_uminus_rat X)) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ tptp.uminus_uminus_int A)) tptp.ring_1_Ints_int))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real A)) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ tptp.uminus1482373934393186551omplex A)) tptp.ring_1_Ints_complex))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger A)) tptp.ring_11222124179247155820nteger))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ tptp.uminus_uminus_rat A)) tptp.ring_1_Ints_rat))))
% 6.19/6.58 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.power_power_int A) N)) tptp.ring_1_Ints_int))))
% 6.19/6.58 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N)) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N)) tptp.ring_1_Ints_complex))))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.ring_1_Ints_complex)))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_real (@ tptp.semiri5074537144036343181t_real N)) tptp.ring_1_Ints_real)))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.ring_1_Ints_rat)))
% 6.19/6.58 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N)) tptp.ring_1_Ints_int)))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ tptp.abs_abs_int A)) tptp.ring_1_Ints_int))))
% 6.19/6.58 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ tptp.abs_abs_Code_integer A)) tptp.ring_11222124179247155820nteger))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ tptp.abs_abs_rat A)) tptp.ring_1_Ints_rat))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ tptp.abs_abs_real A)) tptp.ring_1_Ints_real))))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (@ (@ tptp.member_complex (@ tptp.ring_17405671764205052669omplex Z2)) tptp.ring_1_Ints_complex)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (@ (@ tptp.member_int (@ tptp.ring_1_of_int_int Z2)) tptp.ring_1_Ints_int)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (@ (@ tptp.member_real (@ tptp.ring_1_of_int_real Z2)) tptp.ring_1_Ints_real)))
% 6.19/6.58 (assert (forall ((Z2 tptp.int)) (@ (@ tptp.member_rat (@ tptp.ring_1_of_int_rat Z2)) tptp.ring_1_Ints_rat)))
% 6.19/6.58 (assert (forall ((Q5 tptp.complex) (P (-> tptp.complex Bool))) (=> (@ (@ tptp.member_complex Q5) tptp.ring_1_Ints_complex) (=> (forall ((Z4 tptp.int)) (@ P (@ tptp.ring_17405671764205052669omplex Z4))) (@ P Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int Q5) tptp.ring_1_Ints_int) (=> (forall ((Z4 tptp.int)) (@ P (@ tptp.ring_1_of_int_int Z4))) (@ P Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.member_real Q5) tptp.ring_1_Ints_real) (=> (forall ((Z4 tptp.int)) (@ P (@ tptp.ring_1_of_int_real Z4))) (@ P Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat) (P (-> tptp.rat Bool))) (=> (@ (@ tptp.member_rat Q5) tptp.ring_1_Ints_rat) (=> (forall ((Z4 tptp.int)) (@ P (@ tptp.ring_1_of_int_rat Z4))) (@ P Q5)))))
% 6.19/6.58 (assert (forall ((Q5 tptp.complex)) (=> (@ (@ tptp.member_complex Q5) tptp.ring_1_Ints_complex) (not (forall ((Z4 tptp.int)) (not (= Q5 (@ tptp.ring_17405671764205052669omplex Z4))))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.int)) (=> (@ (@ tptp.member_int Q5) tptp.ring_1_Ints_int) (not (forall ((Z4 tptp.int)) (not (= Q5 (@ tptp.ring_1_of_int_int Z4))))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.real)) (=> (@ (@ tptp.member_real Q5) tptp.ring_1_Ints_real) (not (forall ((Z4 tptp.int)) (not (= Q5 (@ tptp.ring_1_of_int_real Z4))))))))
% 6.19/6.58 (assert (forall ((Q5 tptp.rat)) (=> (@ (@ tptp.member_rat Q5) tptp.ring_1_Ints_rat) (not (forall ((Z4 tptp.int)) (not (= Q5 (@ tptp.ring_1_of_int_rat Z4))))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))))
% 6.19/6.58 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))))
% 6.19/6.58 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))))
% 6.19/6.58 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (= (= (@ (@ tptp.plus_plus_complex A) A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.19/6.58 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.19/6.58 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.19/6.58 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.19/6.58 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 6.19/6.58 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))))
% 6.19/6.58 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_rat))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X)))))))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X)))) (let ((_let_2 (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X)))))))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 6.19/6.58 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X)) tptp.one_one_rat)))
% 6.19/6.58 (assert (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))))
% 6.19/6.58 (assert (forall ((X tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X))))
% 6.19/6.58 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))))
% 6.19/6.58 (assert (forall ((X tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 6.19/6.58 (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)))))))
% 6.19/6.58 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.19/6.59 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))))
% 6.19/6.59 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 6.19/6.59 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M2)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M2)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 6.19/6.59 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.19/6.59 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.19/6.59 (assert (= tptp.archim2898591450579166408c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))))))
% 6.19/6.59 (assert (= tptp.archimedean_frac_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z2) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z2) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z2) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z2) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z2) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.19/6.59 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.19/6.59 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X))))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (not (= X tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X))))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (not (= X tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer) (= X tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat) (= X tptp.zero_zero_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int) (= X tptp.zero_zero_int)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ tptp.semiri8010041392384452111omplex N))) M2))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ tptp.semiri5074537144036343181t_real N))) M2))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ tptp.semiri681578069525770553at_rat N))) M2))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z2) (@ tptp.semiri1316708129612266289at_nat N))) M2))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z2) (@ tptp.semiri1314217659103216013at_int N))) M2))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger) (= (= X Y) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Y))) tptp.one_one_Code_integer))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real) (= (= X Y) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) tptp.one_one_real))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) Y))) tptp.one_one_rat))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Y))) tptp.one_one_int))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A3)) tptp.one_one_complex)) K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A3)) tptp.one_one_real)) K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A3)) tptp.one_one_rat)) K3)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) X) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (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)))))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) Y)))) (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)))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ tptp.semiri8010041392384452111omplex M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ tptp.semiri681578069525770553at_rat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z2) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z2 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z2) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 6.19/6.59 (assert (forall ((R4 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R4) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R4) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.19/6.59 (assert (forall ((R4 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R4))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R4) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R4) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.19/6.59 (assert (forall ((R4 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R4))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R4) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R4) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.19/6.59 (assert (forall ((R4 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R4))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R4) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R4) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.19/6.59 (assert (forall ((R4 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R4))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R4) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R4) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.19/6.59 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A3)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.19/6.59 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A3)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_VEBT_VEBT Xs) Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_o Xs) Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs) Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_int Xs) Xs))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri5044797733671781792omplex N) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M5)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.59 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M5)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.59 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.59 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M5)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.59 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri5044797733671781792omplex N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1408675320244567234ct_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri2265585572941072030t_real N))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.rotate1_VEBT_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o)) (= (@ tptp.size_size_list_o (@ tptp.rotate1_o Xs)) (@ tptp.size_size_list_o Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs)) (@ tptp.size_size_list_nat Xs))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs)) (@ tptp.size_size_list_int Xs))))
% 6.19/6.59 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.19/6.59 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.19/6.59 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.19/6.59 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.19/6.59 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.19/6.59 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.19/6.59 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.19/6.59 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.19/6.59 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.19/6.59 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.19/6.59 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.19/6.59 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M2)) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ tptp.semiri2447717529341329178atural N)) (@ tptp.semiri2447717529341329178atural M2)) tptp.zero_z2226904508553997617atural))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N)))))))))
% 6.19/6.59 (assert (forall ((R4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R4) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R4)))) (@ (@ tptp.power_power_nat N) R4)))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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))))))))))))
% 6.19/6.59 (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))))))))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real) (W tptp.real) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) 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 Z2) M2)) (@ (@ tptp.power_power_real W) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z2) W))))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex) (W tptp.complex) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) 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 Z2) M2)) (@ (@ tptp.power_power_complex W) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z2) W))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P5 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D6))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P5 X3) (@ P5 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (@ P5 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ P (@ (@ tptp.minus_minus_int Y6) X2))))))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P5 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D6))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P5 X3) (@ P5 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D6))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (@ P5 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B5) (@ P (@ (@ tptp.plus_plus_int Y6) X2))))))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (B5 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X4) D6)) T)))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B5) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D6))))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.numera6690914467698888265omplex N)) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M2) (@ tptp.numeral_numeral_real N)) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M2) (@ tptp.numeral_numeral_rat N)) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M2) (@ tptp.numeral_numeral_nat N)) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M2) (@ tptp.numeral_numeral_int N)) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.numeral_numeral_int V)) (= M2 (@ tptp.numeral_numeral_nat V)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M2) N))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z2)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M2 N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M2 N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z2) (@ tptp.numera6690914467698888265omplex N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z2) (@ tptp.numeral_numeral_real N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z2) (@ tptp.numeral_numeral_rat N)) (= Z2 (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z2) _let_1) (= Z2 _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real X)) (@ tptp.real_V7735802525324610683m_real X))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.19/6.59 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.19/6.59 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.19/6.59 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.19/6.59 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri2265585572941072030t_real N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M2))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M2))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ 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)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ 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)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M2))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M2))) (= (@ (@ 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)))))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.19/6.59 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M2))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5074537144036343181t_real N))))
% 6.19/6.59 (assert (forall ((V tptp.num) (V2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V2)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V2))))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) _let_1) (@ (@ tptp.ord_less_eq_int Z2) _let_1)))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z2)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z2)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z2))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z2) (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) _let_1) (@ (@ tptp.ord_less_int Z2) _let_1)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.19/6.59 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.19/6.59 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((X 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 X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X 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 X)) (@ _let_1 X)))))
% 6.19/6.59 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((X 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 X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.19/6.59 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.19/6.59 (assert (forall ((X 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 X))) 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 X))) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.19/6.59 (assert (forall ((X 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 X))) 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 X))) N)) A))))
% 6.19/6.59 (assert (forall ((X 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 X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.19/6.59 (assert (forall ((X 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 X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.19/6.59 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (= tptp.numeral_numeral_nat (lambda ((I2 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I2)))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) A)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N)) tptp.ring_1_Ints_complex)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N)) tptp.ring_1_Ints_real)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.member_rat (@ tptp.numeral_numeral_rat N)) tptp.ring_1_Ints_rat)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N)) tptp.ring_1_Ints_int)))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.19/6.59 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.19/6.59 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.19/6.59 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.19/6.59 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.19/6.59 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (N tptp.nat) (Z2 tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z2) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z2))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (N tptp.nat) (Z2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z2) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z2))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z2 tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z2))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z2 tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z2))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z2))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E2))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (B5 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D6))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D6))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D6))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (B5 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D6))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D6))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D6))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D6))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D6))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D6))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D6))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D6))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D6))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 6.19/6.59 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.real_V7735802525324610683m_real A))))))
% 6.19/6.59 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.inverse_inverse_real (@ tptp.real_V1022390504157884413omplex A))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.19/6.59 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X7 tptp.int)) (@ P X7)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B5) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.minus_minus_int X4) D6) T))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int T) B5) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.minus_minus_int X4) D6) T)))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (B5 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X4) D6)) T)))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int T) B5) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D6))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.plus_plus_int X4) D6) T))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.plus_plus_int X4) D6) T)))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) D6)) T))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D6)))))))))
% 6.19/6.59 (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))))))))))))
% 6.19/6.59 (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))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (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)))))))))))))
% 6.19/6.59 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X7 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X7 M5)) (@ X7 N4)))) E3)))))))))))
% 6.19/6.59 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X7 M5)) (@ X7 N4)))) E3)))))))))))
% 6.19/6.59 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M3)) (@ X8 N2)))) E)))))))) (@ tptp.topolo6517432010174082258omplex X8))))
% 6.19/6.59 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M3)) (@ X8 N2)))) E)))))))) (@ tptp.topolo4055970368930404560y_real X8))))
% 6.19/6.59 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M)) (@ X8 N6)))) E2))))))))))
% 6.19/6.59 (assert (forall ((X8 (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M)) (@ X8 N6)))) E2))))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D6)))))))))
% 6.19/6.59 (assert (forall ((D6 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D6) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X4) D6)) T))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)))))
% 6.19/6.59 (assert (forall ((H tptp.real) (Z2 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 Z2))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z2) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) 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))) H)) (@ _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 H)))))))))))))
% 6.19/6.59 (assert (forall ((H tptp.complex) (Z2 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 Z2))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z2) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) 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))) H)) (@ (@ 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 H))))))))))))
% 6.19/6.59 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 6.19/6.59 (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.log2 (@ 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))))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X23 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X23) (@ tptp.bit0 Y2)) (= X23 Y2))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.19/6.59 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H2 tptp.nat) (L2 tptp.nat) (D4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D4))) L2))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))))
% 6.19/6.59 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))))
% 6.19/6.59 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real Y))) (= X (@ tptp.uminus_uminus_real Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex Y))) (= X (@ tptp.uminus_uminus_real Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y)) (= (@ tptp.uminus_uminus_real X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)) (= (@ tptp.uminus_uminus_real X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex X)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri8010041392384452111omplex N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5044797733671781792omplex N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M2 tptp.one)))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.one_one_Code_natural))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.one_one_Code_natural))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.19/6.59 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M2) _let_1))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M2))) _let_1) (@ (@ tptp.modulo_modulo_nat M2) _let_1)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M2))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M2)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M2)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M2)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M2)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M2)))))
% 6.19/6.59 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.19/6.59 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z2226904508553997617atural)) (= _let_1 tptp.one_one_Code_natural)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_natural)) (= _let_1 tptp.zero_z2226904508553997617atural)))))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.19/6.59 (assert (= tptp.sgn_sgn_complex (lambda ((Z6 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex Z6) (@ tptp.real_V4546457046886955230omplex (@ tptp.real_V1022390504157884413omplex Z6))))))
% 6.19/6.59 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.19/6.59 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.19/6.59 (assert (forall ((X23 tptp.num)) (not (= tptp.one (@ tptp.bit0 X23)))))
% 6.19/6.59 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.19/6.59 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X)) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y)))))))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M2) (@ tptp.suc (@ _let_1 N)))))))
% 6.19/6.59 (assert (forall ((M2 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 M2)) (@ _let_1 N))))))
% 6.19/6.59 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.real_V4546457046886955230omplex X)) N) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 6.19/6.59 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_complex Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_real Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_rat Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_nat Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z2) (@ (@ tptp.plus_plus_int Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex Z2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real)) (= (@ (@ tptp.times_times_real Z2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.rat)) (= (@ (@ tptp.times_times_rat Z2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.nat)) (= (@ (@ tptp.times_times_nat Z2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z2) Z2))))
% 6.19/6.59 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.times_times_int Z2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z2) Z2))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X tptp.code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X3) (@ (@ P X3) (@ (@ tptp.power_8256067586552552935nteger X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ P X3) (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X3) (@ (@ P X3) (@ (@ tptp.power_power_rat X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ (@ P X3) (@ (@ tptp.power_power_int X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 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 M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)))))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.19/6.59 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 6.19/6.59 (assert (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y))))))
% 6.19/6.59 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))))
% 6.19/6.59 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))))
% 6.19/6.59 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.19/6.59 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((A tptp.nat) (M2 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 M2))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.19/6.59 (assert (forall ((A tptp.int) (M2 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 M2))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N) (@ P M5))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N) (@ P M5))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z2)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z2)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z2)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.real_V1803761363581548252l_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real X)) (@ tptp.exp_complex (@ tptp.real_V4546457046886955230omplex X)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ (@ tptp.power_power_rat X) _let_1)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.19/6.59 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.19/6.59 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.19/6.59 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.19/6.59 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.19/6.59 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.19/6.59 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.19/6.59 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.19/6.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.19/6.59 (assert (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide5121882707175180666atural A) _let_1) A) (= (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) tptp.zero_z2226904508553997617atural)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((A tptp.int) (N tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)))) _let_2))))))
% 6.19/6.59 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 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 M2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)))) _let_2))))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)))) _let_2))))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.divide5121882707175180666atural A) _let_2)) (@ _let_1 M2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2)))) _let_2))))))
% 6.19/6.59 (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)))))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z2))) _let_1)))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z2))) _let_1)))))
% 6.19/6.59 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (M2 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)) M2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 6.19/6.59 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ 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))))))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.19/6.59 (assert (= tptp.arcosh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ 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))))))))))
% 6.19/6.59 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 6.19/6.59 (assert (forall ((M2 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 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) 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) M2)))) _let_2)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.cosh_real X) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (= (@ tptp.cosh_complex X) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q5))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q5)) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q5))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q5)) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q5))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q5)) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (= tptp.cosh_real (lambda ((Z6 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z6)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z6)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (= tptp.cosh_complex (lambda ((Z6 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z6)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z6)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.19/6.59 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.19/6.59 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.19/6.59 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.19/6.59 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.59 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.19/6.59 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.59 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.19/6.59 (assert (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M2))))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log2 (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z2))) (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 Z2))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z2))) (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 Z2))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.19/6.59 (assert (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (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.log2 (@ 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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.19/6.59 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (assert (forall ((Z2 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) Z2)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z2) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.19/6.59 (assert (forall ((Z2 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) Z2)) _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 Z2) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.19/6.59 (assert (forall ((Z2 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) Z2)) _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 Z2) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.19/6.59 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.19/6.59 (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.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.19/6.59 (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.log2 (@ 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))))))))))
% 6.19/6.59 (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.log2 (@ 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))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.19/6.59 (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.log2 (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) X)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) Y)))))
% 6.19/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.19/6.59 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M2 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) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M2))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.19/6.59 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.19/6.59 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y6)))))
% 6.19/6.59 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M5) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.19/6.59 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M2)))))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 6.19/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.19/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se7083795435491715335atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se1617098188084679374atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se168947363167071951atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))))
% 6.19/6.59 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y 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 Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y 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 Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 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 X2))) (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2)))))
% 6.19/6.59 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X2 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 X2))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim3151403230148437115or_rat X2)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ tptp.set_set_nat2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((N tptp.int)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.ring_1_of_int_real N)) N)))
% 6.19/6.59 (assert (forall ((N tptp.int)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.ring_1_of_int_rat N)) N)))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.59 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.19/6.59 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.19/6.59 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.19/6.59 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z tptp.list_VEBT_VEBT)) (= Y4 Z)) (lambda ((Xs3 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (= (@ (@ tptp.nth_VEBT_VEBT Xs3) I2) (@ (@ tptp.nth_VEBT_VEBT Ys3) I2))))))))
% 6.19/6.59 (assert (= (lambda ((Y4 tptp.list_o) (Z tptp.list_o)) (= Y4 Z)) (lambda ((Xs3 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I2) (@ (@ tptp.nth_o Ys3) I2))))))))
% 6.19/6.59 (assert (= (lambda ((Y4 tptp.list_nat) (Z tptp.list_nat)) (= Y4 Z)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I2) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 6.19/6.59 (assert (= (lambda ((Y4 tptp.list_int) (Z tptp.list_int)) (= Y4 Z)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I2) (@ (@ tptp.nth_int Ys3) I2))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P I2) X7)))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_VEBT_VEBT Xs3) I2)))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 Bool)) (@ (@ P I2) X7)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_o Xs3) I2)))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.nat)) (@ (@ P I2) X7)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs3) I2)))))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.int)) (@ (@ P I2) X7)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_int Xs3) I2)))))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) (@ (@ tptp.nth_VEBT_VEBT Ys2) I3)))) (= Xs Ys2)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) (@ (@ tptp.nth_o Ys2) I3)))) (= Xs Ys2)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys2) I3)))) (= Xs Ys2)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) (@ (@ tptp.nth_int Ys2) I3)))) (= Xs Ys2)))))
% 6.19/6.59 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.19/6.59 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.19/6.59 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N)) (@ tptp.set_complex2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N)) (@ tptp.set_set_nat2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I2) X))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I3)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X)))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I2)))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I2)))))))
% 6.19/6.59 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I2)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim8280529875227126926d_real X))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim7778729529865785530nd_rat X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_VEBT_VEBT (@ tptp.rotate1_VEBT_VEBT Xs)) N) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_o (@ tptp.rotate1_o Xs)) N) (@ (@ tptp.nth_o Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rotate1_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rotate1_int Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) _let_1)))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((Z2 tptp.real) (M2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z2))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M2)))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.rat) (M2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z2))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z2))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M2)))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X2 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ 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 X)))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ 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 X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ 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 X)))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ 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 X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ 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 X) N))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ 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 X) N))))
% 6.19/6.59 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X2) N4))) (@ (@ tptp.vEBT_VEBT_low X2) N4)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.log2 _let_1) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.19/6.59 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.19/6.59 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.19/6.59 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M2))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) _let_1)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.19/6.59 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.19/6.59 (assert (forall ((X23 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X23) (@ tptp.bit1 X32)))))
% 6.19/6.59 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.19/6.59 (assert (not (= tptp.pi tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)) K))))
% 6.19/6.59 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X24 tptp.num)) (not (= Y (@ tptp.bit0 X24)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 6.19/6.59 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.19/6.59 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) K)))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X) _let_1))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q5))) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q5))) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((N tptp.num) (Q5 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q5))) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))))))))))))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.19/6.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (Q5 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q5)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int Q5)) tptp.zero_zero_int)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (Q5 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q5)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M2))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat Q5)) tptp.zero_zero_nat)))))
% 6.19/6.59 (assert (forall ((M2 tptp.num) (Q5 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q5)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M2))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger Q5)) tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.59 (assert (forall ((Q5 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q5)))) (= (= (@ (@ 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 Q5)) tptp.zero_zero_int)))))
% 6.19/6.59 (assert (forall ((Q5 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q5)))) (= (= (@ (@ 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 Q5)) tptp.zero_zero_nat)))))
% 6.19/6.59 (assert (forall ((Q5 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q5)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q5)) tptp.zero_z3403309356797280102nteger)))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M2)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M2)) N))))
% 6.19/6.59 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ 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))))))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y))))
% 6.19/6.59 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log2 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.19/6.59 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((M2 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)) M2))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.uminus_uminus_real X)) (@ tptp.cos_real X))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.cos_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.cos_complex X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.sin_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)))))
% 6.19/6.59 (assert (= (@ tptp.cot_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.cot_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.cot_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.cot_complex X)))))
% 6.19/6.59 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.19/6.59 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.19/6.59 (assert (= (@ tptp.sin_real tptp.pi) tptp.zero_zero_real))
% 6.19/6.59 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.19/6.59 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.sin_real X))))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.19/6.59 (assert (= (@ tptp.cot_real tptp.pi) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.sin_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.sin_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.zero_zero_complex))
% 6.19/6.59 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.19/6.59 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.19/6.59 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.19/6.59 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.19/6.59 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.19/6.59 (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))
% 6.19/6.59 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.19/6.59 (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)))
% 6.19/6.59 (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)))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))
% 6.19/6.59 (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)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.cot_real X)) (@ tptp.cot_real (@ tptp.real_V1803761363581548252l_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.cot_real X)) (@ tptp.cot_complex (@ tptp.real_V4546457046886955230omplex X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.sin_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (= tptp.cot_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X2)) (@ tptp.sin_complex X2)))))
% 6.19/6.59 (assert (= tptp.cot_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A4))) (= Y (@ _let_1 (@ tptp.sin_real A4))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (not (= (@ tptp.cos_real (@ tptp.arctan X)) tptp.zero_zero_real))))
% 6.19/6.59 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M2)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (X tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M2)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M2)) X))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M2)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X)))))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (X tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M2)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M2)) X))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z2)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z2) W)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z2)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z2) W)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z2))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z2))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z2))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z2))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z2))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z2))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))))
% 6.19/6.59 (assert (= tptp.sin_real (lambda ((X2 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)))) X2)))))
% 6.19/6.59 (assert (= tptp.sin_complex (lambda ((X2 tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.19/6.59 (assert (= tptp.cos_real (lambda ((X2 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)))) X2)))))
% 6.19/6.59 (assert (= tptp.cos_complex (lambda ((X2 tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X2)))))
% 6.19/6.59 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.19/6.59 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.pi)) _let_1)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.19/6.59 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.19/6.59 (assert (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y5) tptp.zero_zero_real)) (= Y5 X3))))))
% 6.19/6.59 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B2) A3)) Acc) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F2) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (@ (@ F2 A3) Acc))))))
% 6.19/6.59 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb3 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb3) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb3) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb3) (@ (@ X Xa) Xc))))))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.19/6.59 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.cos_real Y5) Y)) (= Y5 X3)))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z2)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z2)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z2)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z2)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z2)) _let_1)))))))
% 6.19/6.59 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z2))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z2)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((W tptp.real) (Z2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z2))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 6.19/6.59 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.19/6.59 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y) (forall ((Y5 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)) Y5) (@ (@ tptp.ord_less_eq_real Y5) _let_1) (= (@ tptp.sin_real Y5) Y)) (= Y5 X3)))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.19/6.59 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N4 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.19/6.59 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.19/6.59 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.19/6.59 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.19/6.59 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.19/6.59 (assert (forall ((Z2 tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z2) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z2 (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) 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) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) 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)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.19/6.59 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.19/6.59 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X)) Y) (@ (@ tptp.dvd_dvd_Code_integer X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 6.19/6.59 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.19/6.59 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M2))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.19/6.59 (assert (forall ((M2 tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M2))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.19/6.59 (assert (forall ((M2 tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M2))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.19/6.59 (assert (forall ((M2 tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M2))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.19/6.59 (assert (forall ((M2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M2)) K) (@ (@ tptp.dvd_dvd_int M2) K))))
% 6.19/6.59 (assert (forall ((M2 tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M2)) K) (@ (@ tptp.dvd_dvd_real M2) K))))
% 6.19/6.59 (assert (forall ((M2 tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M2)) K) (@ (@ tptp.dvd_dvd_Code_integer M2) K))))
% 6.19/6.59 (assert (forall ((M2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M2)) K) (@ (@ tptp.dvd_dvd_rat M2) K))))
% 6.19/6.59 (assert (= (@ tptp.tan_real tptp.pi) tptp.zero_zero_real))
% 6.19/6.59 (assert (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.tan_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.complex)) (= (@ tptp.tan_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.tan_complex X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.19/6.59 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.modulo8411746178871703098atural B) A) tptp.zero_z2226904508553997617atural))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))))
% 6.19/6.59 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.19/6.59 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.19/6.59 (assert (forall ((X tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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))))
% 6.19/6.59 (assert (forall ((M2 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 M2) N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)))))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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)))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (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))))))))))
% 6.19/6.59 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N))) (let ((_let_3 (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo8411746178871703098atural A) _let_2))))))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (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))))))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.19/6.59 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (=> (@ (@ tptp.dvd_dvd_nat N) M2) (= M2 N)))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M2)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M2) N))))
% 6.19/6.59 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M2) N))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.tan_real X)) (@ tptp.tan_real (@ tptp.real_V1803761363581548252l_real X)))))
% 6.19/6.59 (assert (forall ((X tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.tan_real X)) (@ tptp.tan_complex (@ tptp.real_V4546457046886955230omplex X)))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.19/6.59 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.19/6.59 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.19/6.59 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.19/6.59 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.19/6.59 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.19/6.59 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.19/6.59 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.19/6.59 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.19/6.59 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.19/6.59 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.19/6.59 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.59 (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))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 6.19/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.19/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K3))))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K3 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K3))))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.19/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.19/6.60 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 6.19/6.60 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))))
% 6.19/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K2))))))))
% 6.19/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.19/6.60 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.19/6.60 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.19/6.60 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z2)))))))
% 6.19/6.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z2)))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z2)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 6.19/6.60 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.19/6.60 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C))) (=> (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ _let_1 A))))))
% 6.19/6.60 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D)))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (= (@ tptp.tan_real (@ tptp.arctan Y)) Y)))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int X4) Z4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z4 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z4 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int Z4) X4) (= _let_1 _let_1)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 6.19/6.60 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.19/6.60 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_Code_natural (lambda ((A3 tptp.code_natural) (B2 tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural B2) A3) tptp.zero_z2226904508553997617atural))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.dvd_dvd_Code_natural B) A))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.19/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.19/6.60 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.19/6.60 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))))))
% 6.19/6.60 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N)))))))
% 6.19/6.60 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 M2)))))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y3)) D5) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y3)) D5)))))))))
% 6.19/6.60 (assert (= tptp.cot_real (lambda ((X2 tptp.real)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 6.19/6.60 (assert (= tptp.cot_complex (lambda ((X2 tptp.complex)) (@ tptp.invers8013647133539491842omplex (@ tptp.tan_complex X2)))))
% 6.19/6.60 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ tptp.inverse_inverse_real (@ tptp.cot_real X2)))))
% 6.19/6.60 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ tptp.invers8013647133539491842omplex (@ tptp.cot_complex X2)))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (D6 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D6) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D6))) T))))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D6))) T))))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (D6 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D6) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D6))) T))))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D6))) T))))))))
% 6.19/6.60 (assert (forall ((D tptp.code_integer) (D6 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D6) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D6))) T)))))))))
% 6.19/6.60 (assert (forall ((D tptp.real) (D6 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D6) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D6))) T)))))))))
% 6.19/6.60 (assert (forall ((D tptp.rat) (D6 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D6) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D6))) T)))))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D6))) T)))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.19/6.60 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D5 tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D5))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (Q5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q5) (@ (@ tptp.modulo_modulo_nat N) Q5)) (@ (@ tptp.dvd_dvd_nat Q5) (@ (@ tptp.minus_minus_nat M2) N))))))
% 6.19/6.60 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.19/6.60 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.19/6.60 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.19/6.60 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.19/6.60 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.19/6.60 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.19/6.60 (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 ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B3)))))))))))))))
% 6.19/6.60 (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 ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B3)))))))))))))))
% 6.19/6.60 (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 ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B3)))))))))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.19/6.60 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.19/6.60 (assert (= (lambda ((Y4 tptp.code_integer) (Z tptp.code_integer)) (= Y4 Z)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.19/6.60 (assert (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.19/6.60 (assert (= (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N)))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))))
% 6.19/6.60 (assert (forall ((Q5 tptp.nat) (N tptp.nat) (R4 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R4) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q5))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q5)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q5)))))))))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.60 (assert (forall ((R4 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R4) N) (=> (@ (@ tptp.ord_less_eq_nat R4) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R4)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R4))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.modulo8411746178871703098atural A) _let_1) tptp.zero_z2226904508553997617atural)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)) (= (@ (@ tptp.modulo8411746178871703098atural A) _let_1) tptp.one_one_Code_natural)))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (or (@ _let_1 A) (= M2 tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (and (@ _let_1 A) (not (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2) A)) (not (= (@ _let_1 A) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z2226904508553997617atural))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_natural))))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_natural))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X3)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y) (forall ((Y5 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)) Y5) (@ (@ tptp.ord_less_real Y5) _let_1) (= (@ tptp.tan_real Y5) Y)) (= Y5 X3)))))))))
% 6.19/6.60 (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)))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_real X3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X3) Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X))) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z4) (@ (@ tptp.ord_less_real Z4) _let_1) (= (@ tptp.tan_real Z4) X)))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.19/6.60 (assert (forall ((M2 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 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (M2 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 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.19/6.60 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.19/6.60 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.19/6.60 (assert (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) 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 N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))
% 6.19/6.60 (assert (= tptp.cos_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ tptp.semiri2265585572941072030t_real N4))) tptp.zero_zero_real)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M2) N))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.19/6.60 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.19/6.60 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.19/6.60 (assert (forall ((R4 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R4)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R4 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((L tptp.int) (R4 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R4))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R4 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((L tptp.int) (R4 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R4)) K)) (or (@ _let_1 K) (= R4 tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((L tptp.int) (K tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R4))) (or (@ _let_1 K) (= R4 tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_int (lambda ((D4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int D4)) __flatten_var_0))))
% 6.19/6.60 (assert (= tptp.dvd_dvd_int (lambda ((D4 tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) (@ tptp.uminus_uminus_int T2)))))
% 6.19/6.60 (assert (forall ((K tptp.int) (M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M2) N)) (=> (@ _let_1 N) (@ _let_1 M2))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.19/6.60 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M2) N) (=> (@ (@ tptp.dvd_dvd_int N) M2) (= M2 N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_int M2) N) (not (@ (@ tptp.dvd_dvd_int N) M2))))))
% 6.19/6.60 (assert (forall ((K tptp.int) (M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M2) N))))))
% 6.19/6.60 (assert (forall ((K tptp.int) (M2 tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M2) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 T)))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 6.19/6.60 (assert (forall ((K tptp.int) (N tptp.int) (M2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M2))) (@ _let_1 N)))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.19/6.60 (assert (forall ((Z2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z2) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z2) N)))))
% 6.19/6.60 (assert (forall ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I))))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.ring_17405671764205052669omplex A)) (@ tptp.ring_17405671764205052669omplex B))) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) tptp.ring_1_Ints_rat))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_int (@ (@ tptp.divide_divide_int (@ tptp.ring_1_of_int_int A)) (@ tptp.ring_1_of_int_int B))) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.19/6.60 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M2) N)) M2) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D6)) T)))))))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D6)) T))))))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (B5 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D6)) T))))))))))
% 6.19/6.60 (assert (forall ((D tptp.int) (D6 tptp.int) (B5 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D6) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D6)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D6)) T)))))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((Z2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z2))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z2)) M2) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z2) (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.19/6.60 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.19/6.60 (assert (= tptp.arctan (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (= (@ tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.60 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.19/6.60 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.19/6.60 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.19/6.60 (assert (forall ((A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.cis A)) (@ tptp.cis (@ tptp.uminus_uminus_real A)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 _let_1)) (@ tptp.ring_17405671764205052669omplex _let_1)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_rat _let_1)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))))
% 6.19/6.60 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.19/6.60 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.19/6.60 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.19/6.60 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M2))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 6.19/6.60 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A) _let_1))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N4)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (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))))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.19/6.60 (assert (= tptp.bit_se569199155075624693atural (lambda ((N4 tptp.nat) (A3 tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_natural (= N4 tptp.zero_zero_nat)) tptp.zero_z2226904508553997617atural) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide5121882707175180666atural A3) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A3) _let_1)))))))
% 6.19/6.60 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.19/6.60 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y)))))))
% 6.19/6.60 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y))))))))
% 6.19/6.60 (assert (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.19/6.60 (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)))
% 6.19/6.60 (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))
% 6.19/6.60 (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))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.nat2 (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.19/6.60 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.19/6.60 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.19/6.60 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.19/6.60 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.19/6.60 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.19/6.60 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.19/6.60 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.19/6.60 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.19/6.60 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.19/6.60 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_real (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_rat (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.19/6.60 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.19/6.60 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.19/6.60 (assert (= (@ tptp.invers8013647133539491842omplex tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 6.19/6.60 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))))
% 6.19/6.60 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 6.19/6.60 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.19/6.60 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.19/6.60 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.19/6.60 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.19/6.60 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.19/6.60 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (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)))
% 6.19/6.60 (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)))
% 6.19/6.60 (assert (forall ((Z2 tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z2) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z2))) _let_1)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.60 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.60 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((M2 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 M2) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 6.19/6.60 (assert (forall ((M2 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 M2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 6.19/6.60 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.60 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((P4 Bool) (Q5 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P4) (@ tptp.zero_n2684676970156552555ol_int Q5)) (= P4 Q5))))
% 6.19/6.60 (assert (forall ((P4 Bool) (Q5 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P4) (@ tptp.zero_n2687167440665602831ol_nat Q5)) (= P4 Q5))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (not (or (and P4 (not (@ P tptp.one_one_complex))) (and (not P4) (not (@ P tptp.zero_zero_complex))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (not (or (and P4 (not (@ P tptp.one_one_real))) (and (not P4) (not (@ P tptp.zero_zero_real))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (not (or (and P4 (not (@ P tptp.one_one_rat))) (and (not P4) (not (@ P tptp.zero_zero_rat))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (not (or (and P4 (not (@ P tptp.one_one_int))) (and (not P4) (not (@ P tptp.zero_zero_int))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (not (or (and P4 (not (@ P tptp.one_one_nat))) (and (not P4) (not (@ P tptp.zero_zero_nat))))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (and (=> P4 (@ P tptp.one_one_complex)) (=> (not P4) (@ P tptp.zero_zero_complex))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (and (=> P4 (@ P tptp.one_one_real)) (=> (not P4) (@ P tptp.zero_zero_real))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (and (=> P4 (@ P tptp.one_one_rat)) (=> (not P4) (@ P tptp.zero_zero_rat))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (and (=> P4 (@ P tptp.one_one_int)) (=> (not P4) (@ P tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (and (=> P4 (@ P tptp.one_one_nat)) (=> (not P4) (@ P tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P6 Bool)) (@ (@ (@ tptp.if_complex P6) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.19/6.60 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P6 Bool)) (@ (@ (@ tptp.if_real P6) tptp.one_one_real) tptp.zero_zero_real))))
% 6.19/6.60 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_rat P6) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.19/6.60 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))))
% 6.19/6.60 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((W tptp.complex) (Z2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z2) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z2)))))))
% 6.19/6.60 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 6.19/6.60 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M2))))
% 6.19/6.60 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A4) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.19/6.60 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo8411746178871703098atural _let_2) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.19/6.60 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.19/6.60 (assert (forall ((M2 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 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 6.19/6.60 (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)))))))))
% 6.19/6.60 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 6.19/6.60 (assert (forall ((M2 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 M2))) (= (@ (@ 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) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 6.19/6.60 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M2) 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 M2))) (@ (@ 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) M2)))))))))))))))))))
% 6.19/6.60 (assert (= tptp.modulo_modulo_int (lambda ((K3 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 K3))) (@ 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)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))))
% 6.19/6.60 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) 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 M2)))) (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) M2)))))) _let_1)))))))))))))))))
% 6.19/6.60 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ 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 K3) (@ 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) K3))))))))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.19/6.60 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.arg Z2))) (=> (not (= Z2 tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ 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))))))
% 6.19/6.60 (assert (forall ((Z2 tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z2) X))))))
% 6.19/6.60 (assert (forall ((Z2 tptp.complex)) (= (= (@ tptp.csqrt Z2) tptp.one_one_complex) (= Z2 tptp.one_one_complex))))
% 6.19/6.60 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.60 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.arg Z2))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.19/6.60 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M3)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (=> (= M3 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M3)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi 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 Mi) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M3)) (=> (= M3 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M3)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X4) N2))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi 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 Mi) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M3)) (=> (= M3 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M3)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X4) N2))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2)))))))))))))))))))))))))))))))
% 6.19/6.60 (assert (forall ((X23 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X23) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X23 Y2))))
% 6.19/6.60 (assert (forall ((X23 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X23) (@ tptp.some_num Y2)) (= X23 Y2))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y6 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y6)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.19/6.60 (assert (forall ((X tptp.option_num)) (= (forall ((Y6 tptp.num)) (not (= X (@ tptp.some_num Y6)))) (= X tptp.none_num))))
% 6.19/6.60 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y6 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y6))))))
% 6.19/6.60 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y6 tptp.num)) (= X (@ tptp.some_num Y6))))))
% 6.19/6.60 (assert (forall ((Mi2 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 Mi2) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.19/6.60 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.19/6.60 (assert (forall ((Deg tptp.nat) (Mi2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) Deg) TreeList) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi2) (= X Ma)))))))
% 6.19/6.60 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.19/6.60 (assert (forall ((Mi2 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) Deg) TreeList) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi2) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M2))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M2)) N))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M2))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi2 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) Deg) TreeList) Summary)) X))))))))
% 6.19/6.60 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.19/6.60 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8040316288895769887atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M2)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M2) N))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M2)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M2) N))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M3 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M3)))))))
% 6.19/6.60 (assert (forall ((X23 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X23)))))
% 6.19/6.60 (assert (forall ((X23 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X23)))))
% 6.19/6.60 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X23 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X23)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.19/6.60 (assert (forall ((Option tptp.option_num) (X23 tptp.num)) (=> (= Option (@ tptp.some_num X23)) (not (= Option tptp.none_num)))))
% 6.19/6.60 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X24 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X24))))))))
% 6.19/6.60 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X24 tptp.num)) (not (= Y (@ tptp.some_num X24))))))))
% 6.19/6.60 (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 ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.19/6.60 (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 ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.19/6.60 (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 ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.19/6.60 (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 ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.19/6.60 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A4 tptp.product_prod_nat_nat) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A4)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.19/6.60 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A4)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.19/6.60 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A4 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.19/6.60 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X) Y)))) _let_1))))))
% 6.19/6.60 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.19/6.60 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.19/6.60 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.19/6.60 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.19/6.60 (assert (forall ((Mi2 tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi2) (= X Ma)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 6.19/6.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.19/6.60 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) Y))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M2) A)) N) (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) A)) N) (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.19/6.60 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((V tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy2) Uz)) X))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.19/6.60 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M2)))))))
% 6.19/6.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.19/6.60 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N4) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))))))
% 6.19/6.60 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X23 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X23)) (@ (@ tptp.plus_plus_nat (@ X X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((X (-> tptp.num tptp.nat)) (X23 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X23)) (@ (@ tptp.plus_plus_nat (@ X X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) (@ _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)))))))))))
% 6.19/6.60 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.19/6.60 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N4))))))))
% 6.19/6.60 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 6.19/6.60 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_int))))
% 6.19/6.60 (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 ((J tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J)))) (= (@ (@ 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))))))))))
% 6.19/6.60 (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 ((J tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J)))) (= (@ (@ 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))))))))))
% 6.19/6.60 (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 ((J tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J)))) (= (@ (@ 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))))))))))
% 6.19/6.60 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.19/6.60 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.19/6.60 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.19/6.60 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 6.19/6.60 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi2 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi2 Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.19/6.60 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi2 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi2 Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.19/6.60 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A23 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N4))) (@ (@ 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 N4) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N4)) (= A23 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X2) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 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 N4))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X2) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.19/6.60 (assert (forall ((L tptp.num) (R4 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q5) R4)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R4))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R4))))))))))
% 6.19/6.60 (assert (forall ((L tptp.num) (R4 tptp.int) (Q5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q5) R4)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R4))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R4))))))))))
% 6.19/6.60 (assert (forall ((L tptp.num) (R4 tptp.code_integer) (Q5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q5) R4)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R4))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R4))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B5) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B5))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A2) B5) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B5))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B5) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B5))))
% 6.19/6.60 (assert (forall ((Q5 tptp.nat) (R4 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q5) R4)) (= R4 tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((Q5 tptp.int) (R4 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R4 tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_num) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys2)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8326237132889035090at_num (@ (@ tptp.product_nat_num Xs) Ys2)) N) (@ (@ tptp.product_Pair_nat_num (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.19/6.60 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B5) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B5)) (@ tptp.uminus5710092332889474511et_nat A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ tptp.uminus5710092332889474511et_nat B5)) (@ (@ tptp.ord_less_eq_set_nat B5) A2))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5))) (= (@ (@ tptp.minus_1356011639430497352at_nat _let_1) B5) _let_1))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B5) _let_1))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5)) (and (@ _let_1 A2) (not (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A2) A2) tptp.bot_bo2099793752762293965at_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A2) tptp.bot_bo2099793752762293965at_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A2) tptp.bot_bo2099793752762293965at_nat) A2)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.19/6.60 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.19/6.60 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (Ys2 tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys2)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.19/6.60 (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)))
% 6.19/6.60 (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)))
% 6.19/6.60 (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)))
% 6.19/6.60 (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)))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.19/6.60 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5)) (not (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5)) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B5)) (not (=> (@ _let_1 A2) (@ _let_1 B5)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M2) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M2) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (Z2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z2)))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (Z2 tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z2)))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.19/6.60 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D5)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (Z2 tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z2) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z2)))))
% 6.19/6.60 (assert (forall ((Y tptp.int) (Z2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z2) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (D6 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) C4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat D6) B5) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) (@ (@ tptp.minus_1356011639430497352at_nat C4) D6))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D6 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D6) B5) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B5)) (@ (@ tptp.minus_minus_set_nat C4) D6))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)) A2)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B5)) A2)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) C4) (= (@ (@ tptp.minus_1356011639430497352at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat C4) A2)) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B5) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (= (@ (@ tptp.minus_minus_set_nat B5) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (B5 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B5) (exists ((B3 tptp.complex)) (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B5) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (B5 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B5) (exists ((B3 tptp.real)) (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B5) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B5) (exists ((B3 tptp.set_nat)) (@ (@ tptp.member_set_nat B3) (@ (@ tptp.minus_2163939370556025621et_nat B5) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B5) (exists ((B3 tptp.int)) (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B5) (exists ((B3 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.minus_1356011639430497352at_nat B5) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B5) (exists ((B3 tptp.nat)) (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A2))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V3)) TreeList2) S2)) X3)))))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se2773287842338716102atural A) tptp.one_one_Code_natural) (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se2773287842338716102atural tptp.one_one_Code_natural) A) (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M5) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.19/6.60 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy) Uz2)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3)))))))))))
% 6.19/6.60 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy)) Uz2)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X3)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc2)) X3)))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd)) X3)))))))))))
% 6.19/6.60 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M2))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M2) 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)))))))))))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int) (Q5 tptp.int) (R4 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 Q5))) (=> (@ (@ 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 R4)) (@ (@ (@ 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 R4)) tptp.one_one_int)))))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 6.19/6.60 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (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 K3) _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 K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus612125837232591019t_real A2))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2))))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B5)) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (B5 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ (@ tptp.member_complex X) B5) (= (@ (@ tptp.minus_811609699411566653omplex (@ (@ tptp.insert_complex X) A2)) B5) (@ (@ tptp.minus_811609699411566653omplex A2) B5)))))
% 6.19/6.60 (assert (forall ((X tptp.real) (B5 tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) B5) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X) A2)) B5) (@ (@ tptp.minus_minus_set_real A2) B5)))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (B5 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B5) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A2)) B5) (@ (@ tptp.minus_2163939370556025621et_nat A2) B5)))))
% 6.19/6.60 (assert (forall ((X tptp.int) (B5 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) B5) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A2)) B5) (@ (@ tptp.minus_minus_set_int A2) B5)))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) B5) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) B5) (@ (@ tptp.minus_1356011639430497352at_nat A2) B5)))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (B5 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B5) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A2)) B5) (@ (@ tptp.minus_minus_set_nat A2) B5)))))
% 6.19/6.60 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex A2) (@ tptp.uminus8566677241136511917omplex (@ (@ tptp.insert_complex B) tptp.bot_bot_set_complex))) (not (@ (@ tptp.member_complex B) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A2) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A2)))))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M2) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M2)) tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M2) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M2)) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M2) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M2)) tptp.zero_z3403309356797280102nteger))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (B5 tptp.set_complex) (A2 tptp.set_complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B5))) (let ((_let_2 (@ tptp.insert_complex X))) (let ((_let_3 (@ (@ tptp.minus_811609699411566653omplex (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member_complex X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (B5 tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B5))) (let ((_let_2 (@ tptp.insert_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member_real X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (B5 tptp.set_set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B5))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (B5 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B5))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member_int X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B5))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (B5 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B5))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B5))) (let ((_let_4 (@ (@ tptp.member_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 6.19/6.60 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.19/6.60 (assert (forall ((K tptp.int) (L tptp.int) (Q5 tptp.int) (R4 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q5) R4)) (= (@ (@ tptp.divide_divide_int K) L) Q5))))
% 6.19/6.60 (assert (forall ((X tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex X))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ (@ tptp.minus_811609699411566653omplex (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_complex)) A2)))))
% 6.19/6.60 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_real)) A2)))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_set_nat)) A2)))))
% 6.19/6.60 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_int)) A2)))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A2)))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_nat)) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B5))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B5))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B5))))))
% 6.19/6.60 (assert (forall ((A tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex A))) (=> (@ (@ tptp.member_complex A) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))) A2)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.member_real A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) A2)))))
% 6.19/6.60 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_1 tptp.bot_bot_set_set_nat))) A2)))))
% 6.19/6.60 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) A2)))))
% 6.19/6.60 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A2)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B5)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B5)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B5)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ _let_1 tptp.bot_bot_set_int))))))
% 6.19/6.60 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (= (@ tptp.uminus6524753893492686040at_nat (@ _let_1 A2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.uminus6524753893492686040at_nat A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (B5 tptp.set_complex) (X tptp.complex) (C4 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B5))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_complex X) A2))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (B5 tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_set_nat) (B5 tptp.set_set_nat) (X tptp.set_nat) (C4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B5))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_set_nat X) A2))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (B5 tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B5))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8440522571783428010at_nat X) A2))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))))
% 6.19/6.60 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.19/6.60 (assert (forall ((L tptp.int) (K tptp.int) (Q5 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q5) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B5) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B5) (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B5) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B5))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X) A2))) (let ((_let_3 (@ tptp.insert_complex X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (let ((_let_2 (@ (@ tptp.member_set_nat X) A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B5 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B5 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B5)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 6.19/6.60 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I2)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I2) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3))))))
% 6.19/6.60 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.19/6.60 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.19/6.60 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.19/6.60 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R4 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q5))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q5) R4)) (=> (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) R4))))))))))
% 6.19/6.60 (assert (forall ((K tptp.int) (L tptp.int) (Q5 tptp.int) (R4 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 Q5) R4)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q5)) R4)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (@ (@ tptp.ord_less_int R4) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int R4) tptp.zero_zero_int))) (=> (not _let_2) (= Q5 tptp.zero_zero_int)))))))))))
% 6.19/6.60 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M5 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.19/6.60 (assert (forall ((R4 tptp.int) (L tptp.int) (K tptp.int) (Q5 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L)) R4)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q5) R4)))))))
% 6.19/6.60 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N4 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 M5)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.19/6.60 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L2)))) (exists ((R tptp.int) (L2 tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R)) (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R))))))))
% 6.19/6.60 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ 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)) (=> (= A33 (@ (@ 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)))))))))))))
% 6.19/6.60 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M5) N4)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.unique5026877609467782581ep_nat N4) (@ (@ tptp.unique5055182867167087721od_nat M5) (@ tptp.bit0 N4)))))))
% 6.19/6.60 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M5) N4)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.unique5024387138958732305ep_int N4) (@ (@ tptp.unique5052692396658037445od_int M5) (@ tptp.bit0 N4)))))))
% 6.19/6.60 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M5) N4)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.unique4921790084139445826nteger N4) (@ (@ tptp.unique3479559517661332726nteger M5) (@ tptp.bit0 N4)))))))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int) (Q5 tptp.int) (R4 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 Q5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R4)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R4)))))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((Q5 tptp.int) (R4 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q5) R4)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R4 tptp.zero_zero_int)))))))
% 6.19/6.60 (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))))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M2) N))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z2))) (=> (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)) Z2)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.19/6.60 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L3)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L3) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))) (@ (@ P K2) L3)))))) (@ (@ P A0) A1)))))
% 6.19/6.60 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J)) (@ (@ P I3) J)))) (@ (@ P A0) A1)))))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M2)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int)) tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sinh_real X) (@ tptp.sinh_real Y)) (= X Y))))
% 6.19/6.60 (assert (= (@ tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.sinh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sinh_real X)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ tptp.sinh_complex (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sinh_complex X)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.sinh_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ tptp.sinh_real X)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.19/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.19/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.19/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.19/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.19/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) N)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.produc6174133586879617921nteger (@ (@ tptp.unique3479559517661332726nteger tptp.one) N)))))
% 6.19/6.60 (assert (forall ((M2 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 M2))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M2) N)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M2) N))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ tptp.arsinh_real (@ tptp.sinh_real X)) X)))
% 6.19/6.60 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.19/6.60 (assert (= tptp.unique6322359934112328802ux_nat (lambda ((Qr tptp.product_prod_nat_nat)) (= (@ tptp.product_snd_nat_nat Qr) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (= tptp.unique6319869463603278526ux_int (lambda ((Qr tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int Qr) tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)) (@ tptp.exp_complex X))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)) (@ tptp.exp_real X))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex X)) (@ tptp.exp_complex X))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X)) (@ tptp.sinh_real X)) (@ tptp.exp_real X))))
% 6.19/6.60 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex X2)))))
% 6.19/6.60 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.cosh_real X)) (@ tptp.sinh_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)) (@ tptp.uminus_uminus_real (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X))) (@ tptp.cosh_complex X))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X))) (@ tptp.cosh_real X))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (@ (@ tptp.member_real (@ tptp.exp_real X)) (@ (@ tptp.insert_real tptp.one_one_real) (@ (@ tptp.insert_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.bot_bot_set_real))))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sinh_complex X) tptp.zero_zero_complex) (@ (@ tptp.member_complex (@ tptp.exp_complex X)) (@ (@ tptp.insert_complex tptp.one_one_complex) (@ (@ tptp.insert_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.bot_bot_set_complex))))))
% 6.19/6.60 (assert (= tptp.sinh_real (lambda ((Z6 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z6)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z6)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (assert (= tptp.sinh_complex (lambda ((Z6 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z6)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z6)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) tptp.one_one_real)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_2)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_2)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy) Uz2)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))))
% 6.19/6.60 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) X) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N) L))))
% 6.19/6.60 (assert (forall ((A Bool) (F (-> tptp.nat Bool)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_o A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_nat A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.19/6.60 (assert (forall ((A tptp.option_num) (F (-> tptp.nat tptp.option_num)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_option_num A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 6.19/6.60 (assert (forall ((A Bool) (F (-> tptp.nat Bool)) (V tptp.num) (N tptp.nat)) (= (@ (@ (@ tptp.case_nat_o A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (V tptp.num) (N tptp.nat)) (= (@ (@ (@ tptp.case_nat_nat A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N)))))
% 6.19/6.60 (assert (forall ((A tptp.option_num) (F (-> tptp.nat tptp.option_num)) (V tptp.num) (N tptp.nat)) (= (@ (@ (@ tptp.case_nat_option_num A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X)))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) A) (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) A) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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_se7788150548672797655nteger N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.19/6.60 (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_se545348938243370406it_int N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.19/6.60 (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_se547839408752420682it_nat N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.19/6.60 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.pred_numeral L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.19/6.60 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.19/6.60 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.19/6.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.19/6.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.19/6.60 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A6 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (not (@ (@ tptp.member_complex X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus612125837232591019t_real (lambda ((A6 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (not (@ (@ tptp.member_real X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (not (@ (@ tptp.member_list_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A6)))))))
% 6.19/6.60 (assert (forall ((P (-> tptp.real Bool))) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (not (@ P X2)))) (@ tptp.uminus612125837232591019t_real (@ tptp.collect_real P)))))
% 6.19/6.60 (assert (forall ((P (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (not (@ P X2)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P)))))
% 6.19/6.60 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ P X2)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 6.19/6.60 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ P X2)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 6.19/6.60 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ P X2)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 6.19/6.60 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A6 tptp.set_complex)) (@ tptp.collect_complex (@ tptp.uminus1680532995456772888plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus612125837232591019t_real (lambda ((A6 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ tptp.uminus5770388063884162150_nat_o (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6)))))))
% 6.19/6.60 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6)))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se7788150548672797655nteger N))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 A))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ _let_1 A))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.19/6.60 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.19/6.60 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.19/6.60 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.19/6.60 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.19/6.60 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.19/6.60 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.19/6.60 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)))))
% 6.19/6.60 (assert (forall ((H (-> Bool Bool)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> Bool tptp.nat)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> Bool tptp.option_num)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.nat Bool)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.nat tptp.nat)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.nat tptp.option_num)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.option_num Bool)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.option_num tptp.nat)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X2 tptp.nat)) (@ H (@ F22 X2)))) Nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat N) M2)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M2))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat M2) N)) (@ (@ tptp.bit_se545348938243370406it_int M2) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M2))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se6528837805403552850or_nat M2) N)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se6528837805403552850or_nat M2) N)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.19/6.60 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.19/6.60 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.19/6.60 (assert (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.19/6.60 (assert (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.19/6.60 (assert (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.19/6.60 (assert (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.19/6.60 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X25 tptp.nat)) X25))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M2)) N))))
% 6.19/6.60 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.19/6.60 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A6))) (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A6))) (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.minus_2270307095948843157_nat_o (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A6))) (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) B6)))))))
% 6.19/6.60 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B6)))))))
% 6.19/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) A)))) (@ tptp.collect_real (lambda ((C3 tptp.real)) (@ (@ tptp.dvd_dvd_real C3) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 6.19/6.60 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.19/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.19/6.60 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.19/6.60 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.19/6.60 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.19/6.60 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.19/6.60 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.19/6.60 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N4))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A3))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N4)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))
% 6.19/6.60 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A3))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N4)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M2) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M2) N)) A))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M2) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat M2) N)) A))))))
% 6.19/6.60 (assert (forall ((Z3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z2) Z3))) (let ((_let_2 (@ tptp.nat2 Z2))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z3)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z3) 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)))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M2) K)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M2))))))
% 6.19/6.60 (assert (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N4))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (Q5 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M2) Q5)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q5) (@ (@ tptp.minus_minus_nat N) M2))))))
% 6.19/6.60 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= N4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.19/6.60 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.19/6.60 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.19/6.60 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.19/6.60 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.19/6.60 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.19/6.60 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)) tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 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 A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.19/6.60 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.19/6.60 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.19/6.60 (assert (forall ((Uy2 tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.19/6.60 (assert (forall ((Mi2 tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) _let_1) TreeList) Vc)) X) (or (= X Mi2) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.19/6.60 (assert (forall ((Mi2 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi2)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma))) _let_1) TreeList) Summary)) X) (=> (not (= X Mi2)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V3)) TreeList2) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V3)) TreeList2) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V3)) TreeList2) S2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa Mi) (= Xa Ma2))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc2))) (not (or (= Xa Mi) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))))))))
% 6.19/6.60 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.19/6.60 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N4 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 M5)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.19/6.60 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa Mi) (= Xa Ma2)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc2))) (or (= Xa Mi) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy))) Y) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa Mi) (= Xa Ma2)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc2))) (= Y (not (or (= Xa Mi) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))
% 6.19/6.60 (assert (forall ((Bs tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ (@ tptp.groups9119017779487936845_o_nat tptp.zero_n2687167440665602831ol_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Bs)) N) (and (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N)))))
% 6.19/6.60 (assert (forall ((Bs tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Bs)) N) (and (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N)))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (= Y (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy) Uz2))) Y) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (= Y (not (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))))))
% 6.19/6.60 (assert (= tptp.ring_1_of_int_int (lambda ((K3 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 K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.19/6.60 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.19/6.60 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.19/6.60 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.19/6.60 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 6.19/6.60 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z2) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.19/6.60 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z2) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.19/6.60 (assert (forall ((Z2 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 Z2) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z2) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups3708469109370488835omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_int (@ F X3)) tptp.ring_1_Ints_int))) (@ (@ tptp.member_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups713298508707869441omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_int (@ F X3)) tptp.ring_1_Ints_int))) (@ (@ tptp.member_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups6464643781859351333omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups7440179247065528705omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups766887009212190081x_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ F tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ F tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.19/6.60 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.19/6.60 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I2)))) _let_1)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I2)))) _let_1)))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G M2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N4 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 6.19/6.60 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 6.19/6.60 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 6.19/6.60 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 6.19/6.60 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M2)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.19/6.60 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N4 tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N4) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 6.19/6.60 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N4 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N4) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 6.19/6.60 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N4 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N4) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 6.19/6.60 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N4) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 6.19/6.60 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N4) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.rat)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.60 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.19/6.60 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 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 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.19/6.60 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) tptp.bot_bot_set_nat) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups705719431365010083at_int G) tptp.bot_bot_set_nat) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) tptp.bot_bot_set_int) tptp.one_one_int)))
% 6.19/6.60 (assert (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.19/6.60 (assert (= (@ tptp.suminf_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.19/6.60 (assert (= (@ tptp.suminf_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J2))))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J2))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A2) tptp.one_one_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A2) tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A2) tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A2) tptp.one_one_complex)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.one_one_complex)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A2) tptp.one_one_complex)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.one_one_complex)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A2) tptp.one_one_complex)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (= (@ G A4) tptp.one_one_complex)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A2) tptp.one_one_complex)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.one_one_complex)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.one_one_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.one_one_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (= (@ G A4) tptp.one_one_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.one_one_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.rat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups225925009352817453ex_rat G) A2) tptp.one_one_rat)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.one_one_rat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A2) tptp.one_one_rat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.one_one_rat)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) 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.groups766887009212190081x_real F) A2)) tptp.one_one_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) 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.groups225925009352817453ex_rat F) A2)) tptp.one_one_rat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) 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))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) 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.groups861055069439313189ex_nat F) A2)) tptp.one_one_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) 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))))
% 6.19/6.60 (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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.19/6.60 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 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 (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I))))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I))))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M2) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M2 N) (=> (not (= M2 tptp.zero_zero_nat)) (= X Y))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (= R I)) (@ F R)) tptp.zero_zero_real)))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (= R I)) (@ F R)) tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (= R I)) (@ F R)) tptp.zero_zero_int)))))
% 6.19/6.60 (assert (@ tptp.summable_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)))
% 6.19/6.60 (assert (@ tptp.summable_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (@ tptp.summable_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.set_nat) (N tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I) X))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I) X))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I) X))))
% 6.19/6.60 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.19/6.60 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (@ tptp.bit_ri7632146776885996613nteger X))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 6.19/6.60 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 6.19/6.60 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X)) X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.60 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.bit_ri7632146776885996613nteger X)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.19/6.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ tptp.inc N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.19/6.60 (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))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.19/6.60 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N4)))) (@ tptp.summable_real F))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N4)))) (@ tptp.summable_complex F))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N4)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N4)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4))))))))
% 6.19/6.60 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) (@ tptp.summable_real F))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real X) N4)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z2)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex X) N4)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 6.19/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_complex N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_real N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_set_nat) (N tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs) N) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_set_nat N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_o N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_nat N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X))) (= Xs (@ (@ tptp.replicate_int N) X))))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X) Xs))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X) Xs))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (= X3 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X) Xs))))
% 6.19/6.60 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X) Xs))))
% 6.19/6.60 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.19/6.60 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.19/6.60 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.19/6.60 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N4)))) (@ tptp.uminus_uminus_real (@ tptp.suminf_real F))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N4)))) (@ tptp.uminus1482373934393186551omplex (@ tptp.suminf_complex F))))))
% 6.19/6.60 (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 ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_real)))))))
% 6.19/6.60 (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 ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_nat)))))))
% 6.19/6.60 (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 ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_int)))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A3)) tptp.one_one_Code_integer))))
% 6.19/6.60 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A3)) tptp.one_one_int))))
% 6.19/6.60 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A3)) tptp.one_one_Code_integer))))
% 6.19/6.60 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A3)) tptp.one_one_int))))
% 6.19/6.60 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A3) tptp.one_one_Code_integer)))))
% 6.19/6.60 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A3) tptp.one_one_int)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ F N4)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N4))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z2) N4)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z2) N4)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z2) N4)))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z2) N4)))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))))))
% 6.19/6.60 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.19/6.60 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.19/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B) N2) (@ (@ tptp.bit_se1146084159140164899it_int A) N2))) (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ (@ tptp.minus_minus_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ _let_1 A))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N)))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2))))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2))))))))
% 6.19/6.60 (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 ((I2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real X) N4)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z2)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4))))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex X) N4)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4))))))))
% 6.19/6.60 (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)))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M2)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (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)))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((X tptp.complex)) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N4))) (@ (@ tptp.power_power_complex X) N4))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N4))) (@ (@ tptp.power_power_real X) N4))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))
% 6.19/6.60 (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))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bitM N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))))))
% 6.19/6.60 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bitM N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.bit_se2923211474154528505it_int M2) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N))) tptp.zero_zero_int))))
% 6.19/6.60 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 6.19/6.60 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 6.19/6.60 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M2)))))
% 6.19/6.60 (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)))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z2) N4))))) Z2))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z2) N4))))) Z2))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z2) N4))))) Z2) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z2) N4))))) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z2) N4))))) Z2) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z2) N4))))) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (Z2 tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ tptp.summable_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ F I2)) (@ (@ tptp.power_power_real Z2) I2))))))))))
% 6.19/6.60 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int A)) N) (and (not (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N))))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.19/6.60 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.19/6.60 (assert (forall ((C tptp.real) (N5 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 N5) 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)))))
% 6.19/6.60 (assert (forall ((C tptp.real) (N5 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 N5) 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)))))
% 6.19/6.60 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.19/6.60 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 6.19/6.60 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_2))) _let_4))))))))))))))))))))))))))
% 6.19/6.60 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) 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 Xa) _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) Xa)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_int (@ F X3)) tptp.ring_1_Ints_int))) (@ (@ tptp.member_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups5754745047067104278omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_int (@ F X3)) tptp.ring_1_Ints_int))) (@ (@ tptp.member_int (@ (@ tptp.groups1932886352136224148al_int F) A2)) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups2073611262835488442omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.member_int (@ F X3)) tptp.ring_1_Ints_int))) (@ (@ tptp.member_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) tptp.ring_1_Ints_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups3049146728041665814omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.member_real (@ F X3)) tptp.ring_1_Ints_real))) (@ (@ tptp.member_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.ring_1_Ints_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.member_complex (@ F X3)) tptp.ring_1_Ints_complex))) (@ (@ tptp.member_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) tptp.ring_1_Ints_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 6.19/6.60 (assert (forall ((F (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.complex tptp.int)) (A2 tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_real (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X2)))) A2))))
% 6.19/6.60 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.19/6.60 (assert (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.19/6.60 (assert (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G) tptp.bot_bot_set_int) tptp.zero_zero_real)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) tptp.bot_bot_set_nat) tptp.zero_zero_nat)))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) tptp.bot_bot_set_complex) tptp.zero_zero_complex)))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) tptp.bot_bot_set_int) tptp.zero_zero_int)))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups6591440286371151544t_real G) tptp.bot_bot_set_nat) tptp.zero_zero_real)))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I2 tptp.int)) (@ tptp.abs_abs_int (@ F I2)))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ tptp.abs_abs_real (@ F I2)))) A2))))
% 6.19/6.60 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.19/6.60 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (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) M2))) (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))))))))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_real (= R I)) (@ F R)) tptp.zero_zero_real))) (@ F I))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_nat (= R I)) (@ F R)) tptp.zero_zero_nat))) (@ F I))))
% 6.19/6.60 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R tptp.nat)) (@ (@ (@ tptp.if_int (= R I)) (@ F R)) tptp.zero_zero_int))) (@ F I))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5808333547571424918x_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.rat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5058264527183730370ex_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A2) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3906332499630173760nt_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5693394587270226106ex_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.real tptp.nat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1935376822645274424al_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((G (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups4541462559716669496nt_nat G) A2) tptp.zero_zero_nat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A2) (= (@ G A4) tptp.zero_zero_nat)))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) A2) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ G X3) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) A2) tptp.zero_zero_complex))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ G X3) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) A2) tptp.zero_zero_int))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ G X3) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G) A2) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)) (@ (@ tptp.sums_real F) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)) (@ (@ tptp.sums_int F) tptp.zero_zero_int))))
% 6.19/6.60 (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 ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) (@ (@ tptp.minus_minus_real A) B))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ F N4)))) (@ tptp.uminus_uminus_real A)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N4)))) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) A2)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R4 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R4) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) R4))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R4 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) R4))) A2))))
% 6.19/6.60 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.uminus1482373934393186551omplex (@ F X2)))) A2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.uminus_uminus_int (@ F X2)))) A2) (@ tptp.uminus_uminus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.uminus_uminus_real (@ F X2)))) A2) (@ tptp.uminus_uminus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_real (@ F X3)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.19/6.60 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.suc X3))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.19/6.60 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 6.19/6.60 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N4)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.19/6.60 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.19/6.60 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I2) N)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I2)))) _let_1)))))
% 6.19/6.60 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I2)))) _let_1)))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (Z2 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N4 M2)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z2) N4)))) (@ (@ tptp.power_power_complex Z2) M2))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (Z2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N4 M2)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z2) N4)))) (@ (@ tptp.power_power_real Z2) M2))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (Z2 tptp.int)) (@ (@ tptp.sums_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N4 M2)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z2) N4)))) (@ (@ tptp.power_power_int Z2) M2))))
% 6.19/6.60 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ A tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ A N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ A tptp.zero_zero_nat))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.19/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (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))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_int (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.plus_plus_real (@ G M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I2))) (@ F I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M2)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M2)))))))
% 6.19/6.60 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I2))) (@ F I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M2)))))))
% 6.19/6.60 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.19/6.61 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.19/6.61 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.19/6.61 (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 ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _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))))))))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I2 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I2 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I2 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I2 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I2 tptp.complex)) (@ (@ tptp.times_times_real (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I2 tptp.real)) (@ (@ tptp.times_times_real (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I5) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I2 tptp.int)) (@ (@ tptp.times_times_real (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I2 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I2 tptp.real)) (@ (@ tptp.times_times_rat (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I2)) (@ X I2)))) I5)) B))) Delta))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M2)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M2))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M2))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M2))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N4)))) tptp.one_one_real))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N))))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.rat)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.int)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.nat)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.real)) (M2 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 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) X))))
% 6.19/6.61 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ F (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ 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))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I2)) D)))) (@ (@ 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) D))))))))
% 6.19/6.61 (assert (forall ((A tptp.rat) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I2)) D)))) (@ (@ 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) D))))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I2)) D)))) (@ (@ 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) D))))))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I2)) D)))) (@ (@ 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) D))))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I2)) D)))) (@ (@ 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) D))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I2) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I2)) D)))) (@ (@ 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) D)))) _let_1))))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (D 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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I2)) D)))) (@ (@ 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) D)))) _let_1))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N))))) (let ((_let_4 (= X 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N))))) (let ((_let_4 (= X 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M2) (@ (@ tptp.plus_plus_nat M2) N))))) (let ((_let_4 (= X 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 M2)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (forall ((R4 tptp.complex) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R4) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R4) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R4) _let_1))))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R4) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R4) _let_1))))))
% 6.19/6.61 (assert (forall ((R4 tptp.real) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R4) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R4) _let_1))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (not (=> (not (= Xa Mi)) (=> (not (= Xa 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 Xa) _let_2))) _let_4))))))))))))))))))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z2)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z2) N4)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z2)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z2) N4)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy) _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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi) (= Xa Ma2)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Mi) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.61 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_nat G) A2))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (let ((_let_1 (@ tptp.groups8294997508430121362at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))) (let ((_let_4 (@ (@ tptp.member_set_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))) tptp.zero_zero_complex))))
% 6.19/6.61 (assert (forall ((I5 tptp.set_nat) (Z2 (-> tptp.nat tptp.complex)) (W (-> tptp.nat tptp.complex))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z2 I3))) tptp.one_one_real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I3))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z2) I5)) (@ (@ tptp.groups6464643781859351333omplex W) I5)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z2 I2)) (@ W I2))))) I5))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.19/6.61 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi) (= Xa Ma2))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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 Mi) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _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) Vd))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa Mi) (= Xa Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) 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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (or (= Xa Mi) (= Xa Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.19/6.61 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M5)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((H tptp.real) (F (-> tptp.real tptp.real)) (J2 (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B7 tptp.real)) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J2 M5)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B7) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.19/6.61 (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 ((I2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) (@ F I2)) (@ G I2)))) (@ 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 ((I2 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) tptp.one_one_nat)))) _let_1))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 6.19/6.61 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D5))) (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))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))))))
% 6.19/6.61 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.19/6.61 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M2)))))
% 6.19/6.61 (assert (= (@ tptp.diffs_real tptp.sin_coeff) tptp.cos_coeff))
% 6.19/6.61 (assert (forall ((R4 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R4) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R4) N))) N))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 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 M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M2)) tptp.one_one_nat)) M2))))
% 6.19/6.61 (assert (= (@ tptp.diffs_real tptp.cos_coeff) (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N4)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M2) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N)) M2)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R4 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M2) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R4) K3))))) (@ tptp.set_ord_atMost_nat R4)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M2) N)) R4))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J) (= (@ B J) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ (@ tptp.power_power_nat X) I2)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R) K3))))) (@ tptp.set_ord_atMost_nat R))) (@ (@ tptp.power_power_nat X) R)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat I2) (@ (@ tptp.binomial N) I2)))) (@ 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))))))
% 6.19/6.61 (assert (= tptp.arg (lambda ((Z6 tptp.complex)) (@ (@ (@ tptp.if_real (= Z6 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z6) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.19/6.61 (assert (= tptp.arctan (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y6))))))))
% 6.19/6.61 (assert (= tptp.ln_ln_real (lambda ((X2 tptp.real)) (@ tptp.the_real (lambda ((U2 tptp.real)) (= (@ tptp.exp_real U2) X2))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.19/6.61 (assert (= tptp.arccos (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y6)))))))
% 6.19/6.61 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R 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) R)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R)))))) __flatten_var_0))))
% 6.19/6.61 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R 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) R)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R)))))) __flatten_var_0))))
% 6.19/6.61 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real))))))
% 6.19/6.61 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))
% 6.19/6.61 (assert (= tptp.arcsin (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y6))))))))
% 6.19/6.61 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M5) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M5)) (@ (@ 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 M5) N4)) N4))))))
% 6.19/6.61 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)))
% 6.19/6.61 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat M2) tptp.bot_bot_set_nat))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N) (@ P M5))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N) (@ P M5))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.19/6.61 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.19/6.61 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M5) N4)) (@ (@ tptp.modulo_modulo_nat M5) N4)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J))))) (=> (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ (@ tptp.ord_less_nat J) N) (@ (@ tptp.ord_less_eq_nat (@ B J)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ B I2)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (= tptp.code_T6385005292777649522of_nat tptp.semiri1314217659103216013at_int))
% 6.19/6.61 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R 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) R)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R)))))) __flatten_var_0))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B5) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B5)) (= A2 B5))))))
% 6.19/6.61 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.19/6.61 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (@ tptp.uminus1351360451143612070nteger L))))
% 6.19/6.61 (assert (= tptp.unique3479559517661332726nteger (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M5))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N5) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N5))))
% 6.19/6.61 (assert (= tptp.finite_finite_nat (lambda ((N7 tptp.set_nat)) (exists ((M5 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N7) (@ (@ tptp.ord_less_nat X2) M5)))))))
% 6.19/6.61 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 6.19/6.61 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I)))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 6.19/6.61 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 6.19/6.61 (assert (= tptp.one_one_int tptp.one_one_int))
% 6.19/6.61 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M2)))))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat N4) K))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))))))
% 6.19/6.61 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.19/6.61 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 6.19/6.61 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.19/6.61 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) I)))))))
% 6.19/6.61 (assert (= tptp.code_integer_of_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.19/6.61 (assert (= tptp.int_ge_less_than2 (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z6) (@ (@ tptp.ord_less_int Z7) Z6))))))))
% 6.19/6.61 (assert (= tptp.int_ge_less_than (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z7) (@ (@ tptp.ord_less_int Z7) Z6))))))))
% 6.19/6.61 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 6.19/6.61 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_int Xa) X))))
% 6.19/6.61 (assert (forall ((X tptp.int)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int X)))))
% 6.19/6.61 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 6.19/6.61 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa) X)))))
% 6.19/6.61 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa) X)))))
% 6.19/6.61 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M5 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_int M5) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S3)))))))
% 6.19/6.61 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M3) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N6) (@ (@ tptp.member_nat N6) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.19/6.61 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M5 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N4) (@ (@ tptp.member_nat N4) S3)))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.19/6.61 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L2)) (@ (@ tptp.modulo364778990260209775nteger K3) L2)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z2)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.re Z2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (N tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (R4 tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.real_V4546457046886955230omplex R4))) (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) R4))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z2)) (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) (@ tptp.real_V1022390504157884413omplex Z2)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) (@ tptp.numeral_numeral_real W)))))
% 6.19/6.61 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (= (@ tptp.re (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus_uminus_real (@ tptp.re X)))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.19/6.61 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_2 (@ tptp.re Z2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.19/6.61 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (= tptp.csqrt (lambda ((Z6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z6))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z6))) (let ((_let_4 (@ tptp.im Z6))) (@ (@ 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)))))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.im Z2))) (= (@ tptp.im (@ tptp.csqrt Z2)) (@ (@ 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 Z2)) (@ tptp.re Z2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.61 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y6))) (let ((_let_3 (@ tptp.re Y6))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (R4 tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.real_V4546457046886955230omplex R4))) (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) R4))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z2)) (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) (@ tptp.real_V1022390504157884413omplex Z2)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z2)) (@ tptp.uminus_uminus_real (@ tptp.im Z2)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) (@ tptp.numeral_numeral_real W)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex) (N tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.19/6.61 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.19/6.61 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (= (@ tptp.im (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus_uminus_real (@ tptp.im X)))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.19/6.61 (assert (= tptp.uminus1482373934393186551omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real (@ tptp.re X2))) (@ tptp.uminus_uminus_real (@ tptp.im X2))))))
% 6.19/6.61 (assert (= tptp.minus_minus_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X2)) (@ tptp.re Y6))) (@ (@ tptp.minus_minus_real (@ tptp.im X2)) (@ tptp.im Y6))))))
% 6.19/6.61 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y6))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.19/6.61 (assert (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z2))) (=> (not (= Z2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.19/6.61 (assert (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.19/6.61 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 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) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 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)) S4)))))) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((R4 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R4) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R4) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R4))) (@ tptp.im Z2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (forall ((R4 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R4) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R4) Z2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R4)) (@ tptp.re Z2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z2) (@ tptp.cnj Z2)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z2)))) tptp.imaginary_unit))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.19/6.61 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (= (@ tptp.cnj Z2) tptp.one_one_complex) (= Z2 tptp.one_one_complex))))
% 6.19/6.61 (assert (forall ((X tptp.complex)) (= (@ tptp.cnj (@ tptp.uminus1482373934393186551omplex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.cnj X)))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.19/6.61 (assert (= (@ tptp.cnj tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.19/6.61 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.19/6.61 (assert (forall ((R4 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R4) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z2) R4)) (@ (@ tptp.divide_divide_real (@ tptp.re Z2)) (@ tptp.re R4))))))
% 6.19/6.61 (assert (forall ((R4 tptp.complex) (Z2 tptp.complex)) (=> (@ (@ tptp.member_complex R4) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z2) R4)) (@ (@ tptp.divide_divide_real (@ tptp.im Z2)) (@ tptp.re R4))))))
% 6.19/6.61 (assert (forall ((Z2 tptp.complex)) (= (@ tptp.im (@ tptp.cnj Z2)) (@ tptp.uminus_uminus_real (@ tptp.im Z2)))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.complex2 A))) (= (@ tptp.cnj (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 6.19/6.61 (assert (forall ((T tptp.real)) (= (@ tptp.cnj (@ tptp.cis T)) (@ tptp.cis (@ tptp.uminus_uminus_real T)))))
% 6.19/6.61 (assert (= tptp.cnj (lambda ((Z6 tptp.complex)) (@ (@ tptp.complex2 (@ tptp.re Z6)) (@ tptp.uminus_uminus_real (@ tptp.im Z6))))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.19/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.19/6.61 (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)))))))))
% 6.19/6.61 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 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 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ 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))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ 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))))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.19/6.61 (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)))
% 6.19/6.61 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) _let_1) _let_1))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.19/6.61 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ 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 M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.19/6.61 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M5 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M5) K3)) (@ (@ tptp.product_Pair_nat_nat M5) (@ (@ tptp.minus_minus_nat K3) M5))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M5) _let_1)))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))))
% 6.19/6.61 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y6 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y6)))))))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.19/6.61 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.19/6.61 (assert (forall ((N tptp.num) (M2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M2) (@ tptp.bit0 N)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ 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 M2) (@ tptp.bit0 N)))))))
% 6.19/6.61 (assert (forall ((N tptp.num) (M2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M2) (@ tptp.bitM N)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ 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 M2) (@ tptp.bitM N)))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.19/6.61 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M2) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M2))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M2) N))))))
% 6.19/6.61 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z6)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z6) tptp.one_one_int)))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N4 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 M5)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.19/6.61 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))))
% 6.19/6.61 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 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 (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M2) N)) (@ (@ tptp.divide_divide_nat M2) N))))
% 6.19/6.61 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_integer K) L)) (@ (@ tptp.divide6298287555418463151nteger K) L))))
% 6.19/6.61 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_abs K) L)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 6.19/6.61 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z6)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z6) tptp.one_one_int)))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N)) Q5) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q5)) (@ (@ tptp.times_times_nat N) Q5)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q5)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q5))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q5)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q5))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N)) Q5) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q5)) (@ (@ tptp.plus_plus_nat N) Q5)))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R4 (@ (@ tptp.plus_plus_rat S2) T3)))))))))))
% 6.19/6.61 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.19/6.61 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M2)) M2) (@ (@ tptp.ord_max_nat N) M2))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M2) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M4)))) M2)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M2) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M4) N)))) M2)))))
% 6.19/6.61 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.19/6.61 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P4)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.61 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 6.19/6.61 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R)))))
% 6.19/6.61 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R)))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat) (N tptp.int) (D tptp.int)) (=> (= (@ tptp.quotient_of R4) (@ (@ tptp.product_Pair_int_int N) D)) (= R4 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D))))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat) (P4 tptp.int) (Q5 tptp.int)) (=> (= (@ tptp.quotient_of R4) (@ (@ tptp.product_Pair_int_int P4) Q5)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q5))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R4)))))
% 6.19/6.61 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A3)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 6.19/6.61 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P4)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P4)))) tptp.one_one_int))))
% 6.19/6.61 (assert (= tptp.ord_less_rat (lambda ((P6 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P6)))))
% 6.19/6.61 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((P4 tptp.rat) (Q5 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P4) Q5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D4))))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P4)))))
% 6.19/6.61 (assert (forall ((Q5 tptp.int) (P4 tptp.int)) (=> (@ (@ tptp.ord_less_int Q5) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q5)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P4)) (@ tptp.uminus_uminus_int Q5)))))))
% 6.19/6.61 (assert (forall ((P4 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((R4 tptp.product_prod_int_int) (P4 tptp.int) (Q5 tptp.int)) (=> (= (@ tptp.normalize R4) (@ (@ tptp.product_Pair_int_int P4) Q5)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q5))))
% 6.19/6.61 (assert (forall ((Q5 tptp.int) (S tptp.int) (P4 tptp.int) (R4 tptp.int)) (=> (not (= Q5 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q5)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R4) S))) (= (@ (@ tptp.times_times_int P4) S) (@ (@ tptp.times_times_int R4) Q5)))))))
% 6.19/6.61 (assert (forall ((P4 tptp.rat) (Q5 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P4) Q5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int C3) B2))))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P4)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= tptp.normalize (lambda ((P6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P6))) (let ((_let_2 (@ tptp.product_fst_int_int P6))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((M2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int M2) tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.gcd_gcd_int X) Y))))
% 6.19/6.61 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M2) N)) (or (not (= M2 tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 6.19/6.61 (assert (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.19/6.61 (assert (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 6.19/6.61 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int X) tptp.zero_zero_int) (@ tptp.abs_abs_int X))))
% 6.19/6.61 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int tptp.zero_zero_int) X) (@ tptp.abs_abs_int X))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 6.19/6.61 (assert (forall ((Q5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.frct Q5))) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.19/6.61 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 6.19/6.61 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X) Y))))))
% 6.19/6.61 (assert (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L2) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L2))))))))
% 6.19/6.61 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.19/6.61 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 6.19/6.61 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.19/6.61 (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))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L2)) S4)))))) _let_1))))))))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)))
% 6.19/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.gcd_gcd_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.19/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.gcd_gcd_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M2) tptp.one_one_nat) tptp.one_one_nat)))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M2) _let_1) _let_1))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M2) N)) (or (not (= M2 tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.gcd_gcd_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.gcd_gcd_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ (@ tptp.gcd_gcd_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.19/6.61 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ tptp.nat2 (@ (@ tptp.gcd_gcd_int K) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M2) N)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M2)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 6.19/6.61 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 6.19/6.61 (assert (= tptp.gcd_gcd_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y6 tptp.zero_zero_nat)) X2) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X2) Y6))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y) (and (=> _let_1 (= Y X)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M2) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M2)) K)))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.19/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X3))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.19/6.61 (assert (= tptp.gcd_gcd_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat (@ tptp.nat2 (@ tptp.abs_abs_int X2))) (@ tptp.nat2 (@ tptp.abs_abs_int Y6)))))))
% 6.19/6.61 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.19/6.61 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.divide_divide_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 6.19/6.61 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.19/6.61 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) N)))) N)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.19/6.61 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I2) N)))) (@ tptp.suc N))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M10)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M10) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M10) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M10) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M10) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.19/6.61 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.19/6.61 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 6.19/6.61 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))))
% 6.19/6.61 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))))
% 6.19/6.61 (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 ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))) N)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) N))))
% 6.19/6.61 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (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 ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N6)) S3))))))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X2))) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X2))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M5) N4) (not (= M5 N4))))))
% 6.19/6.61 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.code_int_of_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.61 (assert (= (@ tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))))
% 6.19/6.61 (assert (forall ((X tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger X)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer X)))))
% 6.19/6.61 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 6.19/6.61 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X) Xa)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 6.19/6.61 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X) Xa)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 6.19/6.61 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))))
% 6.19/6.61 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.19/6.61 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa) X)))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M10) (= (@ tptp.gcd_Gcd_nat M10) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M10) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (@ P (@ tptp.abs_Integ Y3))) (@ P X))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N5) (= (@ tptp.gcd_Gcd_nat N5) tptp.one_one_nat))))
% 6.19/6.61 (assert (forall ((Z2 tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z2 (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 6.19/6.61 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X2))) X)))))
% 6.19/6.61 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))) Xa) X))))
% 6.19/6.61 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))) Xa) X))))
% 6.19/6.61 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0))) Xa) X)))))
% 6.19/6.61 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0))) Xa) X)))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (forall ((Q5 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q5)) Q5)))
% 6.19/6.61 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.19/6.61 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N))))))))
% 6.19/6.61 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 tptp.nat) (Z6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.19/6.61 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 tptp.nat) (Z6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U2) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.19/6.61 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M5) N4))) M5)))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.nat_prod_encode X) (@ tptp.nat_prod_encode Y)) (= X Y))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= tptp.nat2 (lambda ((X2 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X2)))))
% 6.19/6.61 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M2)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2))))
% 6.19/6.61 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X2))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.19/6.61 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.19/6.61 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0))))))
% 6.19/6.61 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (J2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J2) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J2))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.19/6.61 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.19/6.61 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.19/6.61 (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))))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.fract A) B))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M10) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M10) N5))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J2)))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J2)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J2)))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int A)) B))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.19/6.61 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.19/6.61 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.19/6.61 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.19/6.61 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.19/6.61 (assert (forall ((A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.fract tptp.zero_zero_int))) (= (@ _let_1 A) (@ _let_1 C)))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.19/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((P (-> tptp.rat Bool)) (Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ P (@ (@ tptp.fract A4) B3)))) (@ P Q5))))
% 6.19/6.61 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.19/6.61 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.19/6.61 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.zero_zero_int) tptp.zero_zero_rat)))
% 6.19/6.61 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract tptp.zero_zero_int) K) tptp.zero_zero_rat)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 6.19/6.61 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 6.19/6.61 (assert (= tptp.fract (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K3)) (@ tptp.ring_1_of_int_rat L2)))))
% 6.19/6.61 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.19/6.61 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.19/6.61 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.19/6.61 (assert (forall ((N tptp.int) (M2 tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M2) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M2) N)) tptp.one_one_rat)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M2))) (= (@ (@ 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 M2))) (@ (@ 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))))))
% 6.19/6.61 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M2) tptp.none_num)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N5)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N5)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.19/6.61 (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 ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))))))
% 6.19/6.61 (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 ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))))))
% 6.19/6.61 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.19/6.61 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.19/6.61 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M5 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M5)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.19/6.61 (assert (= tptp.gcd_Gcd_int (lambda ((K7 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K7))))))
% 6.19/6.61 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M2)) (@ 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 M2) (@ tptp.bitM N))))))
% 6.19/6.61 (assert (forall ((N tptp.num) (M2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M2) (@ tptp.bitM N))))))
% 6.19/6.61 (assert (forall ((N tptp.num) (M2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M2) (@ tptp.bit0 N))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M2))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M2)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M2)))))
% 6.19/6.61 (assert (forall ((R4 tptp.num) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R4)) (@ tptp.bit0 M2)) (@ (@ (@ 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 R4)) M2)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M2)) (@ 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 M2) (@ tptp.bit0 N))))))
% 6.19/6.61 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M2)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N4) M2)))) N))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M2)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N4) M2))))) N))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M2) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M2)) (@ 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 M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M2)))))
% 6.19/6.61 (assert (@ tptp.fun_is_measure_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((X tptp.rat)) (=> (not (@ tptp.positive X)) (=> (not (= X tptp.zero_zero_rat)) (@ tptp.positive (@ tptp.uminus_uminus_rat X))))))
% 6.19/6.61 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y6) X2)))))
% 6.19/6.61 (assert (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ 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)))))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit0 N2))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit1 N2))) _let_1)) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_and_not_num M3) N2)))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2))))))))))))))))))))))
% 6.19/6.61 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M5 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X2 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P6 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P6)))) (lambda ((P6 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P6))))) X2))) A3))) (@ (@ tptp.product_Pair_nat_num N4) M5)))))
% 6.19/6.61 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit0 N2))) _let_4)) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit1 N2))) _let_1)) (=> (=> (exists ((M3 tptp.num)) (= X (@ tptp.bit0 M3))) (=> _let_2 _let_4)) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (=> (=> (exists ((M3 tptp.num)) (= X (@ tptp.bit1 M3))) _let_3) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2)))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2)))))))))))))))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M2)) tptp.one) tptp.none_num)))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N2))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2))))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2)))))))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Q3 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q3))) (and (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real _let_1) Y)))))))
% 6.19/6.61 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.19/6.61 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X2)) _let_1)))))))
% 6.19/6.61 (assert (= tptp.uminus_uminus_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2))))))
% 6.19/6.61 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 6.19/6.61 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))
% 6.19/6.61 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ 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 (@ tptp.product_snd_int_int X)) _let_1))))))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.positive (@ tptp.abs_Rat X)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.uminus_uminus_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X))) (@ tptp.product_snd_int_int X)))))))
% 6.19/6.61 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y6))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_1))))))))
% 6.19/6.61 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.19/6.61 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.19/6.61 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y6))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_1))))))))
% 6.19/6.61 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M2) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M2) N)) I))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M2) N)) Q5) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M2) Q5)) (@ (@ tptp.times_times_nat N) Q5)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q5)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q5))))))
% 6.19/6.61 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R4 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M2) (@ (@ (@ tptp.bit_concat_bit N) K) L)) R4) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M2) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M2) N)) L) R4)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M2) (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M2) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M2) N)) L)))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M2) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M4)))) M2))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M2) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M4) N)))) M2))))
% 6.19/6.61 (assert (= tptp.inf_inf_int tptp.ord_min_int))
% 6.19/6.61 (assert (= tptp.cnj (lambda ((A3 tptp.complex)) (@ (@ tptp.rcis (@ tptp.real_V1022390504157884413omplex A3)) (@ tptp.uminus_uminus_real (@ tptp.arg A3))))))
% 6.19/6.61 (assert (= tptp.cis (@ tptp.rcis tptp.one_one_real)))
% 6.19/6.61 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real R1) R22)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.19/6.61 (assert (forall ((R4 tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R4) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R4)) (@ tptp.uminus_uminus_real A)))))
% 6.19/6.61 (assert (= tptp.quotient_of (lambda ((X2 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 (= X2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.19/6.61 (assert (forall ((Q5 tptp.int) (P4 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P4) Q5))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q5) (=> (@ (@ tptp.algebr932160517623751201me_int P4) Q5) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.19/6.61 (assert (forall ((Q5 tptp.rat)) (not (forall ((A4 tptp.int) (B3 tptp.int)) (=> (= Q5 (@ (@ tptp.fract A4) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (not (@ (@ tptp.algebr932160517623751201me_int A4) B3))))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.rat Bool)) (Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.algebr932160517623751201me_int A4) B3) (@ P (@ (@ tptp.fract A4) B3))))) (@ P Q5))))
% 6.19/6.61 (assert (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ tptp.abs_abs_int X) tptp.one_one_int)))))))
% 6.19/6.61 (assert (forall ((Q5 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (= Q5 (@ (@ tptp.fract A4) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (not (= A4 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A4) B3)))))) (= Q5 tptp.zero_zero_rat))))
% 6.19/6.61 (assert (forall ((R4 tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_fst_int_int X3))) (and (= R4 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_fst_int_int Y5))) (=> (and (= R4 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y5 X3)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.algebr934650988132801477me_nat M2) N))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X tptp.one_one_nat)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 6.19/6.61 (assert (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X3)))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X)))))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X3) (@ (@ tptp.ord_less_real X3) Y))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri5074537144036343181t_real N2))) (not (@ (@ tptp.algebr934650988132801477me_nat M3) N2)))))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa) (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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y (not (and (= Deg2 Xa) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT 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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 6.19/6.61 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I2 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.19/6.61 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I2 tptp.int) (N4 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat))))))))
% 6.19/6.61 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (= Xa 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))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (= Deg2 Xa) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (= Xa 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))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (= Deg2 Xa) (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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (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)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT 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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))))))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N5))))) (@ (@ 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 M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N5))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M2) (= (@ tptp.groups4561878855575611511st_nat L2) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M2)) tptp.one_one_nat)) N5))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A7 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A7) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N2))) A7)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M5) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.19/6.61 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N4 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) tptp.uminus_uminus_int) tptp.uminus_uminus_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) tptp.suc) tptp.suc))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.ord_less_int) tptp.ord_less_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y4 tptp.num) (Z tptp.num)) (= Y4 Z))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y4 tptp.num) (Z tptp.num)) (= Y4 Z))) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)))) (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))) (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)))) tptp.minus_minus_nat) tptp.minus_minus_nat))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)))) tptp.minus_minus_int) tptp.minus_minus_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)))) tptp.divide_divide_int) tptp.divide_divide_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re6650684261131312217nt_int (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) tptp.semiri1314217659103216013at_int) tptp.semiri1314217659103216013at_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) tptp.ratrel)) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))))
% 6.19/6.61 (assert (= tptp.vanishes (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X7 N4))) R)))))))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R4 tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N6))) R4))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X2)) _let_1))))) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X2)) _let_1))))))
% 6.19/6.61 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X2)) _let_1))))) tptp.inverse_inverse_rat))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) tptp.positive))
% 6.19/6.61 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.19/6.61 (assert (= (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int) tptp.semiring_1_Nats_int))
% 6.19/6.61 (assert (not (@ tptp.finite_finite_int tptp.top_top_set_int)))
% 6.19/6.61 (assert (= (@ (@ tptp.image_2486076414777270412at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))))
% 6.19/6.61 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.19/6.61 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))) tptp.pcr_rat)) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))) tptp.fract))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X2))) (@ tptp.product_snd_int_int X2)))) tptp.uminus_uminus_rat))
% 6.19/6.61 (assert (= tptp.root (lambda ((N4 tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N4)))) X2)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.19/6.61 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) tptp.pcr_int) (lambda ((N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X2)))) tptp.uminus_uminus_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 6.19/6.61 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real) (D6 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D6 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D6 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D6) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D5) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H3))) (@ F X)))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D5) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H3))))))))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (Y tptp.real) (X tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ F (@ tptp.uminus_uminus_real X2)))) (@ tptp.uminus_uminus_real Y)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H3) D5) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H3) D5) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F3 Z4)))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (= (@ F X) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L tptp.zero_zero_real))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M2)) _let_1)))))
% 6.19/6.61 (assert (forall ((Z2 tptp.real) (R4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z6 tptp.real)) (@ (@ tptp.powr_real Z6) R4))) (@ (@ tptp.times_times_real R4) (@ (@ tptp.powr_real Z2) (@ (@ tptp.minus_minus_real R4) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log2 B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (R4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M2) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R4))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R4) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R4) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M2)) _let_1)))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M2) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R4) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R4) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M2) _let_3)) _let_2)))) _let_1)))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F3 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L4 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F3 X0))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N2))) (@ (@ F3 X0) N2)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L4) (=> (forall ((N2 tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N2)) (@ (@ F Y3) N2)))) (@ (@ tptp.times_times_real (@ L4 N2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.19/6.61 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.19/6.61 (assert (forall ((X tptp.real) (D6 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D6 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D6 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D6) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.19/6.61 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.19/6.61 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.19/6.61 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X3) N4)))))) (=> (@ (@ 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 ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N4))))))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X0) N4))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.19/6.61 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.19/6.61 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.19/6.61 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real H) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 6.19/6.61 (assert (forall ((H 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) H) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N)))))))))))
% 6.19/6.61 (assert (forall ((H 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) H) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 6.19/6.61 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 6.19/6.61 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 6.19/6.61 (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 ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.19/6.61 (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 ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M5)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B5 tptp.real)) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M))) (@ (@ tptp.minus_minus_real (@ (@ Diff M) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real U2) P6)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B5) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real T4) P6)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B5) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))))
% 6.19/6.61 (assert (= (@ (@ tptp.image_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.nat_int_encode X) (@ tptp.nat_int_encode Y)) (= X Y))))
% 6.19/6.61 (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 ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X4))))))))))
% 6.19/6.61 (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 ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (not (= (@ F X4) tptp.zero_zero_real))))))))))
% 6.19/6.61 (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 ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R3)) (@ (@ tptp.ord_less_real (@ F X4)) tptp.zero_zero_real)))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arctan)))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arsinh_real)))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.ln_ln_real))))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_betw_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.19/6.61 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (= (@ G (@ F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) G)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F3 C2))))))))))))
% 6.19/6.61 (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 ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.19/6.61 (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 ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.19/6.61 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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)))))))))
% 6.19/6.61 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.19/6.61 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat 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 (@ G (@ tptp.suc N2))) (@ G N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G N2))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L3)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.19/6.61 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.19/6.61 (assert (forall ((R4 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R4) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))) (@ tptp.topolo2815343760600316023s_real R4)) tptp.at_top_nat)))
% 6.19/6.61 (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 ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.19/6.61 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.19/6.61 (assert (forall ((R4 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R4) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))))) (@ tptp.topolo2815343760600316023s_real R4)) tptp.at_top_nat)))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N4)))) N4))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.19/6.61 (assert (forall ((R4 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R4) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))))) (@ tptp.topolo2815343760600316023s_real R4)) tptp.at_top_nat)))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4))))))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4)))))))))
% 6.19/6.61 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K2 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.19/6.61 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K2 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.19/6.61 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))))))))
% 6.19/6.61 (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 ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)))) L3)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ tptp.suc I2)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.cosh_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sinh_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arsinh_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_nat_int tptp.semiri1314217659103216013at_int) tptp.at_top_int) tptp.at_top_nat))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_1) tptp.at_top_real)))))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) K)) (@ tptp.exp_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F4) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F4) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))
% 6.19/6.61 (assert (= tptp.real_V975177566351809787t_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y6)))))
% 6.19/6.61 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y6)))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_top_real) F4))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.19/6.61 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sinh_real) tptp.at_bot_real) tptp.at_bot_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arsinh_real) tptp.at_bot_real) tptp.at_bot_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.cosh_real) tptp.at_top_real) tptp.at_bot_real))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 6.19/6.61 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.uminus_uminus_real X2)))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_bot_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.19/6.61 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.19/6.61 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G0 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X2)) (@ G0 X2)))) F4) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F4) _let_1))))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_bot_real) F4))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.19/6.61 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F3 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.19/6.61 (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))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) G))) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X3) (@ (@ tptp.ord_less_real X3) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.19/6.61 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L3 tptp.real) (Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L3) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L3)))))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arsinh_real (@ F X2))))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arsinh_real)))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) tptp.sin_real)))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) tptp.cos_real)))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arcosh_real (@ F X2)))))))))
% 6.19/6.61 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.19/6.61 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (@ (@ tptp.member_real (@ F X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.artanh_real (@ F X2)))))))))
% 6.19/6.61 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F3 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F3 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.19/6.61 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.19/6.61 (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 ((M5 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M5)) M5))))))
% 6.19/6.61 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)))) tptp.top_top_set_real))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (= tptp.complete_Inf_Inf_int (lambda ((X7 tptp.set_int)) (@ tptp.uminus_uminus_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int tptp.uminus_uminus_int) X7))))))
% 6.19/6.61 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log2 B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.19/6.61 (assert (= (@ (@ tptp.image_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.19/6.61 (assert (forall ((X tptp.int)) (= (@ tptp.nat_int_decode (@ tptp.nat_int_encode X)) X)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_int_encode (@ tptp.nat_int_decode N)) N)))
% 6.19/6.61 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inj_on2178005380612969504at_nat tptp.nat_prod_encode) A2)))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.inj_on_nat_int tptp.nat_int_decode) A2)))
% 6.19/6.61 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.inj_on_int_nat tptp.nat_int_encode) A2)))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) N5) (@ (@ tptp.ord_less_eq_nat K) N2))) (@ (@ tptp.inj_on_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) K))) N5))))
% 6.19/6.61 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_int_decode X) (@ tptp.nat_int_decode Y)) (= X Y))))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_betw_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.19/6.61 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (or (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X) N))))))
% 6.19/6.61 (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 ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N4)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 6.19/6.61 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.19/6.61 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 6.19/6.61 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N4)))) tptp.uminus_uminus_real))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N4)) (@ Y8 N4)))) tptp.plus_plus_real))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y8 N4)))) tptp.times_times_real))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))) tptp.positive2))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 6.19/6.61 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y) (@ tptp.positive2 (@ (@ tptp.times_times_real X) Y))))))
% 6.19/6.61 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X) Y))))))
% 6.19/6.61 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (not (@ tptp.positive2 X)) (=> (not (= X tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X))))))
% 6.19/6.61 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y6) X2)))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.19/6.61 (assert (= tptp.positive2 (lambda ((X2 tptp.real)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ (@ tptp.rep_real X2) N4))))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4))))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y8 N4)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y8 N4)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N4)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N4)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N4)) (@ Y8 N4)))) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N4)) (@ Y8 N4)))))
% 6.19/6.61 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.one_one_rat)) (lambda ((N4 tptp.nat)) tptp.one_one_rat)))
% 6.19/6.61 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.realrel) (lambda ((Y4 tptp.real) (Z tptp.real)) (= Y4 Z))))
% 6.19/6.61 (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 ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N4)))) __flatten_var_0))) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N4)))) __flatten_var_0))))
% 6.19/6.61 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (lambda ((X7 (-> tptp.nat tptp.rat))) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X7 N4)))))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 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 Y6))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y)))))
% 6.19/6.61 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.19/6.61 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 6.19/6.61 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.abs_Integ X) (@ tptp.abs_Integ Y)) (@ (@ tptp.intrel X) Y))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X2)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X2)))))
% 6.19/6.61 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) _let_1) _let_1)))
% 6.19/6.61 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.19/6.61 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 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 X2) V4) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.intrel) (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0)))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X2) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0)))))
% 6.19/6.61 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X N4)))))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((Y3 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y3) Y3) (@ P (@ tptp.real2 Y3)))) (@ P X))))
% 6.19/6.61 (assert (= tptp.field_7254667332652039916t_real (lambda ((X2 tptp.rat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) X2)))))
% 6.19/6.61 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.zero_zero_rat))))
% 6.19/6.61 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.one_one_rat))))
% 6.19/6.61 (assert (= tptp.ring_1_of_int_real (lambda ((X2 tptp.int)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.ring_1_of_int_rat X2))))))
% 6.19/6.61 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X2 tptp.nat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X2))))))
% 6.19/6.61 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X N4))))))))
% 6.19/6.61 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa N4)) (@ X N4)))))))))
% 6.19/6.61 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa N4)) (@ X N4)))))))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J2))))))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J2))))))))
% 6.19/6.61 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.positive2 (@ tptp.real2 X)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X N4)))))))))))
% 6.19/6.61 (assert (= tptp.upto_aux (lambda ((I2 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I2)) Js) (@ (@ (@ tptp.upto_aux I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.19/6.61 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X7 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X7)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X7 N4)))) __flatten_var_0)))))
% 6.19/6.61 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X7 N4))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X8 N4)) (@ (@ tptp.plus_plus_rat (@ Y7 N4)) R))))))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ (@ tptp.realrel X8) X8))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (forall ((X tptp.rat)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) X))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4))))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((X10 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X10) (@ P (@ tptp.real2 X10)))) (@ P X))))
% 6.19/6.61 (assert (= tptp.pcr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y6 tptp.real)) (and (@ tptp.cauchy X2) (= (@ tptp.real2 X2) Y6)))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N6))) B3)))))))
% 6.19/6.61 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y7) (=> (@ (@ tptp.ord_less_real X) (@ tptp.real2 Y7)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.field_7254667332652039916t_real (@ Y7 N2))))))))
% 6.19/6.61 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y7) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.field_7254667332652039916t_real (@ Y7 N2)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.real2 Y7))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y tptp.real)) (=> (@ tptp.cauchy X8) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X8 N2))) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) Y)))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X8)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4)))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.times_times_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4)))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4)))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4)))) (@ (@ tptp.realrel X8) Y7))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (= (@ tptp.real2 X8) (@ tptp.real2 Y7)) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4)))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (=> (@ tptp.cauchy Y7) (=> (not (@ tptp.vanishes Y7)) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4)))) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X8 N4))) (@ tptp.inverse_inverse_rat (@ Y7 N4))))))))))))
% 6.19/6.61 (assert (= tptp.realrel (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X7) (@ tptp.cauchy Y8) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X7 N4)) (@ Y8 N4))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K2 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ tptp.uminus_uminus_rat (@ X8 N6))))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ X8 N6))))))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.positive2 (@ tptp.real2 X8)) (exists ((R tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R) (@ X8 N4)))))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ tptp.abs_abs_rat (@ X8 N6))))))))))))
% 6.19/6.61 (assert (= tptp.cauchy (lambda ((X7 (-> tptp.nat tptp.rat))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X7 M5)) (@ X7 N4)))) R)))))))))))
% 6.19/6.61 (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 ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M3)) (@ X8 N2)))) R3)))))))) (@ tptp.cauchy X8))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R4 tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K2 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M)) (@ X8 N6)))) R4))))))))))
% 6.19/6.61 (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 ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4))))))))))))
% 6.19/6.61 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (not (@ tptp.positive2 (@ tptp.real2 X8))) (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X8 N4)) R))))))))))
% 6.19/6.61 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X7 N4)) (@ Y8 N4))))))
% 6.19/6.61 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X7 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X7 N4)) (@ Y8 N4))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))))
% 6.19/6.61 (assert (= tptp.cr_real (lambda ((X2 (-> tptp.nat tptp.rat)) (Y6 tptp.real)) (and (@ (@ tptp.realrel X2) X2) (= (@ tptp.real2 X2) Y6)))))
% 6.19/6.61 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (= (@ tptp.nat_list_encode X) (@ tptp.nat_list_encode Y)) (= X Y))))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_be8532844293280997160at_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.19/6.61 (assert (forall ((A2 tptp.set_list_nat)) (@ (@ tptp.inj_on_list_nat_nat tptp.nat_list_encode) A2)))
% 6.19/6.61 (assert (= (@ (@ tptp.image_list_nat_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.19/6.61 (assert (= tptp.pcr_real tptp.cr_real))
% 6.19/6.61 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2)))))))))))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.19/6.61 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs2))))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J2))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J2)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J2)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (= (= (@ (@ tptp.upto I) J2) tptp.nil_int) (@ (@ tptp.ord_less_int J2) I))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J2)) (@ (@ tptp.ord_less_int J2) I))))
% 6.19/6.61 (assert (forall ((J2 tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J2) I) (= (@ (@ tptp.upto I) J2) tptp.nil_int))))
% 6.19/6.61 (assert (forall ((I tptp.int) (K tptp.nat) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J2) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J2)) K) _let_1)))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J2) I)) tptp.one_one_int)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 6.19/6.61 (assert (forall ((M2 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 M2)))) (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)))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (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)))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J2)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K))))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.upto J2) K))))))))
% 6.19/6.61 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.19/6.61 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3)))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J2) (= (@ (@ tptp.upto I) J2) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J2))))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.19/6.61 (assert (= tptp.upto (lambda ((I2 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I2) J3)) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J2) (= (@ _let_1 J2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) tptp.nil_int)))))))
% 6.19/6.61 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K)))))))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.19/6.61 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X3) Xs2))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (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)))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) N))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J2)) I))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J2)) (@ (@ tptp.minus_minus_nat J2) I))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (= (= (@ (@ tptp.upt I) J2) tptp.nil_nat) (or (= J2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J2) I)))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (K tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J2)) K) _let_1)))))
% 6.19/6.61 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q5)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q5))))))
% 6.19/6.61 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) (@ tptp.suc M5))))))
% 6.19/6.61 (assert (= tptp.set_ord_lessThan_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N4)))))
% 6.19/6.61 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N4) (@ tptp.suc M5))))))
% 6.19/6.61 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) M5)))))
% 6.19/6.61 (assert (= tptp.set_ord_atMost_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N4))))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (= (@ (@ tptp.upt I) J2) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J2))))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J2) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J2) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J2) Xs)))))
% 6.19/6.61 (assert (= tptp.upt (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I2) J3)) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J3))) tptp.nil_nat))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J2) (= (@ _let_1 (@ tptp.suc J2)) (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat I2) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((I tptp.int) (J2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J2))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) N)))) N))))
% 6.19/6.61 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) N)))) (@ tptp.abs_abs_int N)))))
% 6.19/6.61 (assert (forall ((N tptp.int) (M2 tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M2) N) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D4))) (and (@ _let_1 M2) (@ _let_1 N))))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X7 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X7)))))
% 6.19/6.61 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M5))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M2) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_1 M2) (@ _let_1 N))))))))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M10) (=> (not (= M10 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M10)) (= (@ tptp.gcd_Gcd_nat M10) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M5 tptp.nat)) (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M5))))) M10)))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (@ P N) (=> (@ Q M2) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K2 tptp.nat)) (= (@ P (@ tptp.suc K2)) (@ Q K2))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.19/6.61 (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 ((M5 tptp.nat)) (@ P (@ tptp.suc M5))))))))))
% 6.19/6.61 (assert (= tptp.comple1385675409528146559p_real (lambda ((X7 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z6 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) X7) (@ (@ tptp.ord_less_eq_real X2) Z6))))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.19/6.61 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.19/6.61 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.19/6.61 (assert (forall ((I tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (= (@ tptp.last_nat (@ (@ tptp.upt I) J2)) (@ (@ tptp.minus_minus_nat J2) tptp.one_one_nat)))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y 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))) (=> (= Xa _let_1) (=> (= Y (@ 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))) (=> (= Xa _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ 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 ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_and_not_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y (@ 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))) (=> (= Xa _let_1) (=> (= Y 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))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y 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))) (=> (= Xa _let_1) (=> (= Y (@ 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))) (=> (= Xa _let_1) (=> (= Y (@ 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 ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit0 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit1 M3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit0 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) _let_1))))))))) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit1 M3))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))) (not (forall ((M3 tptp.num)) (=> (= X (@ tptp.bit1 M3)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) _let_1))))))))))))))))))))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z2))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z2)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M5) N4) (not (= M5 N4))))) tptp.zero_zero_nat))
% 6.19/6.61 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X2))) (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X2))) tptp.zero_zero_nat))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((F4 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F4)) (@ tptp.finite_finite_nat F4))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A2)) (@ (@ tptp.insert_nat N) (@ _let_1 A2))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))))
% 6.19/6.61 (assert (forall ((K tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.euclid3395696857347342551nt_int K)) tptp.one_one_int)))
% 6.19/6.61 (assert (= tptp.euclid3398187327856392827nt_nat (lambda ((N4 tptp.nat)) tptp.one_one_nat)))
% 6.19/6.61 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (= (@ tptp.euclid3395696857347342551nt_int K) (@ tptp.sgn_sgn_int K)))))
% 6.19/6.61 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.19/6.61 (assert (@ tptp.transp_nat_rat tptp.realrel))
% 6.19/6.61 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M5 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M5)))))))
% 6.19/6.61 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M5 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N4))) false) M5))))
% 6.19/6.61 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int))))))))
% 6.19/6.61 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.19/6.61 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P6 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P6)))))
% 6.19/6.61 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M2)) (@ (@ tptp.nat_prod_decode_aux K) M2))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_prod_decode X) (@ tptp.nat_prod_decode Y)) (= X Y))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_prod_encode (@ tptp.nat_prod_decode N)) N)))
% 6.19/6.61 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat_prod_decode (@ tptp.nat_prod_encode X)) X)))
% 6.19/6.61 (assert (@ tptp.order_7092887310737990675l_real tptp.tanh_real))
% 6.19/6.61 (assert (@ tptp.order_7092887310737990675l_real tptp.sinh_real))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.inj_on5538052773655684606at_nat tptp.nat_prod_decode) A2)))
% 6.19/6.61 (assert (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_be8693218025023041337at_nat tptp.nat_prod_decode) tptp.top_top_set_nat) tptp.top_to4669805908274784177at_nat))
% 6.19/6.61 (assert (= (@ (@ tptp.image_5846123807819985514at_nat tptp.nat_prod_decode) tptp.top_top_set_nat) tptp.top_to4669805908274784177at_nat))
% 6.19/6.61 (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 ((X4 tptp.nat) (Y5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X4) Y5) (@ tptp.nat_prod_decode N2)) (@ P Y5))) (@ P _let_1))))) (@ P A0)))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N2 tptp.nat)) (=> (= X (@ tptp.suc N2)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.cons_nat X2) (@ tptp.nat_list_decode Y6)))) (@ tptp.nat_prod_decode N2)))))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_list_encode (@ tptp.nat_list_decode N)) N)))
% 6.19/6.61 (assert (forall ((X tptp.list_nat)) (= (@ tptp.nat_list_decode (@ tptp.nat_list_encode X)) X)))
% 6.19/6.61 (assert (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat)))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.inj_on_nat_list_nat tptp.nat_list_decode) A2)))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.nat_list_decode X) (@ tptp.nat_list_decode Y)) (= X Y))))
% 6.19/6.61 (assert (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.cons_nat X2) (@ tptp.nat_list_decode Y6)))) (@ tptp.nat_prod_decode N)))))))
% 6.19/6.61 (assert (@ (@ (@ tptp.bij_be6293887246118711976st_nat tptp.nat_list_decode) tptp.top_top_set_nat) tptp.top_top_set_list_nat))
% 6.19/6.61 (assert (= (@ (@ tptp.image_nat_list_nat tptp.nat_list_decode) tptp.top_top_set_nat) tptp.top_top_set_list_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.cons_nat X2) (@ tptp.nat_list_decode Y6)))) (@ tptp.nat_prod_decode N)))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.cons_nat X2) (@ tptp.nat_list_decode Y6)))) (@ tptp.nat_prod_decode N2))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 6.19/6.61 (assert (= tptp.powr_real2 (lambda ((B2 tptp.real) (I2 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 B2))) (let ((_let_32 (@ tptp.archim6058952711729229775r_real I2))) (let ((_let_33 (@ (@ (@ (@ (@ _let_12 false) false) true) true) true))) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real B2) 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 B2) I2)))) (@ (@ (@ tptp.if_real (= (@ tptp.ring_1_of_int_real _let_32) I2)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) I2)) (@ _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 I2))))))) (@ (@ 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 B2) I2)))))))))))))))))))))))))))))))))))))))))
% 6.19/6.61 (assert (= tptp.powr_real2 tptp.powr_real))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ tptp.code_int_of_integer (@ tptp.code_integer_of_nat X)) (@ tptp.semiri1314217659103216013at_int X))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.code_int_of_integer (@ tptp.code_integer_of_nat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.19/6.61 (assert (= (@ tptp.code_integer_of_nat tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 6.19/6.61 (assert (= tptp.code_integer_of_nat (lambda ((X2 tptp.nat)) (@ tptp.code_integer_of_int (@ tptp.semiri1314217659103216013at_int X2)))))
% 6.19/6.61 (assert (= (@ tptp.code_integer_of_nat tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.19/6.61 (assert (= tptp.code_integer_of_nat (@ (@ (@ tptp.map_fu6290471996055670595nteger tptp.id_nat) tptp.code_integer_of_int) tptp.semiri1314217659103216013at_int)))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) J3)) M2)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M2)) (lambda ((R tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) R)))))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.produc457027306803732586at_nat A2))) (= (@ _let_1 (lambda ((Uu3 tptp.nat)) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 (lambda ((I2 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) I2))))) (@ _let_1 (lambda ((I2 tptp.nat)) (@ (@ tptp.set_or6659071591806873216st_nat (@ (@ tptp.minus_minus_nat M2) I2)) M2))))))))
% 6.19/6.61 (assert (= (@ (@ tptp.filtermap_real_real tptp.ln_ln_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_bot_real))
% 6.19/6.61 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Gcd_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_gcd_int) Xs) tptp.zero_zero_int))))
% 6.19/6.61 (assert (= (@ (@ tptp.filtermap_real_real tptp.ln_ln_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (= (@ (@ tptp.filtermap_real_real tptp.exp_real) tptp.at_top_real) tptp.at_top_real))
% 6.19/6.61 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real X2) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.19/6.61 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))))
% 6.19/6.61 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (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))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))))
% 6.19/6.61 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 X)) (= X tptp.one_one_nat))))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.one_on7984719198319812577d_enat) (= X tptp.one_one_nat))))
% 6.19/6.61 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 tptp.one_one_nat)))
% 6.19/6.61 (assert (forall ((A Bool) (B Bool) (Uu tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) Uu) _let_1))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M2)) (not (forall ((K2 tptp.nat)) (=> (= N (@ tptp.extended_enat2 K2)) (not (@ (@ tptp.ord_less_nat K2) M2))))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M2))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) N))))
% 6.19/6.61 (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)))))))))
% 6.19/6.61 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Gcd_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_gcd_nat) Xs) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_1) (not (= Y _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))) (=> (= X (@ (@ _let_1 TreeList2) Summary2)) (=> (= Xa tptp.extend5688581933313929465d_enat) (not (= Y (@ (@ _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)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))) (=> (= Xa (@ tptp.extended_enat2 L3)) (not (= Y (@ (@ (@ (@ 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)))))))))))))))))
% 6.19/6.61 (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)))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat)))
% 6.19/6.61 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (not (= X tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) X) Y))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (=> (not (= N tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) N) tptp.zero_z5237406670263579293d_enat))))
% 6.19/6.61 (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)))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.19/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_enat2 A)) tptp.extend5688581933313929465d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.19/6.61 (assert (not (= tptp.extend5688581933313929465d_enat tptp.one_on7984719198319812577d_enat)))
% 6.19/6.61 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.19/6.61 (assert (forall ((Z2 tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z2) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z2)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z2))))))
% 6.19/6.61 (assert (forall ((X tptp.produc7272778201969148633d_enat)) (=> (forall ((A4 Bool) (B3 Bool) (Uu2 tptp.extended_enat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ tptp.vEBT_Leaf A4) B3)) Uu2)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (@ (@ 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) (L3 tptp.nat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (@ tptp.extended_enat2 L3))))))))))
% 6.19/6.61 (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))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa) Y) (=> (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_1) Xa))))))) (=> (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))) (=> (= X _let_2) (=> (= Xa tptp.extend5688581933313929465d_enat) (=> (= Y (@ (@ _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)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L3 tptp.nat)) (let ((_let_1 (@ tptp.extended_enat2 L3))) (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 L3) (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat Deg2) _let_3))))) (=> (= Xa _let_1) (=> (= Y (@ (@ _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)))))))))))))))))))
% 6.19/6.61 (assert (= tptp.minus_3235023915231533773d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((Y6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat X2) Y6)))) tptp.zero_z5237406670263579293d_enat) B2))) tptp.extend5688581933313929465d_enat) A3))))
% 6.19/6.61 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M5 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P6 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P6)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N4))) (@ (@ (@ tptp.if_Extended_enat (= N4 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M5))))
% 6.19/6.61 (assert (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N4 tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N4)))) tptp.extend5688581933313929465d_enat)))
% 6.19/6.61 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4))) (= (@ tptp.finite_card_nat K7) K3))))))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat) (M2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M2)) (@ (@ tptp.minus_3235023915231533773d_enat N) M2))))
% 6.19/6.61 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) tptp.one_on7984719198319812577d_enat) N)))
% 6.19/6.61 (assert (forall ((Y tptp.nat) (X tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y) (@ tptp.extended_eSuc X)) (exists ((N4 tptp.nat)) (and (= Y (@ tptp.suc N4)) (= (@ tptp.extended_enat2 N4) X))))))
% 6.19/6.61 (assert (forall ((X tptp.extended_enat) (Y tptp.nat)) (= (= (@ tptp.extended_eSuc X) (@ tptp.extended_enat2 Y)) (exists ((N4 tptp.nat)) (and (= Y (@ tptp.suc N4)) (= X (@ tptp.extended_enat2 N4)))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ tptp.suc N)))))
% 6.19/6.61 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)))
% 6.19/6.61 (assert (= tptp.extended_eSuc (lambda ((N4 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat N4) tptp.one_on7984719198319812577d_enat))))
% 6.19/6.61 (assert (forall ((Q5 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) Q5) (@ tptp.extended_eSuc Q5))))
% 6.19/6.61 (assert (forall ((Q5 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat Q5) tptp.one_on7984719198319812577d_enat) (@ tptp.extended_eSuc Q5))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.quotie3684837364556693515t_real tptp.realrel) tptp.real2) tptp.rep_real) tptp.cr_real))
% 6.19/6.61 (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)))))))))))))
% 6.19/6.61 (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))))))))))))
% 6.19/6.61 (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))))))))))))
% 6.19/6.61 (assert (forall ((X1 Bool) (X23 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X23) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.19/6.61 (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))))))))))))
% 6.19/6.61 (assert (forall ((X1 Bool) (X23 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X23) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.19/6.61 (assert (= tptp.cr_int (lambda ((X2 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.int)) (@ (@ (lambda ((Y4 tptp.int) (Z tptp.int)) (= Y4 Z)) (@ tptp.abs_Integ X2)) __flatten_var_0))))
% 6.19/6.61 (assert (= tptp.pcr_int tptp.cr_int))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.quotie1194848508323700631at_int tptp.intrel) tptp.abs_Integ) tptp.rep_Integ) tptp.cr_int))
% 6.19/6.61 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (= tptp.uminus1351360451143612070nteger (@ (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int) tptp.uminus_uminus_int)))
% 6.19/6.61 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))))
% 6.19/6.61 (assert (= tptp.divide6298287555418463151nteger (@ (@ (@ tptp.map_fu8272188784021352819nteger tptp.code_int_of_integer) (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int)) tptp.divide_divide_int)))
% 6.19/6.61 (assert (= tptp.minus_8373710615458151222nteger (@ (@ (@ tptp.map_fu8272188784021352819nteger tptp.code_int_of_integer) (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int)) tptp.minus_minus_int)))
% 6.19/6.61 (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 ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))))
% 6.19/6.61 (assert (= tptp.code_sub (lambda ((Xa4 tptp.num) (X2 tptp.num)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int Xa4)) (@ tptp.numeral_numeral_int X2))))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Xa tptp.num)) (= (@ tptp.code_int_of_integer (@ (@ tptp.code_sub X) Xa)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Xa)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_dup (@ (@ tptp.code_sub M2) N))) tptp.one_one_Code_integer))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M2)) (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_dup (@ (@ tptp.code_sub M2) N))) tptp.one_one_Code_integer))))
% 6.19/6.61 (assert (@ (@ tptp.monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (@ (@ tptp.monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo7531315842566124627t_real (@ tptp.power_power_real X))))))
% 6.19/6.61 (assert (= tptp.gcd_lcm_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A3)) (@ tptp.abs_abs_int B2))) (@ (@ tptp.gcd_gcd_int A3) B2)))))
% 6.19/6.61 (assert (forall ((M2 tptp.int) (N tptp.int)) (= (= (@ (@ tptp.gcd_lcm_int M2) N) tptp.zero_zero_int) (or (= M2 tptp.zero_zero_int) (= N tptp.zero_zero_int)))))
% 6.19/6.61 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.gcd_lcm_int M2) N) tptp.one_one_int) (and (or (= M2 tptp.one_one_int) (= M2 _let_1)) (or (= N tptp.one_one_int) (= N _let_1)))))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.gcd_lcm_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.gcd_lcm_int X) Y))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.gcd_lcm_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.19/6.61 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (=> (not (= N tptp.zero_zero_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int M2) N))))))
% 6.19/6.61 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ (@ tptp.dvd_dvd_int A) D) (@ (@ tptp.dvd_dvd_int B) D) (forall ((E3 tptp.int)) (=> (and (@ (@ tptp.dvd_dvd_int A) E3) (@ (@ tptp.dvd_dvd_int B) E3)) (@ (@ tptp.dvd_dvd_int D) E3)))) (= D (@ (@ tptp.gcd_lcm_int A) B)))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int X) Y))))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_lcm_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_lcm_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.19/6.61 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Lcm_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_lcm_int) Xs) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.gcd_lcm_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.gcd_lcm_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.gcd_lcm_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_lcm_nat M2) N)))))
% 6.19/6.61 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.gcd_lcm_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ (@ tptp.gcd_lcm_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.19/6.61 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.gcd_lcm_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ tptp.nat2 (@ (@ tptp.gcd_lcm_int K) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.19/6.61 (assert (= tptp.gcd_lcm_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X2) Y6)) (@ (@ tptp.gcd_gcd_nat X2) Y6)))))
% 6.19/6.61 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M2) N)))))))
% 6.19/6.61 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Lcm_int K5))))
% 6.19/6.61 (assert (= tptp.gcd_lcm_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A3)) (@ tptp.abs_abs_Code_integer B2))) (@ (@ tptp.gcd_gcd_Code_integer A3) B2)))))
% 6.19/6.61 (assert (= tptp.gcd_lcm_int (lambda ((X2 tptp.int) (Y6 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_lcm_nat (@ tptp.nat2 (@ tptp.abs_abs_int X2))) (@ tptp.nat2 (@ tptp.abs_abs_int Y6)))))))
% 6.19/6.61 (assert (= tptp.gcd_Lcm_int (lambda ((K7 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Lcm_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K7))))))
% 6.19/6.61 (assert (forall ((N5 tptp.set_nat)) (= (@ tptp.gcd_Lcm_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N5)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Lcm_nat N5)))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) A2) (= (@ tptp.gcd_Lcm_nat A2) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (= (@ tptp.gcd_Lcm_nat A2) tptp.zero_zero_nat) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))))
% 6.19/6.61 (assert (= (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat M10)) (= (@ tptp.gcd_Lcm_nat M10) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Lcm_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_lcm_nat) Xs) tptp.one_one_nat))))
% 6.19/6.61 (assert (forall ((M10 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M10) (=> (not (= M10 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M10)) (=> (forall ((M3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.member_nat M3) M10) (=> (@ (@ tptp.member_nat N2) M10) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M3) N2)) M10)))) (= (@ tptp.gcd_Lcm_nat M10) (@ tptp.lattic8265883725875713057ax_nat M10))))))))
% 6.19/6.61 (assert (= tptp.gcd_Lcm_nat (lambda ((M7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ tptp.finite_finite_nat M7)) (@ (@ (@ tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat) tptp.one_one_nat) M7)) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (= (@ tptp.unit_f2748546683901255202or_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.unit_f2748546683901255202or_nat (@ tptp.suc N)) tptp.one_one_nat)))
% 6.19/6.61 (assert (= tptp.unit_f2748546683901255202or_nat (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) tptp.one_one_nat))))
% 6.19/6.61 (assert (@ (@ tptp.comm_monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (@ (@ tptp.comm_monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 6.19/6.61 (assert (= tptp.times_times_num (lambda ((M5 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.times_times_nat (@ tptp.nat_of_num M5)) (@ tptp.nat_of_num N4))))))
% 6.19/6.61 (assert (= tptp.ord_less_eq_num (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_of_num M5)) (@ tptp.nat_of_num N4)))))
% 6.19/6.61 (assert (= (@ tptp.nat_of_num tptp.one) tptp.one_one_nat))
% 6.19/6.61 (assert (forall ((X tptp.num)) (not (= (@ tptp.nat_of_num X) tptp.zero_zero_nat))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_of_num X))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (= (@ tptp.nat_of_num (@ tptp.inc X)) (@ tptp.suc (@ tptp.nat_of_num X)))))
% 6.19/6.61 (assert (= (lambda ((Y4 tptp.num) (Z tptp.num)) (= Y4 Z)) (lambda ((X2 tptp.num) (Y6 tptp.num)) (= (@ tptp.nat_of_num X2) (@ tptp.nat_of_num Y6)))))
% 6.19/6.61 (assert (= tptp.nat_of_num tptp.numeral_numeral_nat))
% 6.19/6.61 (assert (forall ((X tptp.num)) (= (@ tptp.num_of_nat (@ tptp.nat_of_num X)) X)))
% 6.19/6.61 (assert (= tptp.ord_less_num (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_nat (@ tptp.nat_of_num M5)) (@ tptp.nat_of_num N4)))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit0 X)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.plus_plus_num X) Y)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.times_times_num X) Y)) (@ (@ tptp.times_times_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 6.19/6.61 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.sqr X)) (@ (@ tptp.times_times_nat _let_1) _let_1)))))
% 6.19/6.61 (assert (= (@ tptp.nat_of_num tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit1 X)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.nat_of_num (@ tptp.num_of_nat N)) N))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit1 N)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 6.19/6.61 (assert (= tptp.plus_plus_num (lambda ((M5 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num M5)) (@ tptp.nat_of_num N4))))))
% 6.19/6.61 (assert (forall ((X tptp.rat)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.ratreal X)) (@ tptp.archim3151403230148437115or_rat X))))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ tptp.ratreal (@ (@ tptp.minus_minus_rat X) Y)))))
% 6.19/6.61 (assert (forall ((X tptp.rat)) (= (@ tptp.inverse_inverse_real (@ tptp.ratreal X)) (@ tptp.ratreal (@ tptp.inverse_inverse_rat X)))))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ tptp.ratreal (@ (@ tptp.plus_plus_rat X) Y)))))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.times_times_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ tptp.ratreal (@ (@ tptp.times_times_rat X) Y)))))
% 6.19/6.61 (assert (= tptp.one_one_real (@ tptp.ratreal tptp.one_one_rat)))
% 6.19/6.61 (assert (forall ((X tptp.rat)) (= (@ tptp.uminus_uminus_real (@ tptp.ratreal X)) (@ tptp.ratreal (@ tptp.uminus_uminus_rat X)))))
% 6.19/6.61 (assert (= tptp.ratreal tptp.field_7254667332652039916t_real))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.19/6.61 (assert (= tptp.zero_zero_real (@ tptp.ratreal tptp.zero_zero_rat)))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.divide_divide_real (@ tptp.ratreal X)) (@ tptp.ratreal Y)) (@ tptp.ratreal (@ (@ tptp.divide_divide_rat X) Y)))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))))
% 6.19/6.61 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ (@ tptp.minus_1356011639430497352at_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.id_nat2)))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6)))))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N))))))
% 6.19/6.61 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.19/6.61 (assert (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than D))))
% 6.19/6.61 (assert (forall ((D tptp.int)) (@ tptp.wf_int (@ tptp.int_ge_less_than2 D))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))))
% 6.19/6.61 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y6) N) (@ (@ tptp.ord_less_eq_nat X2) Y6))))))))
% 6.19/6.61 (assert (forall ((N tptp.code_natural)) (let ((_let_1 (@ tptp.code_nat_of_natural N))) (=> (not (= N tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc tptp.zero_zero_nat))) _let_1)))))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ (@ tptp.minus_7197305767214868737atural X) Xa)) (@ (@ tptp.minus_minus_nat (@ tptp.code_nat_of_natural X)) (@ tptp.code_nat_of_natural Xa)))))
% 6.19/6.61 (assert (= (@ tptp.code_nat_of_natural tptp.one_one_Code_natural) tptp.one_one_nat))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ (@ tptp.divide5121882707175180666atural X) Xa)) (@ (@ tptp.divide_divide_nat (@ tptp.code_nat_of_natural X)) (@ tptp.code_nat_of_natural Xa)))))
% 6.19/6.61 (assert (= (@ tptp.code_nat_of_natural tptp.zero_z2226904508553997617atural) tptp.zero_zero_nat))
% 6.19/6.61 (assert (= (@ (@ tptp.minus_7197305767214868737atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural))
% 6.19/6.61 (assert (= tptp.ord_le5570908160329646204atural (lambda ((X2 tptp.code_natural) (Xa4 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X2)) (@ tptp.code_nat_of_natural Xa4)))))
% 6.19/6.61 (assert (forall ((N tptp.code_natural)) (= (@ tptp.code_int_of_integer (@ tptp.code_i5400310926305786745atural N)) (@ tptp.semiri1314217659103216013at_int (@ tptp.code_nat_of_natural N)))))
% 6.19/6.61 (assert (forall ((X tptp.code_natural)) (= (@ tptp.code_int_of_integer (@ tptp.code_i5400310926305786745atural X)) (@ tptp.semiri1314217659103216013at_int (@ tptp.code_nat_of_natural X)))))
% 6.19/6.61 (assert (= tptp.log (lambda ((B2 tptp.code_natural) (I2 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (or (@ (@ tptp.ord_le1926595141338095240atural B2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural I2) B2))) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.log B2) (@ (@ tptp.divide5121882707175180666atural I2) B2)))))))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.log X))) (let ((_let_2 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_1 Xa) Y) (and (=> _let_2 (= Y tptp.one_one_Code_natural)) (=> (not _let_2) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_1 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))))))))
% 6.19/6.61 (assert (= tptp.minus_shift (lambda ((R tptp.code_natural) (K3 tptp.code_natural) (L2 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (@ (@ tptp.ord_le5570908160329646204atural K3) L2)) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural R) K3)) L2)) (@ (@ tptp.minus_7197305767214868737atural K3) L2)))))
% 6.19/6.61 (assert (forall ((V tptp.code_natural) (W tptp.code_natural)) (let ((_let_1 (@ tptp.bit1 tptp.one))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.bit0 _let_1))) (let ((_let_4 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3)))))))))))))))) (let ((_let_5 (@ tptp.bit0 tptp.one))) (let ((_let_6 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_5)))))) (let ((_let_7 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_7)))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V) W)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 _let_10))) _let_11) (@ (@ tptp.plus_p4538020629002901425atural _let_8) tptp.one_one_Code_natural))) tptp.one_one_Code_natural)) (@ (@ tptp.produc3574140220909816553atural _let_11) _let_8))))))))))))))))
% 6.19/6.61 (assert (= tptp.range (lambda ((K3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.log (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))) K3)) (lambda ((L2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V4) (@ (@ tptp.times_2397367101498566445atural L2) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) tptp.one_one_Code_natural)) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V4) K3)) __flatten_var_0))) __flatten_var_0))))
% 6.19/6.61 (assert (= tptp.inc_shift (lambda ((V4 tptp.code_natural) (K3 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (= V4 K3)) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural K3) tptp.one_one_Code_natural)))))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ (@ tptp.accp_P8126237942716283194atural tptp.log_rel) (@ (@ tptp.produc3574140220909816553atural X) Xa)))) (let ((_let_2 (@ tptp.log X))) (let ((_let_3 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_2 Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y tptp.one_one_Code_natural)) (=> (not _let_3) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_2 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))) (not _let_1))))))))))
% 6.19/6.61 (assert (= tptp.code_i5400310926305786745atural (@ (@ (@ tptp.map_fu2787874002554666395nteger tptp.code_nat_of_natural) tptp.code_integer_of_int) tptp.semiri1314217659103216013at_int)))
% 6.19/6.61 (assert (= tptp.zero_z2226904508553997617atural (@ tptp.code_natural_of_nat tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.minus_7197305767214868737atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ (@ tptp.minus_minus_nat Xa) X)))))
% 6.19/6.61 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.divide5121882707175180666atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ (@ tptp.divide_divide_nat Xa) X)))))
% 6.19/6.61 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ (@ tptp.ord_less_nat Xa) X))))
% 6.19/6.61 (assert (= tptp.one_one_Code_natural (@ tptp.code_natural_of_nat tptp.one_one_nat)))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ tptp.code_i5400310926305786745atural (@ tptp.code_natural_of_nat X)) (@ tptp.code_integer_of_int (@ tptp.semiri1314217659103216013at_int X)))))
% 6.19/6.61 (assert (forall ((X tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ tptp.code_Suc X)) (@ tptp.suc (@ tptp.code_nat_of_natural X)))))
% 6.19/6.61 (assert (forall ((N tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural (@ tptp.code_Suc N)) tptp.one_one_Code_natural) N)))
% 6.19/6.61 (assert (forall ((X tptp.nat)) (= (@ tptp.code_Suc (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ tptp.suc X)))))
% 6.19/6.61 (assert (= tptp.code_Suc (@ (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat) tptp.suc)))
% 6.19/6.61 (assert (= tptp.divide5121882707175180666atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.divide_divide_nat)))
% 6.19/6.61 (assert (= tptp.minus_7197305767214868737atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.minus_minus_nat)))
% 6.19/6.61 (assert (@ (@ (@ tptp.quotie6776551016481293500at_int tptp.intrel) tptp.abs_Integ) tptp.rep_Integ))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.19/6.61 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re7876454716742015248nteger (lambda ((Y4 tptp.num) (Z tptp.num)) (= Y4 Z))) (@ (@ tptp.bNF_re6501075790457514782nteger (lambda ((Y4 tptp.num) (Z tptp.num)) (= Y4 Z))) tptp.code_pcr_integer)) (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))) tptp.code_sub))
% 6.19/6.61 (assert (@ (@ tptp.code_pcr_integer tptp.one_one_int) tptp.one_one_Code_integer))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re6321650412969554871eger_o tptp.code_pcr_integer) (@ (@ tptp.bNF_re6574881592172037608er_o_o tptp.code_pcr_integer) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.ord_less_int) tptp.ord_le6747313008572928689nteger))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re398004352372739002nteger tptp.code_pcr_integer) (@ (@ tptp.bNF_re3379532845092657523nteger tptp.code_pcr_integer) tptp.code_pcr_integer)) tptp.divide_divide_int) tptp.divide6298287555418463151nteger))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re398004352372739002nteger tptp.code_pcr_integer) (@ (@ tptp.bNF_re3379532845092657523nteger tptp.code_pcr_integer) tptp.code_pcr_integer)) tptp.minus_minus_int) tptp.minus_8373710615458151222nteger))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3379532845092657523nteger tptp.code_pcr_integer) tptp.code_pcr_integer) tptp.uminus_uminus_int) tptp.uminus1351360451143612070nteger))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re4153400068438556298nteger (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z))) tptp.code_pcr_integer) tptp.semiri1314217659103216013at_int) tptp.code_integer_of_nat))
% 6.19/6.61 (assert (@ (@ tptp.code_pcr_integer tptp.zero_zero_int) tptp.zero_z3403309356797280102nteger))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re5252274238750452962nteger tptp.code_pcr_natural) tptp.code_pcr_integer) tptp.semiri1314217659103216013at_int) tptp.code_i5400310926305786745atural))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re3704215830270325841atural tptp.code_pcr_natural) tptp.code_pcr_natural) tptp.suc) tptp.code_Suc))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re88643428490162567atural tptp.code_pcr_natural) (@ (@ tptp.bNF_re3704215830270325841atural tptp.code_pcr_natural) tptp.code_pcr_natural)) tptp.divide_divide_nat) tptp.divide5121882707175180666atural))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re1639080489988575423ural_o tptp.code_pcr_natural) (@ (@ tptp.bNF_re2785088596696291543al_o_o tptp.code_pcr_natural) (lambda ((Y4 Bool) (Z Bool)) (= Y4 Z)))) tptp.ord_less_nat) tptp.ord_le5570908160329646204atural))
% 6.19/6.61 (assert (@ (@ (@ (@ tptp.bNF_re88643428490162567atural tptp.code_pcr_natural) (@ (@ tptp.bNF_re3704215830270325841atural tptp.code_pcr_natural) tptp.code_pcr_natural)) tptp.minus_minus_nat) tptp.minus_7197305767214868737atural))
% 6.19/6.61 (assert (@ (@ tptp.code_pcr_natural tptp.zero_zero_nat) tptp.zero_z2226904508553997617atural))
% 6.19/6.61 (assert (@ (@ tptp.code_pcr_natural tptp.one_one_nat) tptp.one_one_Code_natural))
% 6.19/6.61 (assert (forall ((L tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.neg L)))))
% 6.19/6.61 (assert (forall ((K tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.neg K)) tptp.zero_zero_int)))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.neg K)) (@ tptp.neg L)) (@ (@ tptp.ord_less_num L) K))))
% 6.19/6.61 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.neg K)) tptp.zero_zero_nat)))
% 6.19/6.61 (assert (forall ((K tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.neg K)) tptp.zero_zero_int)))
% 6.19/6.61 (assert (forall ((L tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.neg L)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.neg K)) (@ tptp.neg L)) (@ (@ tptp.ord_less_eq_num L) K))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.neg M2)) (@ tptp.neg N)) (@ tptp.neg (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.sub tptp.one) (@ tptp.bit0 N)) (@ tptp.neg (@ tptp.bitM N)))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ (@ tptp.sub tptp.one) (@ tptp.bit1 N)) (@ tptp.neg (@ tptp.bit0 N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.neg M2)) (@ tptp.neg N)) (@ (@ tptp.sub N) M2))))
% 6.19/6.61 (assert (= tptp.sub (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))))
% 6.19/6.61 (assert (= (@ (@ tptp.sub tptp.one) tptp.one) tptp.zero_zero_int))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.minus_minus_int (@ tptp.dup (@ (@ tptp.sub M2) N))) tptp.one_one_int))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit1 M2)) (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int (@ tptp.dup (@ (@ tptp.sub M2) N))) tptp.one_one_int))))
% 6.19/6.61 (assert (= (@ tptp.dup tptp.zero_zero_int) tptp.zero_zero_int))
% 6.19/6.61 (assert (= tptp.dup (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ tptp.dup (@ tptp.neg N)) (@ tptp.neg (@ tptp.bit0 N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit0 M2)) (@ tptp.bit0 N)) (@ tptp.dup (@ (@ tptp.sub M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit1 M2)) (@ tptp.bit1 N)) (@ tptp.dup (@ (@ tptp.sub M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit0 M2)) tptp.one) (@ tptp.pos (@ tptp.bitM M2)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit1 M2)) tptp.one) (@ tptp.pos (@ tptp.bit0 M2)))))
% 6.19/6.61 (assert (forall ((N tptp.num)) (= (@ tptp.dup (@ tptp.pos N)) (@ tptp.pos (@ tptp.bit0 N)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.pos K)) (@ tptp.neg L)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.neg K)) (@ tptp.pos L))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.neg M2)) (@ tptp.pos M2))))
% 6.19/6.61 (assert (forall ((M2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.pos M2)) (@ tptp.neg M2))))
% 6.19/6.61 (assert (= tptp.neg (lambda ((N4 tptp.num)) (@ tptp.uminus_uminus_int (@ tptp.pos N4)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.pos K)) (@ tptp.neg L)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.neg K)) (@ tptp.pos L))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.pos M2)) (@ tptp.pos N)) (@ tptp.pos (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.61 (assert (= tptp.pos tptp.numeral_numeral_int))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.pos M2)) (@ tptp.pos N)) (@ tptp.pos (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.pos K)) (@ tptp.pos L)) (@ (@ tptp.ord_less_eq_num K) L))))
% 6.19/6.61 (assert (forall ((L tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.pos L))))
% 6.19/6.61 (assert (forall ((K tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.pos K)) tptp.zero_zero_int))))
% 6.19/6.61 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.pos K)) (@ tptp.nat_of_num K))))
% 6.19/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.pos K)) (@ tptp.pos L)) (@ (@ tptp.ord_less_num K) L))))
% 6.19/6.61 (assert (= tptp.one_one_int (@ tptp.pos tptp.one)))
% 6.19/6.61 (assert (forall ((K tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.pos K)) tptp.zero_zero_int))))
% 6.19/6.61 (assert (forall ((L tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.pos L))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.pos M2)) (@ tptp.pos N)) (@ (@ tptp.sub M2) N))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.pos M2)) (@ tptp.neg N)) (@ tptp.pos (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.neg M2)) (@ tptp.pos N)) (@ tptp.neg (@ (@ tptp.plus_plus_num M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.pos M2)) (@ tptp.neg N)) (@ tptp.neg (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.neg M2)) (@ tptp.pos N)) (@ tptp.neg (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.neg M2)) (@ tptp.neg N)) (@ tptp.pos (@ (@ tptp.times_times_num M2) N)))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.neg M2)) (@ tptp.pos N)) (@ (@ tptp.sub N) M2))))
% 6.19/6.61 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.pos M2)) (@ tptp.neg N)) (@ (@ tptp.sub M2) N))))
% 6.19/6.61 (assert (@ (@ (@ tptp.quotie8700032322157300518t_real tptp.realrel) tptp.real2) tptp.rep_real))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.19/6.61 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X7 tptp.real)) (@ P X7)))))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 6.19/6.61 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X) Y) Y)))
% 6.19/6.61 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tpcvc5 interrupted by timeout.
% 300.12/290.47 /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 1505 CPU time limit exceeded (core dumped) ( read result; case "$result" in
% 300.12/290.47 unsat)
% 300.12/290.47 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 300.12/290.47 ;;
% 300.12/290.47 sat)
% 300.12/290.47 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 300.12/290.47 ;;
% 300.12/290.47 esac; exit 1 )
% 300.12/290.48 Cputime limit exceeded (core dumped) (core dumped)
% 300.12/290.48 % cvc5---1.0.5 exiting
% 300.12/290.48 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------